Merge remote-tracking branch 'cgal/master' into gsoc2022-isosurface

.clang-format

@@ -0,0 +1,35 @@
+---
+Language:        Cpp
+BasedOnStyle:  LLVM
+AccessModifierOffset: -2
+AllowShortFunctionsOnASingleLine: true
+BinPackParameters: false
+BreakConstructorInitializers: BeforeComma
+BreakBeforeBraces: Custom
+BraceWrapping:
+  AfterCaseLabel:  false
+  AfterClass:      true
+  AfterControlStatement: MultiLine
+  AfterEnum:       false
+  AfterFunction:   false
+  AfterNamespace:  false
+  AfterObjCDeclaration: false
+  AfterStruct:     true
+  AfterUnion:      false
+  AfterExternBlock: false
+  BeforeCatch:     false
+  BeforeElse:      false
+  BeforeLambdaBody: false
+  BeforeWhile:     false
+  IndentBraces:    false
+  SplitEmptyFunction: false
+  SplitEmptyRecord: false
+  SplitEmptyNamespace: false
+ColumnLimit:     120
+# Force pointers to the type for C++.
+DerivePointerAlignment: false
+PointerAlignment: Left
+# Control the spaces around conditionals
+SpacesInConditionalStatement: false
+SpaceBeforeParens: false
+...

.devcontainer/doxygen-cgal/Dockerfile

@@ -0,0 +1,55 @@
+# Use an official Fedora as a parent image for the build stage
+FROM fedora:latest AS sources_deps
+
+# Set environment variables to non-interactive
+ENV DEBIAN_FRONTEND=noninteractive
+
+# Install dependencies
+RUN dnf update -y && dnf install -y \
+    wget \
+    make \
+    gcc \
+    gcc-c++ \
+    patch \
+    cmake \
+    bison \
+    flex \
+    unzip \
+    python3 \
+    && dnf clean all
+
+# Copy the patch file to the build context
+COPY cgal-NO_ADDITIONAL_DETAILS.patch .
+
+FROM sources_deps AS build
+
+# Build and install Doxygen from sources
+ARG DOXYGEN_VERSION=1.9.6
+ARG MAKEFLAGS=-j$(nproc)
+RUN if [ -n "$DEBUG"];then set -x && make --version && ls -lZ /tmp && id; fi \
+    && DOXYGEN_VERSION_UNDERSCORE=$(echo ${DOXYGEN_VERSION} | sed 's/\./_/g') \
+    && wget https://github.com/doxygen/doxygen/archive/refs/tags/Release_${DOXYGEN_VERSION_UNDERSCORE}.zip \
+    && unzip Release_${DOXYGEN_VERSION_UNDERSCORE}.zip \
+    && cd doxygen-Release_${DOXYGEN_VERSION_UNDERSCORE} \
+    && patch -p1 < ../cgal-NO_ADDITIONAL_DETAILS.patch \
+    && mkdir build \
+    && cd build \
+    && cmake -G "Unix Makefiles" -DCMAKE_BUILD_TYPE=Release .. \
+    && cmake --build . \
+    && cmake --install . \
+    && mkdir -p /usr/local/share/doc/doxygen && cp ../LICENSE /usr/local/share/doc/doxygen/LICENSE.TXT \
+    && cd ../.. \
+    && rm -rf doxygen-Release_${DOXYGEN_VERSION_UNDERSCORE} Release_${DOXYGEN_VERSION_UNDERSCORE}.zip
+
+# Use a smaller base image for the final stage
+FROM fedora:latest
+
+# Install necessary runtime dependencies
+RUN set -x \
+    && dnf update -y && dnf install -y graphviz 'perl(Getopt::Std)' tex-bibtex cmake python3-lxml python3-pyquery \
+    && dnf clean all
+
+# Copy Doxygen from the build stage
+COPY --from=build /usr/local/bin/doxygen /usr/local/bin
+COPY --from=build /usr/local/share/doc/doxygen/LICENSE.TXT /usr/local/share/doc/doxygen/LICENSE.TXT
+RUN doxygen --version

.devcontainer/doxygen-cgal/Makefile

@@ -0,0 +1,23 @@
+SHELL := /bin/bash
+DOXYGEN_VERSIONS := 1.12.0 1.11.0 1.10.0 1.9.8 1.9.7 1.9.6
+
+.PHONY: all build-% push-% build push
+
+all: build
+	@echo "Use `$(MAKE) push` to push the images to the registry."
+
+build-%:
+	@echo "MAKEFLAGS: $(MAKEFLAGS)"
+	@echo "Building Doxygen version $*..."
+	if [ "$$(getenforce || true)" == "Enforcing" ]; then Z=:z; else Z=; fi; \
+	F="$(MAKEFLAGS)"; F=$${F##*fifo:}; F=$${F%% *}; \
+	if [ -p "$$F" ]; then echo "The GNU make FIFO file exists:"; ls -l $$F; VOLUME_ARGS="-v $$F:$$F$$Z"; echo -- $$VOLUME_ARGS; fi; \
+	podman build --build-arg DOXYGEN_VERSION=$* --build-arg "MAKEFLAGS=$(MAKEFLAGS)" $$VOLUME_ARGS -t cgal/doxygen:$* .
+
+push-%: build-%
+	@echo "Pushing cgal/doxygen:$*..."
+	podman push cgal/doxygen:$*
+
+build: $(foreach version,$(DOXYGEN_VERSIONS),build-$(version))
+
+push: $(foreach version,$(DOXYGEN_VERSIONS),push-$(version))

.devcontainer/doxygen-cgal/cgal-NO_ADDITIONAL_DETAILS.patch

@@ -0,0 +1,44 @@
+diff --git a/src/config.xml b/src/config.xml
+index 13910958a6..31f1354e44 100644
+--- a/src/config.xml
++++ b/src/config.xml
+@@ -893,6 +893,18 @@ Go to the <a href="commands.html">next</a> section or return to the
+  \note This will also disable the warnings about undocumented members
+  that are normally produced when \ref cfg_warnings "WARNINGS" is
+  set to \c YES.
++]]>
++      </docs>
++    </option>
++  </group>
++  <group name='Build' docs='Build related configuration options'>
++    <option type='bool' id='NO_ADDITIONAL_DETAILS' defval='0'>
++      <docs>
++<![CDATA[
++ When the \c EXTRACT_ALL tag is set to \c YES and a member or class
++ as no documentation, no detailed section will be produced if
++ the \c NO_ADDITIONAL_DETAILS tag is set to \c YES.
++ This tag has no effect if the \c EXTRACT_ALL tag is set to \c NO.
+ ]]>
+       </docs>
+     </option>
+diff --git a/src/memberdef.cpp b/src/memberdef.cpp
+index 08d9bf24c5..ab04e994c5 100644
+--- a/src/memberdef.cpp
++++ b/src/memberdef.cpp
+@@ -2501,6 +2501,7 @@ bool MemberDefImpl::hasDetailedDescription() const
+   if (!m_hasDetailedDescriptionCached)
+   {
+     bool extractAll            = Config_getBool(EXTRACT_ALL);
++    bool xAllNoDetailedSec = Config_getBool(NO_ADDITIONAL_DETAILS);
+     bool alwaysDetailedSec     = Config_getBool(ALWAYS_DETAILED_SEC);
+     bool repeatBrief           = Config_getBool(REPEAT_BRIEF);
+     bool briefMemberDesc       = Config_getBool(BRIEF_MEMBER_DESC);
+@@ -2512,7 +2513,7 @@ bool MemberDefImpl::hasDetailedDescription() const
+     // the member has detailed documentation because the user added some comments
+     bool docFilter =
+            // extract all is enabled
+-           extractAll ||
++           (extractAll && !xAllNoDetailedSec) ||
+            // has detailed docs
+            !documentation().isEmpty() ||
+            // has inbody docs

.devcontainer/doxygen-cgal/devcontainer.json

@@ -0,0 +1,16 @@
+{
+    "name": "CGAL Doxygen Dev Container, version 1.12.0, with CGAL patch",
+    "image": "docker.io/cgal/doxygen:1.12.0",
+    "features": {
+        "ghcr.io/devcontainers/features/git:1.3.2": {}
+    },
+    "customizations": {
+        "vscode": {
+            "extensions": [
+                "ms-vscode.cmake-tools",
+                "bbenoist.Doxygen",
+                "ms-vscode.cpptools"
+            ]
+        }
+    },
+}

.devcontainer/doxygen-cgal/distrobox.ini

@@ -0,0 +1,29 @@
+[distrobox-doxygen-1.12.0]
+image=cgal/doxygen:1.12.0
+exported_bins="/usr/local/bin/doxygen /usr/bin/perl /usr/bin/cmake /usr/bin/python3"
+exported_bins_path=$HOME/.local/bin-doxygen-1.12.0
+
+[distrobox-doxygen-1.11.0]
+image=cgal/doxygen:1.11.0
+exported_bins="/usr/local/bin/doxygen /usr/bin/perl /usr/bin/cmake /usr/bin/python3"
+exported_bins_path=$HOME/.local/bin-doxygen-1.11.0
+
+[distrobox-doxygen-1.10.0]
+image=cgal/doxygen:1.10.0
+exported_bins="/usr/local/bin/doxygen /usr/bin/perl /usr/bin/cmake /usr/bin/python3"
+exported_bins_path=$HOME/.local/bin-doxygen-1.10.0
+
+[distrobox-doxygen-1.9.8]
+image=cgal/doxygen:1.9.8
+exported_bins="/usr/local/bin/doxygen /usr/bin/perl /usr/bin/cmake /usr/bin/python3"
+exported_bins_path=$HOME/.local/bin-doxygen-1.9.8
+
+[distrobox-doxygen-1.9.7]
+image=cgal/doxygen:1.9.7
+exported_bins="/usr/local/bin/doxygen /usr/bin/perl /usr/bin/cmake /usr/bin/python3"
+exported_bins_path=$HOME/.local/bin-doxygen-1.9.7
+
+[distrobox-doxygen-1.9.6]
+image=cgal/doxygen:1.9.6
+exported_bins="/usr/local/bin/doxygen /usr/bin/perl /usr/bin/cmake /usr/bin/python3"
+exported_bins_path=$HOME/.local/bin-doxygen-1.9.6

.gitattributes

@@ -44,11 +44,9 @@ Documentation/Doxyfile text eol=lf
 Documentation/pkglist_filter text eol=lf
 Installation/update_CHANGES text eol=lf
 Scripts/developer_scripts/autotest_cgal text eol=lf
-Scripts/developer_scripts/autotest_cgal_with_cmake text eol=lf
 Scripts/developer_scripts/cgal_build text eol=lf
 Scripts/developer_scripts/cgal_depend text eol=lf
 Scripts/developer_scripts/cgal_git_update_hooks_for_client text eol=lf
-Scripts/developer_scripts/cgal_test_with_cmake text eol=lf
 Scripts/developer_scripts/cgal2gml text eol=lf
 Scripts/developer_scripts/check_library_uses_no_gpl_files text eol=lf
 Scripts/developer_scripts/check_licenses text eol=lf
@@ -56,7 +54,6 @@ Scripts/developer_scripts/check_macro_names text eol=lf
 Scripts/developer_scripts/check_no_CGAL_USE_without_includes_before text eol=lf
 Scripts/developer_scripts/check_svn_keywords text eol=lf
 Scripts/developer_scripts/create_cgal_test text eol=lf
-Scripts/developer_scripts/create_cgal_test_with_cmake text eol=lf
 Scripts/developer_scripts/create_internal_release text eol=lf
 Scripts/developer_scripts/create_new_release text eol=lf
 Scripts/developer_scripts/detect_files_with_mixed_eol_styles text eol=lf

.github/workflows/checks.yml

@@ -7,9 +7,8 @@ permissions:
 
 jobs:
   build:
-
+    if: github.repository == 'CGAL/cgal' || github.event_name != 'push'
     runs-on: ubuntu-latest
-    
     steps:
     - uses: actions/checkout@v4
     - name: install dependencies

.github/workflows/cmake-all.yml

@@ -7,9 +7,8 @@ permissions:
 
 jobs:
   cmake-testsuite:
-
+    if: github.repository == 'CGAL/cgal' || github.event_name != 'push'
     runs-on: ubuntu-latest
-
     steps:
     - uses: actions/checkout@v4
     - name: install dependencies
@@ -21,9 +20,8 @@ jobs:
         ctest -L Installation -j $(getconf _NPROCESSORS_ONLN)
 
   cmake-testsuite-with-qt:
-
+    if: github.repository == 'CGAL/cgal' || github.event_name != 'push'
     runs-on: ubuntu-latest
-
     steps:
     - uses: actions/checkout@v4
     - name: install dependencies

.gitignore

@@ -9,7 +9,6 @@ AABB_tree/demo/AABB_tree/Makefile
 AABB_tree/examples/AABB_tree/*.kdev*
 AABB_tree/examples/AABB_tree/*_example
 AABB_tree/examples/AABB_tree/Makefile
-AABB_tree/examples/AABB_tree/cgal_test_with_cmake
 AABB_tree/test/AABB_tree/*.kdev*
 AABB_tree/test/AABB_tree/Makefile
 AABB_tree/test/AABB_tree/aabb_correctness_triangle_test
@@ -19,17 +18,14 @@ AABB_tree/test/AABB_tree/aabb_distance_triangle_test
 AABB_tree/test/AABB_tree/aabb_intersection_triangle_test
 AABB_tree/test/AABB_tree/aabb_naive_vs_tree_distance_segment_test
 AABB_tree/test/AABB_tree/aabb_projection_triangle_test
-AABB_tree/test/AABB_tree/cgal_test_with_cmake
 Algebraic_foundations/test/Algebraic_foundations/Algebraic_extension_traits
 Algebraic_foundations/test/Algebraic_foundations/Algebraic_structure_traits
 Algebraic_foundations/test/Algebraic_foundations/Chinese_remainder_traits
 Algebraic_foundations/test/Algebraic_foundations/Coercion_traits
 Algebraic_foundations/test/Algebraic_foundations/Real_embeddable_traits
 Algebraic_foundations/test/Algebraic_foundations/Scalar_factor_traits
-Algebraic_foundations/test/Algebraic_foundations/cgal_test_with_cmake
 Algebraic_foundations/test/Algebraic_foundations/extended_euclidean_algorithm
 Algebraic_foundations/test/Algebraic_foundations/ipower
-Algebraic_kernel_d/test/Algebraic_kernel_d/cgal_test_with_cmake
 Algebraic_kernel_d/test/Algebraic_kernel_d/rs_isolator
 Alpha_shapes_2/demo/Alpha_shapes_2/Makefile
 Alpha_shapes_2/demo/Alpha_shapes_2/alpha_shapes_2
@@ -38,7 +34,6 @@ Alpha_shapes_2/examples/Alpha_shapes_2/alpha_shapes_2
 Alpha_shapes_3/demo/Alpha_shapes_3/Makefile
 Alpha_shapes_3/demo/Alpha_shapes_3/alpha_shapes_3
 Alpha_shapes_3/demo/Alpha_shapes_3/weighted_alpha_shapes_3
-Alpha_shapes_3/test/Alpha_shapes_3/cgal_test_with_cmake
 Alpha_shapes_3/test/Alpha_shapes_3/test_alpha_shape_3
 Alpha_shapes_3/test/Alpha_shapes_3/test_fixed_alpha_shape_3
 Alpha_shapes_3/test/Alpha_shapes_3/test_weighted_alpha_shape_3
@@ -61,7 +56,6 @@ Arrangement_on_surface_2/examples/Arrangement_on_surface_2/batched_point_locatio
 Arrangement_on_surface_2/examples/Arrangement_on_surface_2/bgl_dual_adapter
 Arrangement_on_surface_2/examples/Arrangement_on_surface_2/bgl_primal_adapter
 Arrangement_on_surface_2/examples/Arrangement_on_surface_2/bounded_planar_vertical_decomposition
-Arrangement_on_surface_2/examples/Arrangement_on_surface_2/cgal_test_with_cmake
 Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circles
 Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circular_arcs
 Arrangement_on_surface_2/examples/Arrangement_on_surface_2/circular_line_arcs
@@ -104,30 +98,24 @@ Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_rational_fu
 Arrangement_on_surface_2/examples/Arrangement_on_surface_2/vertical_ray_shooting
 Arrangement_on_surface_2/test/Arrangement_on_surface_2/test_point_location.cpp
 BGL/examples/BGL_arrangement_2/Makefile
-BGL/examples/BGL_arrangement_2/cgal_test_with_cmake
 BGL/examples/BGL_arrangement_2/dual
 BGL/examples/BGL_arrangement_2/primal
-BGL/test/BGL/cgal_test_with_cmake
 Boolean_set_operations_2/demo/Boolean_set_operations_2/Makefile
 Boolean_set_operations_2/demo/Boolean_set_operations_2/boolean_operations_2
 Box_intersection_d/test/Box_intersection_d/automated_test
 Box_intersection_d/test/Box_intersection_d/benchmark.data
 Box_intersection_d/test/Box_intersection_d/benchmark_box_intersection
 Box_intersection_d/test/Box_intersection_d/box_grid
-Box_intersection_d/test/Box_intersection_d/cgal_test_with_cmake
 Box_intersection_d/test/Box_intersection_d/random_set_test
 CGAL_ImageIO/demo/CGALimageIO/Makefile
-CGAL_ImageIO/demo/CGALimageIO/cgal_test_with_cmake
 CGAL_ImageIO/demo/CGALimageIO/image_to_vtk_viewer
 CGAL_ImageIO/examples/CGALimageIO/Makefile
-CGAL_ImageIO/examples/CGALimageIO/cgal_test_with_cmake
 CGAL_ImageIO/examples/CGALimageIO/convert_raw_image_to_inr
 CGAL_ImageIO/examples/CGALimageIO/makefile
 CGAL_ImageIO/examples/CGALimageIO/test_imageio
 CGAL_ImageIO/src/CGAL_ImageIO/Makefile
 Circular_kernel_3/demo/Circular_kernel_3/Circular_kernel_3_demo
 Circular_kernel_3/demo/Circular_kernel_3/Makefile
-Circular_kernel_3/test/Circular_kernel_3/cgal_test_with_cmake
 Circular_kernel_3/test/Circular_kernel_3/test_Exact_spherical_kernel
 Circular_kernel_3/test/Circular_kernel_3/test_Lazy_Spherical_kernel
 Circular_kernel_3/test/Circular_kernel_3/test_Lazy_spherical_kernel_basics
@@ -138,7 +126,6 @@ Documentation/log/*.*
 Documentation/output
 Documentation/tags/*.*
 Generator/examples/Generator/ball_d
-Generator/examples/Generator/cgal_test_with_cmake
 Generator/examples/Generator/cube_d
 Generator/examples/Generator/grid_d
 Generator/examples/Generator/random_convex_set
@@ -150,7 +137,6 @@ Generator/examples/Generator/random_segments1
 Generator/examples/Generator/random_segments2
 Generator/examples/Generator/sphere_d
 Generator/test/Generator/bug
-Generator/test/Generator/cgal_test_with_cmake
 Generator/test/Generator/random_poly_test
 Generator/test/Generator/rcs_test
 Generator/test/Generator/test_combination_enumerator
@@ -179,7 +165,6 @@ GraphicsView/demo/Triangulation_2/Makefile
 GraphicsView/demo/Triangulation_2/Regular_triangulation_2
 GraphicsView/demo/Triangulation_2/qrc_*.cxx
 GraphicsView/demo/Triangulation_2/ui_*.h
-HalfedgeDS/test/HalfedgeDS/cgal_test_with_cmake
 HalfedgeDS/test/HalfedgeDS/test_hds
 HalfedgeDS/test/HalfedgeDS/test_hds_decorator
 Inscribed_areas/test/Inscribed_areas/Makefile
@@ -189,11 +174,8 @@ Installation/auxiliary/gdb/python/CGAL/printers.pyc
 Installation/auxiliary/gdb/test
 Installation/cmake/modules/*.tmp
 Installation/test/Installation/cgal_test
-/Installation/test/Installation/cgal_test_with_cmake
 Installation/test/Installation/deprecation_warning
-Interpolation/demo/Interpolation/cgal_test_with_cmake
 Intersections_3/test/Intersections_3/bbox_other_do_intersect_test
-Intersections_3/test/Intersections_3/cgal_test_with_cmake
 Intersections_3/test/Intersections_3/circle_other
 Intersections_3/test/Intersections_3/line_line
 Intersections_3/test/Intersections_3/segment_segment
@@ -207,7 +189,6 @@ Jet_fitting_3/examples/Jet_fitting_3/Single_estimation
 Jet_fitting_3/examples/Jet_fitting_3/VC
 Jet_fitting_3/test/Jet_fitting_3/Makefile
 Jet_fitting_3/test/Jet_fitting_3/blind_1pt
-/Jet_fitting_3/examples/Jet_fitting_3/cgal_test_with_cmake
 /Jet_fitting_3/examples/Jet_fitting_3/data_ellipe0.003.off.4ogl.txt
 Kernel_23/test/Kernel_23/Cartesian
 Kernel_23/test/Kernel_23/Dimension
@@ -221,7 +202,6 @@ Kernel_23/test/Kernel_23/Simple_cartesian
 Kernel_23/test/Kernel_23/Simple_homogeneous
 Kernel_23/test/Kernel_23/Test_IO.out
 /Kernel_23/test/Kernel_23/Test-*IO.out
-Kernel_23/test/Kernel_23/cgal_test_with_cmake
 Kernel_23/test/Kernel_23/test_kernel__
 Kinetic_data_structures/demo/Kinetic_data_structures/Delaunay_triangulation_2
 Kinetic_data_structures/demo/Kinetic_data_structures/Delaunay_triangulation_stable_subset_2
@@ -230,13 +210,11 @@ Kinetic_data_structures/demo/Kinetic_data_structures/KDS_Delaunay_triangulation_
 Kinetic_data_structures/demo/Kinetic_data_structures/KDS_generate_data
 Kinetic_data_structures/demo/Kinetic_data_structures/KDS_gui_2
 Kinetic_data_structures/demo/Kinetic_data_structures/Makefile
-Kinetic_data_structures/demo/Kinetic_data_structures/cgal_test_with_cmake
 Kinetic_data_structures/demo/Kinetic_data_structures/generate_data
 Kinetic_data_structures/demo/Kinetic_data_structures/gui_2
 Kinetic_data_structures/test/Kinetic_data_structures/Delaunay_triangulation_2
 Kinetic_data_structures/test/Kinetic_data_structures/Delaunay_triangulation_3
 Kinetic_data_structures/test/Kinetic_data_structures/active_objects_tables
-Kinetic_data_structures/test/Kinetic_data_structures/cgal_test_with_cmake
 Kinetic_data_structures/test/Kinetic_data_structures/exact_kds
 Kinetic_data_structures/test/Kinetic_data_structures/instantaneous_kernel
 Kinetic_data_structures/test/Kinetic_data_structures/numbers
@@ -249,8 +227,6 @@ Kinetic_data_structures/test/Kinetic_data_structures/test_KDS_Delaunay_triangula
 Kinetic_data_structures/test/Kinetic_data_structures/timings
 Linear_cell_complex/demo/Linear_cell_complex/Linear_cell_complex_3.qrc.depends
 Linear_cell_complex/demo/Linear_cell_complex/Linear_cell_complex_3_demo
-Linear_cell_complex/demo/Linear_cell_complex/cgal_test_with_cmake
-Linear_cell_complex/examples/Linear_cell_complex/cgal_test_with_cmake
 Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3
 Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3_triangulation
 Linear_cell_complex/examples/Linear_cell_complex/linear_cell_complex_3_with_colored_vertices
@@ -298,7 +274,6 @@ Mesh_2/demo/Mesh_2/*.core
 Mesh_2/demo/Mesh_2/*.moc
 Mesh_2/demo/Mesh_2/.*.deps
 Mesh_2/demo/Mesh_2/Makefile
-Mesh_2/demo/Mesh_2/cgal_test_with_cmake
 Mesh_2/demo/Mesh_2/conform
 Mesh_2/demo/Mesh_2/depends
 Mesh_2/demo/Mesh_2/filename.edg
@@ -310,7 +285,6 @@ Mesh_2/demo/Mesh_2/semantic.cache
 Mesh_2/doxygen
 Mesh_2/examples/Mesh_2/*.core
 Mesh_2/examples/Mesh_2/.*.deps
-Mesh_2/examples/Mesh_2/cgal_test_with_cmake
 Mesh_2/examples/Mesh_2/conform
 Mesh_2/examples/Mesh_2/conforming
 Mesh_2/examples/Mesh_2/depends
@@ -325,7 +299,6 @@ Mesh_2/test/Mesh_2/*.core
 Mesh_2/test/Mesh_2/.*.deps
 Mesh_2/test/Mesh_2/Makefile
 Mesh_2/test/Mesh_2/bench_double_map
-Mesh_2/test/Mesh_2/cgal_test_with_cmake
 Mesh_2/test/Mesh_2/conform_plus
 Mesh_2/test/Mesh_2/depends
 Mesh_2/test/Mesh_2/my_makefile
@@ -374,7 +347,6 @@ Mesh_3/examples/Mesh_3/.*.deps
 Mesh_3/examples/Mesh_3/random-image.inr
 Mesh_3/examples/Mesh_3/Makefile
 Mesh_3/examples/Mesh_3/applications
-Mesh_3/examples/Mesh_3/cgal_test_with_cmake
 Mesh_3/examples/Mesh_3/cgal_to_medit
 Mesh_3/examples/Mesh_3/chair-after.mesh
 Mesh_3/examples/Mesh_3/chair-after.png
@@ -412,7 +384,6 @@ Mesh_3/examples/Mesh_3/test_off
 /Mesh_3/test/Mesh_3/a.lua
 /Mesh_3/test/Mesh_3/applications
 /Mesh_3/test/Mesh_3/*.cgal
-/Mesh_3/test/Mesh_3/cgal_test_with_cmake
 /Mesh_3/test/Mesh_3/cgal_to_medit
 /Mesh_3/test/Mesh_3/combined_spheres
 /Mesh_3/test/Mesh_3/combined_spheres-with-sphere-oracle
@@ -514,11 +485,9 @@ Min_ellipse_2/.tmp
 Min_ellipse_2/Makefile
 Min_ellipse_2/bin
 Min_ellipse_2/doc_ps
-Minkowski_sum_3/test/Minkowski_sum_3/cgal_test_with_cmake
 Nef_2/test/Nef_2/EPoint-test
 Nef_2/test/Nef_2/Nef_polyhedron_2-test
 Nef_2/test/Nef_2/Polynomial-test
-Nef_2/test/Nef_2/cgal_test_with_cmake
 Nef_2/test/Nef_2/nef_2_point_location
 Nef_3/demo/Nef_3/Makefile
 Nef_3/examples/Nef_3/Makefile
@@ -576,7 +545,6 @@ Number_types/test/Number_types/_test_valid_finite_double
 Number_types/test/Number_types/_test_valid_finite_float
 Number_types/test/Number_types/bench_interval
 Number_types/test/Number_types/cgal_test
-Number_types/test/Number_types/cgal_test_with_cmake
 Number_types/test/Number_types/constant
 Number_types/test/Number_types/double
 Number_types/test/Number_types/doubletst
@@ -627,7 +595,6 @@ Periodic_3_triangulation_3/demo/Periodic_3_triangulation_3/moc_*.cpp
 Periodic_3_triangulation_3/demo/Periodic_3_triangulation_3/ui_*.h
 Periodic_3_triangulation_3/demo/Periodic_Lloyd_3/Periodic_Lloyd_3.qch
 Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/Test_tds_IO_3
-Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/cgal_test_with_cmake
 Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_alpha_shape_3
 Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_delaunay_3
 Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_delaunay_hierarchy_3
@@ -638,7 +605,6 @@ Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_trian
 Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_H_3
 Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_SC_3
 Periodic_3_triangulation_3/test/Periodic_3_triangulation_3/test_periodic_3_triangulation_traits_SH_3
-Point_set_2/test/Point_set_2/cgal_test_with_cmake
 Point_set_2/test/Point_set_2/nearest_nb1
 Point_set_2/test/Point_set_2/nearest_nb_fcn
 Point_set_2/test/Point_set_2/range_search_fcn
@@ -684,7 +650,6 @@ Point_set_processing_3/test/Point_set_processing_3/smoothing_test
 /Polygon_mesh_processing/test/Polygon_mesh_processing/elephant-oriented.off
 /Polygon_mesh_processing/test/Polygon_mesh_processing/elephant-shuffled.off
 /Polygon_mesh_processing/test/Polygon_mesh_processing/blobby_2cc_no_id.off
-/Polygon_mesh_processing/test/Polygon_mesh_processing/cgal_test_with_cmake
 /Polygon_mesh_processing/test/Polygon_mesh_processing/data/U.polylines.txt.off
 /Polygon_mesh_processing/test/Polygon_mesh_processing/data/hole1.txt.off
 /Polygon_mesh_processing/test/Polygon_mesh_processing/data/hole2.txt.off
@@ -708,7 +673,6 @@ Polyhedron/demo/Polyhedron/snapshot.*
 Polyhedron/demo/Polyhedron/ui_*.h
 Polyhedron/test/Polyhedron/*.kdev*
 Polyhedron/test/Polyhedron/Makefile
-Polyhedron/test/Polyhedron/cgal_test_with_cmake
 Polyhedron/test/Polyhedron/test_polyhedron
 Polynomial/test/Polynomial/Exponent_vector
 Polynomial/test/Polynomial/Interpolator
@@ -716,7 +680,6 @@ Polynomial/test/Polynomial/Polynomial_traits_d
 Polynomial/test/Polynomial/Polynomial_type_generator
 Polynomial/test/Polynomial/Polynomial_using_core
 Polynomial/test/Polynomial/Polynomial_using_leda
-Polynomial/test/Polynomial/cgal_test_with_cmake
 Polynomial/test/Polynomial/modular_gcd_utcf_algorithm_M
 Polynomial/test/Polynomial/modular_gcd_utcf_dfai
 Polynomial/test/Polynomial/modular_gcd_utcf_pure_wang
@@ -746,10 +709,8 @@ Polytope_distance_d/.obj
 Polytope_distance_d/.tmp
 Polytope_distance_d/Makefile
 Polytope_distance_d/bin
-Polytope_distance_d/test/Polytope_distance_d/cgal_test_with_cmake
 Polytope_distance_d/test/Polytope_distance_d/test_Polytope_distance_d_d
 Principal_component_analysis/test/Principal_component_analysis/bounding_box
-Principal_component_analysis/test/Principal_component_analysis/cgal_test_with_cmake
 Principal_component_analysis/test/Principal_component_analysis/linear_least_squares_fitting_circles_2
 Principal_component_analysis/test/Principal_component_analysis/linear_least_squares_fitting_cuboids_3
 Principal_component_analysis/test/Principal_component_analysis/linear_least_squares_fitting_points_2
@@ -774,7 +735,6 @@ Principal_component_analysis/test/Principal_component_analysis/test_linear_least
 Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_tetrahedra_3
 Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_triangles_2
 Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_triangles_3
-/Profiling_tools/test/Profiling_tools/cgal_test_with_cmake
 /Profiling_tools/test/Profiling_tools/test_memory_sizer
 /Profiling_tools/test/Profiling_tools/test_timer
 QP_solver/documentation/Degeneracies.aux
@@ -806,7 +766,6 @@ Ridges_3/examples/Ridges_3/Compute_Ridges_Umbilics
 Ridges_3/examples/Ridges_3/Makefile
 Ridges_3/test/Ridges_3/Makefile
 Ridges_3/test/Ridges_3/ridge_test
-STL_Extension/test/STL_Extension/cgal_test_with_cmake
 STL_Extension/test/STL_Extension/test_Cache
 STL_Extension/test/STL_Extension/test_Compact_container
 STL_Extension/test/STL_Extension/test_Concatenate_iterator
@@ -828,7 +787,6 @@ STL_Extension/test/STL_Extension/test_nth_element
 STL_Extension/test/STL_Extension/test_stl_extension
 STL_Extension/test/STL_Extension/test_type_traits
 STL_Extension/test/STL_Extension/test_vector
-SearchStructures/test/RangeSegmentTrees/cgal_test_with_cmake
 SearchStructures/test/RangeSegmentTrees/test_segment_tree_set_2
 Skin_surface_3/.cdtproject
 Skin_surface_3/.project
@@ -839,7 +797,6 @@ Skin_surface_3/test/Skin_surface_3/err.txt
 Skin_surface_3/test/Skin_surface_3/makefile
 Skin_surface_3/test/Skin_surface_3/msgs.txt
 Skin_surface_3/test/Skin_surface_3/subdivision_test
-Spatial_sorting/test/Spatial_sorting/cgal_test_with_cmake
 Stream_lines_2/demo/Stream_lines_2/Makefile
 Stream_lines_2/demo/Stream_lines_2/streamlines
 Surface_mesh_parameterization/examples/Surface_mesh_parameterization/*.eps
@@ -967,20 +924,15 @@ Triangulation/test/Triangulation/output-pcds*
 Triangulation/test/Triangulation/pc
 Triangulation/test/Triangulation/pcds
 Triangulation/test/Triangulation/torture
-/Triangulation/examples/Triangulation/cgal_test_with_cmake
-/Triangulation/test/Triangulation/cgal_test_with_cmake
 /Triangulation/test/Triangulation/output-tds-*
-Triangulation_2/cgal_test_with_cmake
 Triangulation_2/demo/Triangulation_2/Makefile
 Triangulation_2/demo/Triangulation_2/constrained
 Triangulation_2/demo/Triangulation_2/constrained_delaunay_triangulation_2
 Triangulation_2/demo/Triangulation_2/delaunay_triangulation_2
 Triangulation_2/demo/Triangulation_2/regular_triangulation_2
-Triangulation_2/examples/Triangulation_2/cgal_test_with_cmake
 Triangulation_2/examples/Triangulation_2/regular
 Triangulation_2/test/Triangulation_2/Makefile
 Triangulation_2/test/Triangulation_2/T??.triangulation
-Triangulation_2/test/Triangulation_2/cgal_test_with_cmake
 Triangulation_2/test/Triangulation_2/file_tds*
 Triangulation_2/test/Triangulation_2/makefile
 Triangulation_2/test/Triangulation_2/test_cdt_degenerate_case
@@ -998,10 +950,8 @@ Triangulation_2/test/Triangulation_2/test_triangulation_2_bis
 Triangulation_2/test/Triangulation_2/test_triangulation_geom_traits
 Triangulation_2/test/Triangulation_2/test_triangulation_tds
 Triangulation_2/test/Triangulation_2/vrml_tds*
-Triangulation_3/benchmark/Triangulation_3/cgal_test_with_cmake
 Triangulation_3/benchmark/Triangulation_3/simple
 Triangulation_3/examples/Triangulation_3/adding_handles_3
-Triangulation_3/examples/Triangulation_3/cgal_test_with_cmake
 Triangulation_3/examples/Triangulation_3/color
 Triangulation_3/examples/Triangulation_3/fast_location_3
 Triangulation_3/examples/Triangulation_3/find_conflicts_3
@@ -1027,7 +977,6 @@ Triangulation_3/test/Triangulation_3/Test8_triangulation_IO_3_binary
 Triangulation_3/test/Triangulation_3/Test??_triangulation_IO_3
 Triangulation_3/test/Triangulation_3/Test?_triangulation_IO_3
 Triangulation_3/test/Triangulation_3/Test_tds_IO_3
-Triangulation_3/test/Triangulation_3/cgal_test_with_cmake
 Triangulation_3/test/Triangulation_3/makefile
 Triangulation_3/test/Triangulation_3/test_delaunay_3
 Triangulation_3/test/Triangulation_3/test_delaunay_hierarchy_3
@@ -1084,7 +1033,6 @@ ProgramOutput*
 ErrorOutput*
 CompilerOutput*
 error.txt
-cgal_test_with_cmake.log
 
 # File created by the Semantic Bovinator (an Emacs package)
 semantic.cache
@@ -1141,9 +1089,7 @@ Doxyfile
 gmon.*
 
 # Unsorted file names:
-/Point_set_processing_3/test/Point_set_processing_3/cgal_test_with_cmake
 /Point_set_processing_3/test/Point_set_processing_3/read_test
-/Nef_S2/test/Nef_S2/cgal_test_with_cmake
 /Arrangement_on_surface_2/test/Arrangement_on_surface_2/construction_test_suite_generator
 /Arrangement_on_surface_2/test/Arrangement_on_surface_2/ex_kernel_point
 /Arrangement_on_surface_2/test/Arrangement_on_surface_2/ex_kernel_segment
@@ -1191,15 +1137,11 @@ gmon.*
 /Principal_component_analysis/examples/Principal_component_analysis/barycenter
 /Principal_component_analysis/examples/Principal_component_analysis/bounding_box
 /Principal_component_analysis/examples/Principal_component_analysis/centroid
-/Principal_component_analysis/examples/Principal_component_analysis/cgal_test_with_cmake
 /Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_points_2
 /Principal_component_analysis/examples/Principal_component_analysis/linear_least_squares_fitting_triangles_3
-/Polygon/examples/Polygon/cgal_test_with_cmake
-/Polygon/test/Polygon/cgal_test_with_cmake
 /Polygon/test/Polygon/polytest.ascii
 /Polygon/test/Polygon/polytest.binary
 /Polygon/test/Polygon/polytest.pretty
-/Stream_support/test/Stream_support/cgal_test_with_cmake
 /*.html
 /Snap_rounding_2/test/Snap_rounding_2/data/out
 Polygonal_surface_reconstruction/examples/build*

.markdownlint.json

@@ -0,0 +1,7 @@
+{
+        "default": true,
+        "line-length": false,
+        "no-duplicate-heading": {
+                "siblings_only": true
+        }
+}

AABB_tree/benchmark/AABB_tree/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(AABB_traits_benchmark)
 
 find_package(CGAL REQUIRED OPTIONAL_COMPONENTS Core)
@@ -13,7 +13,7 @@ create_single_source_cgal_program("tree_construction.cpp")
 find_package(benchmark QUIET)
 if(benchmark_FOUND)
   create_single_source_cgal_program("tree_creation.cpp")
-  target_link_libraries(tree_creation benchmark::benchmark)
+  target_link_libraries(tree_creation PRIVATE benchmark::benchmark)
 else()
   message(STATUS "NOTICE: The benchmark 'tree_creation.cpp' requires the Google benchmark library, and will not be compiled.")
 endif()

AABB_tree/demo/AABB_tree/CMakeLists.txt

@@ -1,6 +1,6 @@
 # This is the CMake script for compiling the AABB tree demo.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(AABB_tree_Demo)
 
 # Find includes in corresponding build directories

AABB_tree/examples/AABB_tree/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(AABB_tree_Examples)
 
 find_package(CGAL REQUIRED)

AABB_tree/test/AABB_tree/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(AABB_tree_Tests)
 
 find_package(CGAL REQUIRED)

Advancing_front_surface_reconstruction/examples/Advancing_front_surface_reconstruction/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Advancing_front_surface_reconstruction_Examples)
 
 find_package(CGAL REQUIRED)

Advancing_front_surface_reconstruction/test/Advancing_front_surface_reconstruction/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Advancing_front_surface_reconstruction_Tests)
 
 find_package(CGAL REQUIRED)

Algebraic_foundations/doc/Algebraic_foundations/PackageDescription.txt

@@ -5,7 +5,6 @@
 
 /*!
 \addtogroup PkgAlgebraicFoundationsRef
-\todo check generated documentation
 
 \cgalPkgDescriptionBegin{Algebraic Foundations,PkgAlgebraicFoundations}
 \cgalPkgPicture{Algebraic_foundations2.png}

Algebraic_foundations/examples/Algebraic_foundations/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Algebraic_foundations_Examples)
 
 find_package(CGAL REQUIRED)

Algebraic_foundations/include/CGAL/number_utils.h

@@ -21,6 +21,7 @@
 #include <CGAL/Algebraic_structure_traits.h>
 #include <CGAL/Real_embeddable_traits.h>
 #include <CGAL/Kernel/Same_uncertainty.h>
+#include <boost/mpl/if.hpp>
 
 namespace CGAL {
 CGAL_NTS_BEGIN_NAMESPACE

Algebraic_foundations/test/Algebraic_foundations/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Algebraic_foundations_Tests)
 
 find_package(CGAL REQUIRED COMPONENTS Core)

Algebraic_kernel_d/doc/Algebraic_kernel_d/PackageDescription.txt

@@ -16,7 +16,6 @@
 
 /*!
 \addtogroup PkgAlgebraicKernelDRef
-\todo check generated documentation
 \cgalPkgDescriptionBegin{Algebraic Kernel,PkgAlgebraicKernelD}
 \cgalPkgPicture{Algebraic_kernel_d.png}
 \cgalPkgSummaryBegin

Algebraic_kernel_d/examples/Algebraic_kernel_d/CMakeLists.txt

@@ -1,4 +1,4 @@
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Algebraic_kernel_d_Examples)
 
 find_package(CGAL REQUIRED COMPONENTS Core)

Algebraic_kernel_d/test/Algebraic_kernel_d/CMakeLists.txt

@@ -1,4 +1,4 @@
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Algebraic_kernel_d_Tests)
 
 # CGAL and its components

Algebraic_kernel_for_circles/test/Algebraic_kernel_for_circles/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Algebraic_kernel_for_circles_Tests)
 
 find_package(CGAL REQUIRED)

Algebraic_kernel_for_spheres/test/Algebraic_kernel_for_spheres/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Algebraic_kernel_for_spheres_Tests)
 
 find_package(CGAL REQUIRED)

Alpha_shapes_2/examples/Alpha_shapes_2/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Alpha_shapes_2_Examples)
 
 find_package(CGAL REQUIRED)

Alpha_shapes_2/include/CGAL/Alpha_shape_2.h

@@ -1442,7 +1442,7 @@ Alpha_shape_2<Dt,EACT>::find_alpha_solid() const
   // takes O(#alpha_shape) time
   Type_of_alpha alpha_solid = 0;
 
-  if (number_of_vertices()<3) return alpha_solid;
+  if (dimension()!=2) return alpha_solid;
 
   Finite_vertices_iterator vertex_it;
   // only finite vertices

Alpha_shapes_2/test/Alpha_shapes_2/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Alpha_shapes_2_Tests)
 
 find_package(CGAL REQUIRED)

Alpha_shapes_3/demo/Alpha_shapes_3/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Alpha_shapes_3_Demo)
 
 # Find includes in corresponding build directories

Alpha_shapes_3/examples/Alpha_shapes_3/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Alpha_shapes_3_Examples)
 
 find_package(CGAL REQUIRED)

Alpha_shapes_3/test/Alpha_shapes_3/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Alpha_shapes_3_Tests)
 
 find_package(CGAL REQUIRED)

Alpha_wrap_3/benchmark/Alpha_wrap_3/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Alpha_wrap_3_Benchmark)
 
 find_package(CGAL REQUIRED)

Alpha_wrap_3/benchmark/Alpha_wrap_3/Quality/quality_benchmark.cpp

@@ -75,7 +75,7 @@ double mean_min_angle(const Mesh& mesh)
     const Triangle_3 tr = surface_mesh_face_to_triangle(f, mesh);
     std::array<FT, 3> angles = triangle_angles(tr);
 
-    FT min_angle = std::min({angles[0], angles[1], angles[2]});
+    FT min_angle = (std::min)({angles[0], angles[1], angles[2]});
 
     min_angle = min_angle * (180.0 / CGAL_PI);
     mean_min_angle += min_angle;
@@ -93,7 +93,7 @@ double mean_max_angle(const Mesh& mesh)
     const Triangle_3 tr = surface_mesh_face_to_triangle(f, mesh);
     std::array<FT, 3> angles = triangle_angles(tr);
 
-    FT max_angle = std::max({angles[0], angles[1], angles[2]});
+    FT max_angle = (std::max)({angles[0], angles[1], angles[2]});
 
     max_angle = max_angle * (180.0 / CGAL_PI);
     mean_max_angle += max_angle;
@@ -151,8 +151,8 @@ double mean_edge_ratio(const Mesh& mesh,
     FT a = std::sqrt(CGAL::squared_distance(tr[0], tr[1]));
     FT b = std::sqrt(CGAL::squared_distance(tr[1], tr[2]));
     FT c = std::sqrt(CGAL::squared_distance(tr[2], tr[0]));
-    FT min_edge = std::min({a, b, c});
+    FT min_edge = (std::min)({a, b, c});
-    FT max_edge = std::max({a, b, c});
+    FT max_edge = (std::max)({a, b, c});
     FT edge_ratio = max_edge / min_edge;
 
     mean_edge_ratio += edge_ratio;
@@ -181,7 +181,7 @@ double mean_aspect_ratio(const Mesh& mesh,
     FT c = std::sqrt(CGAL::squared_distance(tr[2], tr[0]));
     FT s = 0.5 * (a + b + c);
     FT inscribed_radius = std::sqrt((s * (s - a) * (s - b) * (s - c)) / s);
-    FT max_edge = std::max({a, b, c});
+    FT max_edge = (std::max)({a, b, c});
     FT aspect_ratio = max_edge / inscribed_radius;
     aspect_ratio /= (2. * std::sqrt(3.));  // normalized
     mean_aspect_ratio += aspect_ratio;

Alpha_wrap_3/examples/Alpha_wrap_3/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Alpha_wrap_3_Examples)
 
 find_package(CGAL REQUIRED)

Alpha_wrap_3/include/CGAL/Alpha_wrap_3/internal/Alpha_wrap_triangulation_cell_base_3.h

@@ -97,7 +97,7 @@ template <typename Cb>
 class Cell_base_with_timestamp
   : public Cb
 {
-  std::size_t time_stamp_;
+  std::size_t time_stamp_ = std::size_t(-2);
 
 public:
   using Has_timestamp = CGAL::Tag_true;
@@ -112,7 +112,7 @@ public:
 public:
   template <typename... Args>
   Cell_base_with_timestamp(const Args&... args)
-    : Cb(args...), time_stamp_(-1)
+    : Cb(args...)
   { }
 
   Cell_base_with_timestamp(const Cell_base_with_timestamp& other)

Alpha_wrap_3/test/Alpha_wrap_3/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Alpha_wrap_3_Tests)
 
 find_package(CGAL REQUIRED)

Apollonius_graph_2/doc/Apollonius_graph_2/PackageDescription.txt

@@ -3,7 +3,6 @@
 /// \ingroup PkgApolloniusGraph2Ref
 /*!
 \addtogroup PkgApolloniusGraph2Ref
-\todo check generated documentation
 \cgalPkgDescriptionBegin{2D Apollonius Graphs (Delaunay Graphs of Disks),PkgApolloniusGraph2}
 \cgalPkgPicture{CircleVoronoi.png}
 \cgalPkgSummaryBegin

Apollonius_graph_2/examples/Apollonius_graph_2/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Apollonius_graph_2_Examples)
 
 find_package(CGAL REQUIRED COMPONENTS Core)

Apollonius_graph_2/test/Apollonius_graph_2/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Apollonius_graph_2_Tests)
 
 find_package(CGAL REQUIRED)

Arithmetic_kernel/test/Arithmetic_kernel/CMakeLists.txt

@@ -1,7 +1,7 @@
 # Created by the script cgal_create_cmake_script
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Arithmetic_kernel_Tests)
 
 find_package(CGAL REQUIRED COMPONENTS Core)

Arrangement_on_surface_2/demo/Arrangement_on_surface_2/CMakeLists.txt

@@ -1,6 +1,6 @@
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Arrangement_on_surface_2_Demo)
 
 if(NOT POLICY CMP0070 AND POLICY CMP0053)

Arrangement_on_surface_2/demo/Arrangement_on_surface_2_earth/CMakeLists.txt

@@ -1,6 +1,6 @@
 # This is the CMake script for compiling a CGAL application.
 
-cmake_minimum_required(VERSION 3.12...3.29)
+cmake_minimum_required(VERSION 3.12...3.31)
 project(Arrangement_on_surface_2_earth_Demo)
 
 if(NOT POLICY CMP0070 AND POLICY CMP0053)
@@ -16,27 +16,24 @@ find_package(Qt6 QUIET COMPONENTS Core Gui OpenGL OpenGLWidgets Widgets Xml)
 find_package(CGAL COMPONENTS Qt6)
 find_package(nlohmann_json QUIET 3.9)
 
-if (NOT CGAL_FOUND OR NOT CGAL_Qt6_FOUND OR NOT Qt6_FOUND OR NOT Boost_FOUND OR NOT nlohmann_json_FOUND)
+set(MISSING_DEPS "")
-  if (NOT CGAL_FOUND)
+if (NOT CGAL_FOUND)
-    set(MISSING_DEPS "the CGAL library, ${MISSING_DEPS}")
+  set(MISSING_DEPS "the CGAL library, ${MISSING_DEPS}")
-  endif()
+endif()
-  if (NOT CGAL_Qt6_FOUND)
+if (NOT CGAL_Qt6_FOUND)
-    set(MISSING_DEPS "the CGAL Qt6 component, ${MISSING_DEPS}")
+  set(MISSING_DEPS "the CGAL Qt6 component, ${MISSING_DEPS}")
-  endif()
+endif()
-  if (NOT Qt6_FOUND)
+if (NOT Qt6_FOUND)
-    set(MISSING_DEPS "the Qt6 library, ${MISSING_DEPS}")
+  set(MISSING_DEPS "the Qt6 library, ${MISSING_DEPS}")
-  endif()
+endif()
-  if (NOT Boost_FOUND)
+if (NOT nlohmann_json_FOUND)
-    set(MISSING_DEPS "the Boost library, ${MISSING_DEPS}")
+  set(MISSING_DEPS "JSON for Modern C++ 3.9+ (know as nlohmann_json), ${MISSING_DEPS}")
-  endif()
-  if (NOT nlohmann_json_FOUND)
-    set(MISSING_DEPS "JSON for Modern C++ 3.9+ (know as nlohmann_json), ${MISSING_DEPS}")
-  endif()
-
-  message(STATUS "NOTICE: This project requires ${MISSING_DEPS} and will not be compiled.")
-  return()
 endif()
 
+if (MISSING_DEPS)
+  message(STATUS "NOTICE: This project requires ${MISSING_DEPS}and will not be compiled.")
+  return()
+endif()
 
 
 add_compile_definitions(QT_NO_VERSION_TAGGING)

Arrangement_on_surface_2/demo/Arrangement_on_surface_2_earth/GUI_country_pick_handler.cpp

@@ -62,7 +62,7 @@ void GUI_country_pick_handler::mouse_press_event(QMouseEvent* e) {
         auto sd = sqrt(d);
         auto t1 = (-b - sd) / (2 * a);
         auto t2 = (-b + sd) / (2 * a);
-        if (t1 > 0 && t2 > 0) ti = std::min(t1, t2);
+        if (t1 > 0 && t2 > 0) ti = (std::min)(t1, t2);
         else if (t1 > 0) ti = t1;
         else ti = t2;
       }

Arrangement_on_surface_2/demo/Arrangement_on_surface_2_earth/Main_widget.cpp

@@ -140,7 +140,7 @@ void Main_widget::initializeGL() {
   for (auto& [country_name, triangle_points] : country_triangles_map) {
     auto country_triangles = std::make_unique<Triangles>(triangle_points);
     auto color = QVector4D(rndm(), rndm(), rndm(), 1);
-    auto m = std::max(color.x(), std::max(color.y(), color.z()));
+    auto m = (std::max)(color.x(), (std::max)(color.y(), color.z()));
     color /= m;
     color *= m_dimming_factor;
     color.setW(1);

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Aos_observer.h

@@ -23,26 +23,25 @@ namespace CGAL {
 template <typename Arrangement>
 class Aos_observer {
 public:
-
   /// \name Types
   /// @{
 
-  //! the type of the associated arrangement.
+  /// the type of the associated arrangement.
   typedef unspecified_type Arrangement_2;
 
-  //! the point type.
+  /// the point type.
   typedef typename Arrangement_2::Point_2 Point_2;
 
-  //! the \f$x\f$-monotone curve type.
+  /// the \f$x\f$-monotone curve type.
   typedef typename Arrangement_2::X_monotone_curve_2 X_monotone_curve_2;
 
-  //! the type of a handle to an arrangement vertex.
+  /// the type of a handle to an arrangement vertex.
   typedef typename Arrangement_2::Vertex_handle Vertex_handle;
 
-  //! the type of a handle to an arrangement halfedge.
+  /// the type of a handle to an arrangement halfedge.
   typedef typename Arrangement_2::Halfedge_handle Halfedge_handle;
 
-  //! the type of a handle to an arrangement face.
+  /// the type of a handle to an arrangement face.
   typedef typename Arrangement_2::Face_handle Face_handle;
 
   /*! represents a connected component of the boundary (CCB), either an outer
@@ -77,11 +76,11 @@ public:
   /// \name Notifications on Global Arrangement Operations
   /// @{
 
-  /*! issued just before the attached arrangement is assigned with the contents of another
+  /*! issued just before the attached arrangement is assigned with the contents
-   * arrangement.
+   * of another arrangement.
-   * \param arr The other arrangement. Notice that the arrangement type is the type used to
+   * \param arr The other arrangement. Notice that the arrangement type is the
-   *            instantiate the observer, which is conveniently defined as
+   *            type used to instantiate the observer, which is conveniently
-   *            `Arrangement_2::Base_aos`.
+   *            defined as `Arrangement_2::Base_aos`.
    */
   virtual void before_assign(const typename Arrangement_2::Base_aos& arr);
 
@@ -419,6 +418,6 @@ public:
   virtual void after_remove_inner_ccb(Face_handle f);
 
   /// @}
-
 }; /* end Aos_observer */
+
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_Bezier_curve_traits_2.h

@@ -1,303 +1,265 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2TraitsClasses
-\ingroup PkgArrangementOnSurface2TraitsClasses
+ *
+ * The traits class `Arr_Bezier_curve_traits_2` is a model of the `AosTraits_2`
+ * concept that handles planar B&eacute;zier curves. A planar <I>B&eacute;zier
+ * curve</I> \f$B\f$ is a parametric curve defined by a sequence of <I>control
+ * points</I> \f$p_0, \ldots, p_n\f$ as follows:
 
-The traits class `Arr_Bezier_curve_traits_2` is a model of the `ArrangementTraits_2`
+ * \f{eqnarray*}{
-concept that handles planar B&eacute;zier curves. A planar <I>B&eacute;zier curve</I>
+ *   B(t) = \left(X(t), Y(t)\right) = \ccSum{k=0}{n}{p_k \cdot \frac{n!}{k! (n-k)!} \cdot t^k (1-t)^{n-k}}\ ,
-\f$ B\f$ is a parametric curve defined by a sequence of <I>control points</I>
-\f$ p_0, \ldots, p_n\f$ as follows:
-
-
-\f{eqnarray*}{
-B(t) = \left(X(t), Y(t)\right)
-= \ccSum{k=0}{n}{p_k \cdot \frac{n!}{k! (n-k)!} \cdot
-t^k (1-t)^{n-k}}\ .
 \f}
-where \f$ t \in [0, 1]\f$. The degree of the curve is therefore \f$ n\f$ -
+ * where \f$t \in [0, 1]\f$. The degree of the curve is therefore \f$n\f$,
-namely, \f$ X(t)\f$ and \f$ Y(t)\f$ are polynomials of degree \f$ n\f$. B&eacute;zier curves
+ * namely, \f$X(t)\f$ and \f$Y(t)\f$ are polynomials of degree \f$n\f$.
-have numerous applications in computer graphics and solid modelling. They
+ * B&eacute;zier curves have numerous applications in computer graphics and
-are used, for example, in free-form sketches and for defining the true-type
+ * solid modelling. They are used, for example, in free-form sketches and for
-fonts.
+ * defining the true-type fonts.
 
-In our representation, we assume that the coordinates of all control
+ * In our representation, we assume that the coordinates of all control points
-points are rational numbers (namely they are given as objects of the
+ * are rational numbers (namely they are given as objects of the
-`RatKernel::Point_2` type), so both \f$ X(t)\f$ and \f$ Y(t)\f$ are polynomials
+ * `RatKernel::Point_2` type), so both \f$X(t)\f$ and \f$Y(t)\f$ are
-with rational coefficients. The intersection points between curves are
+ * polynomials with rational coefficients. The intersection points between
-however algebraic numbers, and their exact computation is time-consuming.
+ * curves are however algebraic numbers, and their exact computation is
-The traits class therefore contains a layer of geometric filtering that
+ * time-consuming.  The traits class therefore contains a layer of geometric
-performs all computation in an approximate manner whenever possible, and
+ * filtering that performs all computation in an approximate manner whenever
-it resorts to exact computations only when the approximate computation
+ * possible, and it resorts to exact computations only when the approximate
-fails to produce an unambiguous result.
+ * computation fails to produce an unambiguous result.
 
-We therefore require separate representations of the control points and
+ * We therefore require separate representations of the control points and the
-the intersection points. The `NtTraits` should be instantiated with a class
+ * intersection points. The `NtTraits` should be instantiated with a class that
-that defines nested `Integer`, `Rational` and `Algebraic` number
+ * defines nested `Integer`, `Rational` and `Algebraic` number types and
-types and supports various operations on them, yielding certified computation
+ * supports various operations on them, yielding certified computation results
-results (for example, in can convert rational numbers to algebraic numbers
+ * (for example, in can convert rational numbers to algebraic numbers and can
-and can compute roots of polynomials with integer coefficients).
+ * compute roots of polynomials with integer coefficients).  The other template
-The other template parameters, `RatKernel` and `AlgKernel` should be
+ * parameters, `RatKernel` and `AlgKernel` should be geometric kernels templated
-geometric kernels templated with the `NtTraits::Rational` and
+ * with the `NtTraits::Rational` and `NtTraits::Algebraic` number types,
-`NtTraits::Algebraic` number types, respectively. It is recommended to
+ * respectively. It is recommended to instantiate the
-instantiate the `CORE_algebraic_number_traits` class as the `NtTraits`
+ * `CORE_algebraic_number_traits` class as the `NtTraits` parameter, with
-parameter, with `Cartesian<NtTraits::Rational>` and
+ * `Cartesian<NtTraits::Rational>` and `Cartesian<NtTraits::Algebraic>`
-`Cartesian<NtTraits::Algebraic>` instantiating the two kernel types,
+ * instantiating the two kernel types, respectively. The number types in this
-respectively. The number types in this case are provided by the \core
+ * case are provided by the \core library, with its ability to exactly represent
-library, with its ability to exactly represent simple algebraic numbers.
+ * simple algebraic numbers.
 
-While `Arr_Bezier_curve_traits_2` models the concept
+ * While `Arr_Bezier_curve_traits_2` models the concept
-`ArrangementDirectionalXMonotoneTraits_2`, the implementation of
+ * `AosDirectionalXMonotoneTraits_2`, the implementation of the
-the `Are_mergeable_2` operation does not enforce the input curves
+ * `Are_mergeable_2` operation does not enforce the input curves to have the
-to have the same direction as a precondition. Moreover, `Arr_Bezier_curve_traits_2`
+ * same direction as a precondition. Moreover, `Arr_Bezier_curve_traits_2`
-supports the merging of curves of opposite directions.
+ * supports the merging of curves of opposite directions.
-
+ *
-\cgalModels{ArrangementTraits_2,ArrangementDirectionalXMonotoneTraits_2}
+ * \cgalModels{AosTraits_2,AosDirectionalXMonotoneTraits_2}
-
+ */
-
+template <typename RatKernel, typename AlgKernel, typename NtTraits>
-*/
-template< typename RatKernel, typename AlgKernel, typename NtTraits >
 class Arr_Bezier_curve_traits_2 {
 public:
 
-/// \name Types
+  /// \name Types
-/// @{
+  /// @{
 
-/*!
+  /*! the `NtTraits::Rational` type (and also the `RatKernel::FT` type).
-the `NtTraits::Rational` type
+   */
-(and also the `RatKernel::FT` type).
+  typedef unspecified_type Rational;
-*/
-typedef unspecified_type Rational;
 
-/*!
+  /*! the `NtTraits::Algebraic` type (and also the `AlgKernel::FT` type).
-the `NtTraits::Algebraic` type
+   */
-(and also the `AlgKernel::FT` type).
+  typedef unspecified_type Algebraic;
-*/
-typedef unspecified_type Algebraic;
 
-/// @}
+  /// @}
 
+  /*! The `Curve_2` class nested within the B&eacute;zier traits class is used
+   * to represent a B&eacute;zier curve of arbitrary degree, which is defined by
+   * a sequence of rational control points. In addition to the methods listed
+   * below, the I/O operators \link PkgArrangementOnSurface2op_left_shift
+   * `operator<<` \endlink and \link PkgArrangementOnSurface2op_right_shift
+   * `operator>>` \endlink for standard output-streams are also supported. The
+   * copy constructor and assignment operator are supported as well.
+   */
+  class Curve_2 {
+  public:
 
-/*!
+    /// \name Creation
+    /// @{
 
+    /*! default constructor.
+     */
+    Curve_2();
 
-The `Curve_2` class nested within the B&eacute;zier traits class is used
+    /*! constructs a B&eacute;zier curve as defined by the given range of
-to represent a B&eacute;zier curve of arbitrary degree, which is defined by a
+     * control points. The value-type of `InputIterator` is
-sequence of rational control points. In addition to the methods listed
+     * `RatKernel::Point_2`.
-below, the I/O operators \link PkgArrangementOnSurface2op_left_shift `operator<<` \endlink and \link PkgArrangementOnSurface2op_right_shift `operator>>` \endlink for
+     *
-standard output-streams are also supported. The copy constructor and
+     * \pre The input range must contain at least two control points.
-assignment operator are supported as well.
+     */
+    template <typename InputIterator>
+    Curve_2(InputIterator pts_begin, InputIterator pts_end);
 
-*/
+    /// @}
-class Curve_2 {
-public:
 
-/// \name Creation
+    /// \name Access Functions
-/// @{
+    /// @{
 
-/*!
+    /*! returns the number of control points that define `B`.
-default constructor.
+     */
-*/
+    std::size_t number_of_control_points() const;
-Curve_2 ();
 
-/*!
+    /*! returns the \f$k\f$th control point. Note that the first control point
-constructs a B&eacute;zier curve as defined by the given range of control
+     * equals the curve source, while the last control point equals its
-points. The value-type of `InputIterator` is `RatKernel::Point_2`.
+     * target. The rest of the control points do not lie on the curve.
-\pre The input range must contain at least two control points.
+     *
+     * \pre \f$k\f$ is smaller than the number of control points.
+     */
+    typename RatKernel::Point_2 control_point(std::size_t k) const;
 
-*/
+    /*! returns the point \f$B(t)\f$ on the curve that corresponds to the given
-template <class InputIterator>
+     * rational parameter value.
-Curve_2 (InputIterator pts_begin, InputIterator pts_end);
+     */
+    typename RatKernel::Point_2 operator()(const Rational& t) const;
 
-/// @}
+    /*! returns the point \f$B(t)\f$ on the curve that corresponds to the given
+     * algebraic parameter value.
+     */
+    typename AlgKernel::Point_2 operator()(const Algebraic& t) const;
 
-/// \name Access Functions
+    /// @}
-/// @{
 
-/*!
+  }; /* end Arr_Bezier_curve_traits_2::Curve_2 */
-returns the number of control points that define `B`.
-*/
-size_t number_of_control_points () const;
 
-/*!
+  /*! The `Point_2` class nested within the B&eacute;zier traits class is used
-returns the \f$ k\f$th control point. Note that the first control point equals
+   * to represent: (i) an endpoint of a B&eacute;zier curve, (ii) a vertical
-the curve source, while the last control point equals its target. The rest
+   * tangency point of a curve, used to subdivide it into \f$x\f$-monotone
-of the control points do not lie on the curve.
+   * subcurve, and (iii) an intersection point between two curves. While, points
-\pre \f$ k\f$ is smaller than the number of control points.
+   * of type (i) have rational coordinates and are given as part of the input,
-*/
+   * points of the two latter types have algebraic coordinates. However, to
-typename RatKernel::Point_2 control_point (size_t k) const;
+   * speed up the arrangement construction, such point are not computed in an
+   * exact manner, and instead are given in an approximate representation. Note
+   * that the exact coordinates of a point may only be accessed if it is exactly
+   * computed.
 
-/*!
+   * In addition to the methods listed below, the copy constructor and assignment
-returns the point \f$ B(t)\f$ on the curve that corresponds to the given
+   * operator for `Point_2` objects are also supported.
-rational parameter value.
+   */
-*/
+  class Point_2 {
-typename RatKernel::Point_2 operator() (const Rational& t) const;
+  public:
 
-/*!
+    /// \name Creation
-returns the point \f$ B(t)\f$ on the curve that corresponds to the given
+    /// @{
-algebraic parameter value.
-*/
-typename AlgKernel::Point_2 operator() (const Algebraic& t) const;
 
-/// @}
+    /*!
+      default constructor.
+    */
+    Point_2();
 
-}; /* end Arr_Bezier_curve_traits_2::Curve_2 */
+    /*!
+      constructs the point \f$B(t_0)\f$ on the given curve. As \f$t_0\f$ is an
+      algebraic number, the point has algebraic coordinates.
+    */
+    Point_2(const Curve_2& B, const Algebraic& t_0);
 
+    /*!
+      constructs the point \f$B(t_0)\f$ on the given curve. As \f$t_0\f$ is a
+      rational number, the point has rational coordinates.
+    */
+    Point_2(const Curve_2& B, const Rational& t_0);
 
-/*!
+    /// @}
 
-The `Point_2` class nested within the B&eacute;zier traits class is used
+    /// \name Access Functions
-to represent: (i) an endpoint of a B&eacute;zier curve, (ii) a vertical tangency
+    /// @{
-point of a curve, used to subdivide it into \f$ x\f$-monotone subcurve, and
-(iii) an intersection point between two curves. While, points of type (i) have
-rational coordinates and are given as part of the input, points of the two
-latter types have algebraic coordinates. However, to speed up the arrangement
-construction, such point are not computed in an exact manner, and instead
-are given in an approximate representation. Note that the exact coordinates
-of a point may only be accessed if it is exactly computed.
 
-In addition to the methods listed below, the copy constructor and assignment
+    /*! returns the approximated coordinates of `p`.
-operator for `Point_2` objects are also supported.
+    */
+    std::pair<double, double> approximate() const;
 
-*/
+    /*! returns whether the coordinates of `p` are computed in an exact manner.
-class Point_2 {
+    */
-public:
+    bool is_exact() const;
 
-/// \name Creation
+    /*! returns the \f$x\f$-coordinate of `p`.
-/// @{
+     *
+     * \pre `p` is exactly computed.
+     */
+    Algebraic x() const;
 
-/*!
+    /*! returns the \f$y\f$-coordinate of `p`.
-default constructor.
+     *
-*/
+     * \pre `p` is exactly computed.
-Point_2 ();
+     */
+    Algebraic y() const;
 
-/*!
+    /*! returns whether the coordinates of `p` are rational numbers.
-constructs the point \f$ B(t_0)\f$ on the given curve. As \f$ t_0\f$ is an
+     */
-algebraic number, the point has algebraic coordinates.
+    bool is_rational() const;
-*/
-Point_2 (const Curve_2& B, const Algebraic& t_0);
 
-/*!
+    /*! casts `p` to a point with rational coordinates.
-constructs the point \f$ B(t_0)\f$ on the given curve. As \f$ t_0\f$ is a
+     * \pre `p` has rational coordinates.
-rational number, the point has rational coordinates.
+     */
-*/
+    operator typename RatKernel::Point_2() const;
-Point_2 (const Curve_2& B, const Rational& t_0);
 
-/// @}
+    /// @}
 
-/// \name Access Functions
+  }; /* end Arr_Bezier_curve_traits_2::Point_2 */
-/// @{
 
-/*!
+  /*! The `X_monotone_curve_2` class nested within the B&eacute;zier traits is
-returns the approximated coordinates of `p`.
+   * used to represent \f$x\f$-monotone subcurves of B&eacute;zier curves. The
-*/
+   * subcurve is defined by a supporting B&eacute;zier curve \f$B(t)\f$ and a
-std::pair<double, double> approximate () const;
+   * range of definition in the parameter space \f$[t_1, t_2] \subseteq [0,1]\f$,
+   * where \f$B(t_1)\f$ is the subcurve source and \f$B(t_2)\f$ is its target.
+   * Note that as the point endpoints may only be approximated, the parameter
+   * range defining the subcurve may only be approximately known.
+   *
+   * It is not possible to construct \f$x\f$-monotone subcurves directly.
+   * Instead, use the `Make_x_monotone_2` functor supplied by the traits class to
+   * subdivide a `Curve_2` object into \f$x\f$-monotone subcurves.
+   */
+  class X_monotone_curve_2 {
+  public:
 
-/*!
+    /// \name Access Functions
-returns whether the coordinates of `p` are computed in an exact manner.
+    /// @{
-*/
-bool is_exact () const;
 
-/*!
+    /*! returns the supporting B&eacute;zier curve of `b`.
-returns the \f$ x\f$-coordinate of `p`.
+     */
-\pre `p` is exactly computed.
+    Curve_2 supporting_curve() const;
-*/
-Algebraic x () const;
 
-/*!
+    /*! returns the source point of `b`.
-returns the \f$ y\f$-coordinate of `p`.
+     */
-\pre `p` is exactly computed.
+    Point_2 source() const;
-*/
-Algebraic y () const;
 
-/*!
+    /*! returns the target point of `b`.
-returns whether the coordinates of `p` are rational numbers.
+     */
-*/
+    Point_2 target() const;
-bool is_rational () const;
 
-/*!
+    /*! returns the left (\f$xy\f$-lexicographically smaller) endpoint of `b`.
-casts `p` to a point with rational coordinates.
+     */
-\pre `p` has rational coordinates.
+    Point_2 left() const;
-*/
-operator typename RatKernel::Point_2 () const;
 
-/// @}
+    /*! returns the right (\f$xy\f$-lexicographically smaller) endpoint of `b`.
+     */
+    Point_2 right() const;
 
-}; /* end Arr_Bezier_curve_traits_2::Point_2 */
+    /*! return the approximate parameter range defining the subcurve `b`.
+    */
+    std::pair<double, double> parameter_range() const;
 
-/*!
+    /// @}
 
+  }; /* end Arr_Bezier_curve_traits_2::X_monotone_curve_2 */
 
-The `X_monotone_curve_2` class nested within the B&eacute;zier traits is
+  class Trim_2 {
-used to represent \f$ x\f$-monotone subcurves of B&eacute;zier curves. The subcurve is
+  public:
-defined by a supporting B&eacute;zier curve \f$ B(t)\f$ and a range of definition in
+    /// \name Creation
-the parameter space \f$ [t_1, t_2] \subseteq [0, 1]\f$, where \f$ B(t_1)\f$ is the
+    /// @{
-subcurve source and \f$ B(t_2)\f$ is its target. Note that as the point endpoints
-may only be approximated, the parameter range defining the subcurve may
-only be approximately known.
 
-It is not possible to construct \f$ x\f$-monotone subcurves directly. Instead,
+    /*! Trims the given \f$x\f$-monotone curve to an from `src` to `tgt`.
-use the `Make_x_monotone_2` functor supplied by the traits class to
+     *
-subdivide a `Curve_2` object into \f$ x\f$-monotone subcurves.
+     * \ pre `src` and `tgt` lies on the curve
+     */
+    X_monotone_curve_2(const X_monotone_curve_2& xcv,
+                       const Point_2& src, const Point_2& tgt) const
 
-*/
+    /// @}
-class X_monotone_curve_2 {
-public:
 
-/// \name Access Functions
+  } /* end Arr_Bezier_curve_traits_2::Trim_2 */
-/// @{
-
-/*!
-returns the supporting B&eacute;zier curve of `b`.
-*/
-Curve_2 supporting_curve () const;
-
-/*!
-returns the source point of `b`.
-*/
-Point_2 source () const;
-
-/*!
-returns the target point of `b`.
-*/
-Point_2 target () const;
-
-/*!
-returns the left (\f$ xy\f$-lexicographically smaller) endpoint of `b`.
-*/
-Point_2 left () const;
-
-/*!
-returns the right (\f$ xy\f$-lexicographically smaller) endpoint of `b`.
-*/
-Point_2 right () const;
-
-/*!
-return the approximate parameter range defining the subcurve `b`.
-*/
-std::pair<double, double> parameter_range () const;
-
-/// @}
-
-}; /* end Arr_Bezier_curve_traits_2::X_monotone_curve_2 */
-
-class Trim_2{
-public:
-/// \name Creation
-/// @{
-
-/*!
-Trims the given x-monotone curve to an from src to tgt.
-\ pre `src` and `tgt` lies on the curve
-*/
-
-X_monotone_curve_2(const X_monotone_curve_2& xcv,
-                                const Point_2& src,
-                                const Point_2& tgt)const
-
-/// @}
-
-}/* end Arr_Bezier_curve_traits_2::Trim_2 */
 
 }; /* end Arr_Bezier_curve_traits_2 */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_accessor.h

@@ -18,122 +18,123 @@ namespace CGAL {
 template <typename Arrangement>
 class Arr_accessor {
 public:
+  /// \name Types
+  /// @{
 
-/// \name Types
+  /*! the type of the associated arrangement. */
-/// @{
+  typedef unspecified_type Arrangement_2;
 
-/*! the type of the associated arrangement. */
+  /*! the point type. */
-typedef unspecified_type Arrangement_2;
+  typedef typename Arrangement_2::Point_2 Point_2;
 
-/*! the point type. */
+  /*! the \f$x\f$-monotone curve type. */
-typedef typename Arrangement_2::Point_2 Point_2;
+  typedef typename Arrangement_2::X_monotone_curve_2 X_monotone_curve_2;
 
-/*! the \f$ x\f$-monotone curve type. */
+  /*! */
+  typedef typename Arrangement_2::Vertex_handle Vertex_handle;
 
-typedef typename Arrangement_2::X_monotone_curve_2 X_monotone_curve_2;
+  /*! */
+  typedef typename Arrangement_2::Halfedge_handle Halfedge_handle;
 
-/*! */
+  /*! */
-typedef typename Arrangement_2::Vertex_handle Vertex_handle;
+  typedef typename Arrangement_2::Face_handle Face_handle;
 
-/*! */
+  /*! represents the boundary of a connected component (CCB). */
-typedef typename Arrangement_2::Halfedge_handle Halfedge_handle;
+  typedef typename Arrangement_2::Ccb_halfedge_circulator Ccb_halfedge_circulator;
 
-/*! */
+  /// @}
-typedef typename Arrangement_2::Face_handle Face_handle;
 
-/*! represents the boundary of a connected component (CCB). */
+  /// \name Creation
-typedef typename Arrangement_2::Ccb_halfedge_circulator Ccb_halfedge_circulator;
+  /// @{
 
-/// @}
+  /*! constructs an accessor attached to the given arrangement `arr`. */
+  Arr_accessor(Arrangement_2& arr);
 
-/// \name Creation
+  /// @}
-/// @{
 
-/*! constructs an accessor attached to the given arrangement `arr`. */
+  /// \name Accessing the Notification Functions
-Arr_accessor(Arrangement_2& arr);
 
-/// @}
+  /// @{
 
-/// \name Accessing the Notification Functions
+  /*! notifies the arrangement observer that a global change is going to take
+   * place (for the usage of the global functions that operate on arrangements).
+   */
+  void notify_before_global_change();
 
-/// @{
+  /*! notifies the arrangement observer that a global change has taken place
+   * (for the usage of the global functions that operate on arrangements).
+   */
+  void notify_after_global_change();
 
-/*! notifies the arrangement observer that a global change is going to take
+  /// @}
- * place (for the usage of the global functions that operate on arrangements).
- */
-void notify_before_global_change();
 
-/*! notifies the arrangement observer that a global change has taken place (for
+  /// \name Arrangement Predicates
- * the usage of the global functions that operate on arrangements).
+  /// @{
- */
-void notify_after_global_change();
 
-/// @}
+  /*! locates a place for the curve `c` around the vertex `v` and returns a
+   * halfedge whose target is `v`, where c should be inserted between this
+   * halfedge and the next halfedge around `v` in a clockwise order.
+   */
+  Halfedge_handle
+  locate_around_vertex(Vertex_handle v, const X_monotone_curve_2& c) const;
 
-/// \name Arrangement Predicates
+  /*! counts the number of edges along the path from `e1` to `e2`.  In case the
-/// @{
+   * two halfedges do not belong to the same connected component, the function
+   * returns (-1).
+   */
+  int halfedge_distance(Halfedge_const_handle e1,
+                        Halfedge_const_handle e2) const;
 
-/*! locates a place for the curve `c` around the vertex `v` and returns a
+  /*! determines whether a new halfedge we are about to create, which is to be
- * halfedge whose target is `v`, where c should be inserted between this
+   * associated with the curve `c` and directed from `pred1->target()` to
- * halfedge and the next halfedge around `v` in a clockwise order.
+   * `pred2->target()`, lies on the inner CCB of the new face that will be
- */
+   * created, introducing this new edge.
-Halfedge_handle
+   *
-locate_around_vertex(Vertex_handle v, const X_monotone_curve_2& c) const;
+   * \pre `pred1->target()` and `pred2->target()` are associated with `c`'s
+   *      endpoints.
+   *
+   * \pre `pred1` and `pred2` belong to the same connected component, such that
+   * a new face is created by connecting `pred1->target()` and
+   * `pred2->target()`.
+   */
+  bool is_inside_new_face(Halfedge_handle pred1,
+                          Halfedge_handle pred2,
+                          const X_monotone_curve_2& c) const;
 
-/*! counts the number of edges along the path from `e1` to `e2`.  In case the
+  /*! determines whether a given point lies within the region bounded by a
- * two halfedges do not belong to the same connected component, the function
+   * boundary of the connected component that `he` belongs to.  Note that if the
- * returns (-1).
+   * function returns `true`, then `p` is contained within `he->face()` (but not
-*/
+   * on its boundary), or inside one of the inner CCBs of this face, or it may
-int halfedge_distance(Halfedge_const_handle e1, Halfedge_const_handle e2) const;
+   * coincide with an isolated vertex in this face.
+   */
+  bool point_is_in(const Point_2& p, Halfedge_const_handle he) const;
 
-/*! determines whether a new halfedge we are about to create, which is to be
+  /*! determines whether `he` lies on the outer boundary of its incident face.
- * associated with the curve `c` and directed from `pred1->target()` to
+   */
- * `pred2->target()`, lies on the inner CCB of the new face that will be
+  bool is_on_outer_boundary(Halfedge_const_handle he) const;
- * created, introducing this new edge.
- *
- * \pre `pred1->target()` and `pred2->target()` are associated with `c`'s
- * endpoints.
- *
- * \pre `pred1` and `pred2` belong to the same connected component, such that a
- * new face is created by connecting `pred1->target()` and `pred2->target()`.
-*/
-bool is_inside_new_face(Halfedge_handle pred1,
-Halfedge_handle pred2,
-const X_monotone_curve_2& c) const;
 
-/*! determines whether a given point lies within the region bounded by a
+  /*! determines whether `he` lies on the inner boundary of its incident face
- * boundary of the connected component that `he` belongs to.  Note that if the
+   * (that is, whether it lies on the boundary of one of the inner CCBs of this
- * function returns `true`, then `p` is contained within `he->face()` (but not
+   * face).
- * on its boundary), or inside one of the inner CCBs of this face, or it may
+   */
- * coincide with an isolated vertex in this face.
+  bool is_on_inner_boundary(Halfedge_const_handle he) const;
- */
-bool point_is_in(const Point_2& p, Halfedge_const_handle he) const;
 
-/*! determines whether `he` lies on the outer boundary of its incident face. */
+  /// @}
-bool is_on_outer_boundary(Halfedge_const_handle he) const;
 
-/*! determines whether `he` lies on the inner boundary of its incident face
+  /// \name Arrangement Modifiers
- * (that is, whether it lies on the boundary of one of the inner CCBs of this
+  /// @{
- * face).
- */
-bool is_on_inner_boundary(Halfedge_const_handle he) const;
 
-/// @}
+  /*! creates a new vertex an associates it with the point `p`.
-
+   *
-/// \name Arrangement Modifiers
+   * \pre There is no existing vertex already associated with `p`.
-/// @{
+   */
-
+  Vertex_handle create_vertex(const Point_2& p);
-/*! creates a new vertex an associates it with the point `p`.
- *
- * \pre There is no existing vertex already associated with `p`.
- */
-Vertex_handle create_vertex(const Point_2& p);
 
 /*! inserts the curve `c` as a new inner CCBs (hole) of the face `f`,
  * connecting the two isolated vertices `v1` and `v2`.  `res` is the comparison
  * result between these two end-vertices.  The function returns a handle for one
- * of the new halfedges corresponding to the inserted curve, directed from `v1`
+ * one of the new halfedges corresponding to the inserted curve, directed from
- * to `v2`.
+ * `v1` to `v2`.
  *
  * \pre `v1` and `v2` are associated with `c`'s endpoints, that they lie of
  * `f`'s interior and that and that they have no incident edges.
@@ -160,121 +161,122 @@ Halfedge_handle insert_from_vertex_ex(const X_monotone_curve_2& c,
                                       Vertex_handle v,
                                       Comparison_result res);
 
-/*! inserts the curve `c` into the arrangement, such that both `c`'s endpoints
+  /*! inserts the curve `c` into the arrangement, such that both `c`'s endpoints
- * correspond to existing arrangement vertices, given by `pred1->target()` and
+   * correspond to existing arrangement vertices, given by `pred1->target()` and
- * `pred2->target()`. `res` is the comparison result between these two
+   * `pred2->target()`. `res` is the comparison result between these two
- * end-vertices. The function creates a new halfedge pair that connects the two
+   * end-vertices. The function creates a new halfedge pair that connects the
- * vertices (with `pred1` and `pred2` indicate the exact place for these
+   * two vertices (with `pred1` and `pred2` indicate the exact place for these
- * halfedges around the two target vertices) and returns a handle for the
+   * halfedges around the two target vertices) and returns a handle for the
- * halfedge directed from `pred1->target()` to `pred2->target()`.  The output
+   * halfedge directed from `pred1->target()` to `pred2->target()`.  The output
- * flag `new_face` indicates whether a new face has been created following the
+   * flag `new_face` indicates whether a new face has been created following the
- * insertion of the new curve.
+   * insertion of the new curve.
- *
+   *
- * \pre `pred1->target()` and `pred2->target()` are associated with `c`'s
+   * \pre `pred1->target()` and `pred2->target()` are associated with `c`'s
- * endpoints and that if a new face is created, then `is_inside_new_face (pred1,
+   * endpoints and that if a new face is created, then
- * pred2, c)` is `true`.
+   * `is_inside_new_face(pred1, pred2, c)` is `true`.
- */
+   */
-Halfedge_handle insert_at_vertices_ex(const X_monotone_curve_2& c,
+  Halfedge_handle insert_at_vertices_ex(const X_monotone_curve_2& c,
-                                      Halfedge_handle pred1,
+                                        Halfedge_handle pred1,
-                                      Halfedge_handle pred2,
+                                        Halfedge_handle pred2,
-                                      Comparison_result res, bool& new_face);
+                                        Comparison_result res, bool& new_face);
 
-/*! inserts `v` as an isolated vertex inside `f`.
+  /*! inserts `v` as an isolated vertex inside `f`.
- *
+   *
- * \pre `v->point()` is contained in the interior of the given face.
+   * \pre `v->point()` is contained in the interior of the given face.
- */
+   */
-void insert_isolated_vertex(Face_handle f, Vertex_handle v);
+  void insert_isolated_vertex(Face_handle f, Vertex_handle v);
 
-/*! moves the given hole (inner CCB) from the interior of the face `f1` to the
+  /*! moves the given hole (inner CCB) from the interior of the face `f1` to the
- * face `f2`.
+   * face `f2`.
- *
+   *
- * \pre `hole` is currently contained in `f1` and should be moved to `f2`.
+   * \pre `hole` is currently contained in `f1` and should be moved to `f2`.
- */
+   */
-void move_hole(Face_handle f1, Face_handle f2, Ccb_halfedge_circulator hole);
+  void move_hole(Face_handle f1, Face_handle f2, Ccb_halfedge_circulator hole);
 
-/*! moves the given isolated vertex from the interior of the face `f1`
+  /*! moves the given isolated vertex from the interior of the face `f1`
- * inside the face `f2`.
+   * inside the face `f2`.
- *
+   *
- * \pre `v` is indeed an isolated vertex currently contained in `f1` and should
+   * \pre `v` is indeed an isolated vertex currently contained in `f1` and
- * be moved to `f2`.
+   * should be moved to `f2`.
- */
+   */
-bool move_isolated_vertex(Face_handle f1, Face_handle f2, Vertex_handle v);
+  bool move_isolated_vertex(Face_handle f1, Face_handle f2, Vertex_handle v);
 
-/*! relocates all inner ccbs and isolated vertices to their proper position
+  /*! relocates all inner ccbs and isolated vertices to their proper position
- * immediately after a face has split due to the insertion of a new halfedge,
+   * immediately after a face has split due to the insertion of a new halfedge,
- * namely after `insert_at_vertices_ex()` was invoked and indicated that a new
+   * namely after `insert_at_vertices_ex()` was invoked and indicated that a new
- * face has been created. `he` is the halfedge returned by
+   * face has been created. `he` is the halfedge returned by
- * `insert_at_vertices_ex()`, such that `he->twin()->face` is the face that has
+   * `insert_at_vertices_ex()`, such that `he->twin()->face` is the face that
- * just been split and `he->face()` is the newly created face.
+   * has just been split and `he->face()` is the newly created face.
- */
+   */
-void relocate_in_new_face(Halfedge_handle he);
+  void relocate_in_new_face(Halfedge_handle he);
 
-/*! relocates all inner ccbs in a new face, as detailed above. */
+  /*! relocates all inner ccbs in a new face, as detailed above. */
-void relocate_holes_in_new_face(Halfedge_handle he);
+  void relocate_holes_in_new_face(Halfedge_handle he);
 
-/*! relocates all isolated vertices in a new face, as detailed above. */
+  /*! relocates all isolated vertices in a new face, as detailed above. */
-void relocate_isolated_vertices_in_new_face(Halfedge_handle he);
+  void relocate_isolated_vertices_in_new_face(Halfedge_handle he);
 
-/*! modifies the point associated with the vertex `v` (the point may be
+  /*! modifies the point associated with the vertex `v` (the point may be
- * geometrically different than the one currently associated with `v`).  The
+   * geometrically different than the one currently associated with `v`).  The
- * function returns a handle to the modified vertex (same as `v`).
+   * function returns a handle to the modified vertex (same as `v`).
- *
+   *
- * \pre No other arrangement vertex is already associated with `p`.
+   * \pre No other arrangement vertex is already associated with `p`.
- *
+   *
- * \pre The topology of the arrangement does not change after the vertex point
+   * \pre The topology of the arrangement does not change after the vertex point
- * is modified.
+   * is modified.
- */
+   */
-Vertex_handle modify_vertex_ex(Vertex_handle v, const Point_2& p);
+  Vertex_handle modify_vertex_ex(Vertex_handle v, const Point_2& p);
 
-/*! modifies the \f$ x\f$-monotone curve associated with the edge `e` (the curve
+  /*! modifies the \f$x\f$-monotone curve associated with the edge `e` (the
- * `c` may be geometrically different than the one currently associated with
+   * curve `c` may be geometrically different than the one currently associated
- * `e`).  The function returns a handle to the modified edge (same as `e`).
+   * with `e`).  The function returns a handle to the modified edge (same as
- *
+   * `e`).
- * \pre The interior of `c` is disjoint from all existing arrangement vertices
+   *
- * and edges.
+   * \pre The interior of `c` is disjoint from all existing arrangement vertices
- */
+   * and edges.
-Halfedge_handle modify_edge_ex(Halfedge_handle e, const X_monotone_curve_2& c);
+   */
+  Halfedge_handle modify_edge_ex(Halfedge_handle e, const X_monotone_curve_2& c);
 
-/*! splits a given edge into two at the split point `p`, and associate the
+  /*! splits a given edge into two at the split point `p`, and associate the
- * x-monotone curves `c1` and `c2` with the resulting edges, such that `c1`
+   * \f$x\f$-monotone curves `c1` and `c2` with the resulting edges, such that
- * connects `he->source()` with `p` and `c2` connects `p` with
+   * `c1` connects `he->source()` with `p` and `c2` connects `p` with
- * `he->target()`. The function return a handle to the split halfedge directed
+   * `he->target()`. The function return a handle to the split halfedge directed
- * from `he->source()` to the split point `p`.
+   * from `he->source()` to the split point `p`.
- *
+   *
- * \pre The endpoints of `c1` and `c2` correspond to `p` and to `he`'s
+   * \pre The endpoints of `c1` and `c2` correspond to `p` and to `he`'s
- * end-vertices, as indicated above.
+   * end-vertices, as indicated above.
- */
+   */
-Halfedge_handle split_edge_ex(Halfedge_handle he, const Point_2& p,
+  Halfedge_handle split_edge_ex(Halfedge_handle he, const Point_2& p,
-                              const X_monotone_curve_2& c1,
+                                const X_monotone_curve_2& c1,
-                              const X_monotone_curve_2& c2);
+                                const X_monotone_curve_2& c2);
 
-/*! splits a given edge into two at by the vertex `v`, and associate the
+  /*! splits a given edge into two at by the vertex `v`, and associate the
- * x-monotone curves `c1` and `c2` with the resulting edges, such that `c1`
+   * \f$x\f$-monotone curves `c1` and `c2` with the resulting edges, such that
- * connects `he->source()` with `v` and `c2` connects `v` with
+   * `c1` connects `he->source()` with `v` and `c2` connects `v` with
- * `he->target()`. The function return a handle to the split halfedge directed
+   * `he->target()`. The function return a handle to the split halfedge directed
- * from `he->source()` to `v`.
+   * from `he->source()` to `v`.
- *
+   *
- * \pre The endpoints of `c1` and `c2` correspond to `v` and to `he`'s
+   * \pre The endpoints of `c1` and `c2` correspond to `v` and to `he`'s
- * end-vertices, as indicated above. It is also assumed that `v` has no incident
+   * end-vertices, as indicated above. It is also assumed that `v` has no
- * edges.
+   * incident edges.
- */
+   */
-Halfedge_handle split_edge_ex(Halfedge_handle he, Vertex_handle v,
+  Halfedge_handle split_edge_ex(Halfedge_handle he, Vertex_handle v,
-                              const X_monotone_curve_2& c1,
+                                const X_monotone_curve_2& c1,
-                              const X_monotone_curve_2& c2);
+                                const X_monotone_curve_2& c2);
 
-/*! removes the edge `he` from the arrangement, such that if the edge removal
+  /*! removes the edge `he` from the arrangement, such that if the edge removal
- * causes the creation of a new hole (inner CCB), `he->target()` lies on the
+   * causes the creation of a new hole (inner CCB), `he->target()` lies on the
- * boundary of this hole.  The flags `remove_source` and `remove_target`
+   * boundary of this hole.  The flags `remove_source` and `remove_target`
- * indicate whether the end-vertices of `he` should be removed as well, in case
+   * indicate whether the end-vertices of `he` should be removed as well, in
- * they have no other incident edges.  If the operation causes two faces to
+   * case they have no other incident edges.  If the operation causes two faces
- * merge, the merged face is returned.  Otherwise, the face to which the edge
+   * to merge, the merged face is returned.  Otherwise, the face to which the
- * was incident is returned.
+   * edge was incident is returned.
- */
+   */
-Face_handle remove_edge_ex(Halfedge_handle he,
+  Face_handle remove_edge_ex(Halfedge_handle he,
-                           bool remove_source = true,
+                             bool remove_source = true,
-                           bool remove_target = true);
+                             bool remove_target = true);
-
-/// @}
 
+  /// @}
 }; /* end Arr_accessor */
+
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_algebraic_segment_traits_2.h

@@ -3,22 +3,22 @@ namespace CGAL {
 /*! \ingroup PkgArrangementOnSurface2TraitsClasses
  *
  * The traits class `Arr_algebraic_segment_traits_2` is a model of the
- * `ArrangementTraits_2` concept that handles planar algebraic curves of
+ * `AosTraits_2` concept that handles planar algebraic curves of arbitrary
- * arbitrary degree, and \f$ x\f$-monotone of such curves.  A planar (real)
+ * degree, and \f$x\f$-monotone of such curves.  A planar (real) <I>algebraic
- * <I>algebraic curve</I> is the vanishing set of a polynomial in two variables,
+ * curve</I> is the vanishing set of a polynomial in two variables, that is,
- * that is, the curve is defined by the defining equation \f[
+ * the curve is defined by the defining equation
- * f(x):=\sum_{i+j\leq n} a_{ij} x^i y^j =0, \f] where \f$ n\f$ is the degree of
+ * \f[f(x):=\sum_{i+j\leq n} a_{ij} x^i y^j =0, \f] where \f$n\f$ is the
- * the curve.
+ * degree of the curve.
  *
  * The traits class allows the construction of algebraic curves, by specifying
- * their implicit equation. \f$ x\f$-monotone and vertical segments of a curve
+ * their implicit equation. \f$x\f$-monotone and vertical segments of a curve
  * can also be defined; unbounded curves and segments are supported.  The
  * template parameter `Coefficient` defines the innermost coefficient type of
  * the polynomials. Currently, the types `leda::integer` and `CORE::BigInt` are
  * supported as well as any instance of `CGAL::Sqrt_extension` that is
  * instantiated with one of the integral types above.
  *
- * \cgalModels{ArrangementTraits_2}
+ * \cgalModels{AosTraits_2}
  */
 
 template <typename Coefficient>
@@ -50,8 +50,7 @@ public:
    */
   typedef unspecified_type Algebraic_real_1;
 
-  /*! Typedef from `Algebraic_kernel_1::Bound`
+  /// Typedef from `Algebraic_kernel_1::Bound`
-   */
   typedef unspecified_type Bound;
 
   /// @}
@@ -77,7 +76,6 @@ public:
    */
   class Construct_curve_2 {
   public:
-
     /// \name Object Creation Functors
     /// @{
 
@@ -102,40 +100,41 @@ public:
    */
   class Construct_point_2 {
   public:
-
     /// \name Object Creation Functors
     /// @{
 
     /*! returns a `Point_2` object that represents the `arcno`-th
-     * point in the fiber of `cv` at \f$ x\f$-coordinate `x`,
+     * point in the fiber of `cv` at \f$x\f$-coordinate `x`,
      * counted from the bottom, starting with zero.
+     *
      * \pre (`cv` must not have a vertical line at `x`,
-     * and \f$ 0\leq arcno < c\f$, where \f$ c\f$ is the number of points
+     * and \f$0\leq arcno < c\f$, where \f$c\f$ is the number of points
      * in the fiber of `cv` at `x`.)
      */
-    Point_2 operator() (Algebraic_real_1 x, Curve_2 cv, int arcno);
+    Point_2 operator()(Algebraic_real_1 x, Curve_2 cv, int arcno);
 
     /*! returns a `Point_2` object that represents the
-     * point on `xcv` at \f$ x\f$-coordinate `x`
+     * point on `xcv` at \f$x\f$-coordinate `x`
-     * \pre (`x` is in the \f$ x\f$-range of `xcv`.)
+     *
+     * \pre (`x` is in the \f$x\f$-range of `xcv`.)
      */
-    Point_2 operator() (Algebraic_real_1 x, X_monotone_curve_2 xcv);
+    Point_2 operator()(Algebraic_real_1 x, X_monotone_curve_2 xcv);
 
     /*! returns a `Point_2` object that represents (x,y)
      */
-    Point_2 operator() (Algebraic_real_1 x, Algebraic_real_1 y);
+    Point_2 operator()(Algebraic_real_1 x, Algebraic_real_1 y);
 
     /*! returns a `Point_2` object that represents (x,y)
      */
-    Point_2 operator() (Coefficient x, Coefficient y);
+    Point_2 operator()(Coefficient x, Coefficient y);
 
     /*! returns a `Point_2` object that represents (x,y)
      */
-    Point_2 operator() (Bound x, Bound y);
+    Point_2 operator()(Bound x, Bound y);
 
     /*! returns a `Point_2` object that represents (x,y)
      */
-    Point_2 operator() (int x, int y);
+    Point_2 operator()(int x, int y);
 
     /// @}
 
@@ -145,7 +144,6 @@ public:
    */
   class Construct_x_monotone_segment_2 {
   public:
-
     /// \name Object Creation Functors
     /// @{
 
@@ -162,54 +160,56 @@ public:
      *
      * \pre `end_min` must have a unique \f$x\f$-monotone segment to its right, or
      *      `end_max` must have a unique \f$x\f$-monotone segment to its left.
-     *       Furthermore, `end_min` and `end_max` must be connected by an
+     *      Furthermore, `end_min` and `end_max` must be connected by an
-     *       \f$x\f$-monotone segment of `cv`)
+     *      \f$x\f$-monotone segment of `cv`)
      */
     template <typename OutputIterator>
-    OutputIterator operator() (Curve_2 cv, Point_2 end_min, Point_2 end_max,
+    OutputIterator operator()(Curve_2 cv, Point_2 end_min, Point_2 end_max,
-                               OutputIterator oi);
+                              OutputIterator oi);
 
     /*! inserts a sequence of `X_monotone_curve_2` objects into an output container
      * given through an output iterator.  These segments form an \f$x\f$-monotone
      * (or vertical) segment of the curve `cv`.
      *
-     * If `site_of_p==POINT_IN_INTERIOR`, the maximal segment is
+     * If `site_of_p` == `POINT_IN_INTERIOR`, the maximal segment that contains
-     * returned that contains `p` in its interior.
+     * `p` in its interior is returned .
      *
-     * returned that contains `p` as its left endpoint.
+     * If `site_of_p` == `MIN_ENDPOINT`, the segment that contains
+     * `p` as its left endpoint returned .
      *
-     * returned that contains `p` as its left endpoint.
+     * If `site_of_p` == `MAX_ENDPOINT`, the segment that contains
+     * `p` as its right endpoint returned .
      *
-     * \pre (If `site_of_p==POINT_IN_INTERIOR`, `p`
+     * \pre If `site_of_p` == `POINT_IN_INTERIOR`, `p` must be an interior point
-     * must be an interior point of an \f$x\f$-monotone or a vertical
+     * of an \f$x\f$-monotone or a vertical segment.
-     * segment.
+     *
-     * must either have a unique \f$x\f$-monotone segment to the right,
+     * \pre If `site_of_p` == `MIN_ENDPOINT`, `p` must either have a unique
-     * or a vertical segment from `p` upwards.
+     * \f$x\f$-monotone segment to the right, or a vertical segment from `p` upwards.
-     * must either have a unique \f$x\f$-monotone segment to the left,
+     *
-     * or a vertical segment from `p` downwards.)
+     * \pre If `site_of_p` == `MAX_ENDPOINT`, `p` must either have a unique
+     * \f$x\f$-monotone segment to the left, or a vertical segment from `p` downwards.
      */
     template <typename OutputIterator>
-    OutputIterator operator() (Curve_2 cv, Point_2 p, Site_of_point site_of_p,
+    OutputIterator operator()(Curve_2 cv, Point_2 p, Site_of_point site_of_p,
-                               OutputIterator out);
+                              OutputIterator out);
 
-    /*! inserts a sequence of `X_monotone_curve_2` objects into an output container
+    /*! inserts a sequence of `X_monotone_curve_2` objects into an output
-     * given through an output iterator.  These segments form a straight-line
+     * container given through an output iterator.  These segments form a
-     * segment connecting the points `p` and `q`. If `p` and `q` share the same
+     * straight-line segment connecting the points `p` and `q`. If `p` and `q`
-     * \f$x\f$-coordinate, the constructed vertical segment consists of only one
+     * share the same \f$x\f$-coordinate, the constructed vertical segment
-     * `X_monotone_curve_2` object and can be computed efficiently. In the
+     * consists of only one `X_monotone_curve_2` object and can be computed
-     * non-vertical case, the construction is only possible if `p` and `q` have both
+     * efficiently. In the non-vertical case, the construction is only possible
-     * rational x- and y-coordinates.
+     * if `p` and `q` have both rational \f$x\f$- and \f$y\f$-coordinates.
      *
-     * \pre (`p` must not be equal to `q`.)
+     * \pre `p` must not be equal to `q`.
      */
     template <typename OutputIterator>
-    OutputIterator operator() (Point_2 p, Point_2 q, OutputIterator out);
+    OutputIterator operator()(Point_2 p, Point_2 q, OutputIterator out);
 
     /// @}
-
   }; /* end Arr_algebraic_segment_traits_2::Construct_x_monotone_segment_2 */
 
-  /*! A model of the the `ArrangementTraits_2::Curve_2` concept.
+  /*! A model of the the `AosTraits_2::Curve_2` concept.
    * Represents algebraic curves. Internally, the type stores
    * topological-geometric information about the particular curve.
    * In order to use internal caching, instances should only be created
@@ -223,25 +223,25 @@ public:
 
     /*! returns the defining polynomial of the curve.
      */
-    Polynomial_2 polynomial () const;
+    Polynomial_2 polynomial() const;
 
     /// @}
 
   }; /* end Arr_algebraic_segment_traits_2::Curve_2 */
 
-  /*! A model of the `ArrangementBasicTraits_2::Point_2` concept.
+  /*! A model of the `AosBasicTraits_2::Point_2` concept.
-   * Represents points in \f$ \mathbb{R}^2\f$. Intersection points of algebraic
+   * Represents points in \f$\mathbb{R}^2\f$. Intersection points of algebraic
    * curves are in general non-rational, so we need a data structure that is
    * capable of representing arbitrary points with algebraic coordinates.
    *
    * The traits class represents algebraic coordinates by the type
-   * `Algebraic_real_1`, which is a model of the `AlgebraicReal_1` concept.
+   * `Algebraic_real_1`, which is a model of the `AlgebraicReal_1` concept. A
-   * A point \f$ p\f$ is stored by a triple \f$ (x,cv,arcno)\f$,
+   * point \f$p\f$ is stored by a triple \f$(x,cv,arcno)\f$, where \f$x\f$ is
-   * where \f$ x\f$ is the \f$ x\f$-coordinate of a point, \f$ cv\f$ is an instance
+   * the \f$x\f$-coordinate of a point, \f$cv\f$ is an instance of `Curve_2`
-   * of `Curve_2` that contains the point, (and has no vertical line at \f$ x\f$),
+   * that contains the point, (and has no vertical line at \f$x\f$), and
-   * and \f$ arcno\f$ is an `int`, denoting that \f$ p\f$ is met as the
+   * \f$arcno\f$ is an `int`, denoting that \f$p\f$ is met as the \f$arcno\f$-th
-   * \f$arcno\f$-th point when shooting a vertical ray at \f$ x\f$, starting from
+   * point when shooting a vertical ray at \f$x\f$, starting from \f$-\infty\f$
-   * \f$-\infty\f$ (where counting starts with \f$ 0\f$).
+   * (where counting starts with \f$0\f$).
    *
    * In addition to the methods listed below, the copy constructor and assignment
    * operator for `Point_2` objects are also supported.
@@ -251,53 +251,52 @@ public:
 
   class Point_2 {
   public:
-
     /// \name Modifiers
     /// @{
 
-    /*! returns the \f$ x\f$-coordinate of `p`.
+    /*! returns the \f$x\f$-coordinate of `p`.
      */
-    Algebraic_real_1 x () const;
+    Algebraic_real_1 x() const;
 
-    /*! returns the \f$ y\f$-coordinates of `p`.
+    /*! returns the \f$y\f$-coordinates of `p`.
      *
-     * <B>Attention:</B> As described above, points are not stored
+     * <B>Attention:</B> As described above, points are not stored by their
-     * by their \f$ y\f$-coordinate in `Algebraic_real_1` representation. In fact,
+     * \f$y\f$-coordinate in `Algebraic_real_1` representation. In fact,
      * this representation must be computed on demand, and might become quite
      * costly for points defined by high-degree polynomials. Therefore, it is
      * recommended to avoid to call this function as much as possible.
      */
-    Algebraic_real_1 y () const;
+    Algebraic_real_1 y() const;
 
     /*! returns a `Curve_2` instance that `p`is part of.
      */
-    Curve_2 curve () const;
+    Curve_2 curve() const;
 
     /*! returns the arc number of `p`.
      */
-    int arcno () const;
+    int arcno() const;
 
-    /*! returns double-approximations of the \f$ x\f$- and \f$ y\f$-coordinates.
+    /*! returns double-approximations of the \f$x\f$- and \f$y\f$-coordinates.
      */
-    std::pair<double,double> to_double () const;
+    std::pair<double,double> to_double() const;
 
     /// @}
 
   }; /* end Arr_algebraic_segment_traits_2::Point_2 */
 
-  /*! A model of the `ArrangementBasicTraits_2::X_monotone_curve_2` concept.
+  /*! A model of the `AosBasicTraits_2::X_monotone_curve_2` concept.
    * Represents terminal segments of an algebraic curves, that means vertical
-   * segments or \f$ x\f$-monotone segments with no critical \f$ x\f$-coordinate
+   * segments or \f$x\f$-monotone segments with no critical \f$x\f$-coordinate
-   * in the interior of their \f$ x\f$-range.  Terminal segments might either be
+   * in the interior of their \f$x\f$-range.  Terminal segments might either be
    * bounded or unbounded.  By definition, each interior point of a non-vertical
    * segment has the same arc number (see the documentation of type `Point_2`
    * above, which is called the <I>arc number</I> of the segment (note the arc
    * number at the endpoints might differ).  Such segments are represented
-   * internally by a 4-tuple \f$ (p,q,cv,arcno)\f$, where \f$ p\f$ and \f$ q\f$
+   * internally by a 4-tuple \f$(p,q,cv,arcno)\f$, where \f$p\f$ and \f$q\f$
-   * are the endpoints, \f$ cv\f$ is the <I>supporting curve</I> that the segment
+   * are the endpoints, \f$cv\f$ is the <I>supporting curve</I> that the
-   * belongs to, and arcno is the arc number of the segment.
+   * segment belongs to, and arcno is the arc number of the segment.
    *
-   * Arbitrary (weakly) \f$ x\f$-monotone segments are presented by a range
+   * Arbitrary (weakly) \f$x\f$-monotone segments are presented by a range
    * of `X_monotone_curve_2` instances, whose union equals the segment.
    * The functor `Construct_x_monotone_segment_2` allows their construction.
    * To construct all (maximal) terminal segments of a curve,
@@ -311,34 +310,34 @@ public:
 
     /*! returns the supporting algebraic curve of `s`.
      */
-    Curve_2 curve () const;
+    Curve_2 curve() const;
 
     /*! returns whether `s` is a vertical segment.
      */
-    bool is_vertical () const;
+    bool is_vertical() const;
 
     /*! returns whether `s` has a finite endpoint on the left
      */
-    bool is_finite (CGAL::Arr_curve_end ce) const;
+    bool is_finite(CGAL::Arr_curve_end ce) const;
 
     /*! \pre (The corresponding curve end is finite)
      */
-    Point_2 curve_end (CGAL::Arr_curve_end ce) const;
+    Point_2 curve_end(CGAL::Arr_curve_end ce) const;
 
     /*! returns the arc number of the segment.
      * \pre (The segment is non-vertical)
      */
-    int arcno () const;
+    int arcno() const;
 
-    /*! returns the \f$ x\f$-coordinate of a vertical segment.
+    /*! returns the \f$x\f$-coordinate of a vertical segment.
+     *
      * \pre (The segment is vertical)
      */
-    Algebraic_real_1 x () const;
+    Algebraic_real_1 x() const;
 
     /// @}
 
   }; /* end Arr_algebraic_segment_traits_2::X_monotone_curve_2 */
-
 }; /* end Arr_algebraic_segment_traits_2 */
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_batched_point_location.h

@@ -30,9 +30,8 @@ namespace CGAL {
  */
 template <typename Traits, typename Dcel,
 typename InputIterator, typename OutputIterator>
-OutputIterator locate (const Arrangement_2<Traits, Dcel>& arr,
+OutputIterator locate(const Arrangement_2<Traits, Dcel>& arr,
-                       InputIterator begin,
+                      InputIterator begin, InputIterator end,
-                       InputIterator end,
+                      OutputIterator oi);
-                       OutputIterator oi);
 
 } /* namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_bounded_planar_topology_traits_2.h

@@ -10,18 +10,18 @@ namespace CGAL {
  * The `Arr_bounded_planar_topology_traits_2` template has two parameters:
  * <UL>
  * <LI>The `GeometryTraits_2` template-parameter should be substituted by
- * a model of the `ArrangementBasicTraits_2` concept. The traits
+ * a model of the `AosBasicTraits_2` concept. The traits
  * class defines the types of \f$x\f$-monotone curves and two-dimensional
- * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
+ * points, namely `AosBasicTraits_2::X_monotone_curve_2` and
- * `ArrangementBasicTraits_2::Point_2`,
+ * `AosBasicTraits_2::Point_2`,
  *   respectively, and supports basic geometric predicates on them.
  * <LI>The `Dcel` template-parameter should be substituted by
- * a class that is a model of the `ArrangementDcel` concept. The
+ * a class that is a model of the `AosDcel` concept. The
  * value of this parameter is by default
  * `Arr_default_dcel<Traits>`.
  * </UL>
  *
- * \cgalModels{ArrangementBasicTopologyTraits}
+ * \cgalModels{AosBasicTopologyTraits}
  *
  * \sa `Arr_default_dcel<Traits>`
  * \sa `CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel,x,y>`
@@ -62,10 +62,10 @@ public:
   /// \name Accessors
   /// @{
 
-  /*! obtains the DCEL (const version). */
+  /*! obtains the \dcel (const version). */
   const Dcel& dcel() const;
 
-  /*! obtains the DCEL (non-const version). */
+  /*! obtains the \dcel (non-const version). */
   Dcel& dcel();
 
   /*! obtains the unbounded face (const version). */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_circle_segment_traits_2.h

@@ -3,7 +3,7 @@ namespace CGAL {
 /*! \ingroup PkgArrangementOnSurface2TraitsClasses
  *
  * The class `Arr_circle_segment_traits_2` is a model of the
- * `ArrangementTraits_2` concept and can be used to construct and maintain
+ * `AosTraits_2` concept and can be used to construct and maintain
  * arrangements of circular arcs and line segments.
  *
  * The traits class must be instantiated with a geometric kernel, such that the
@@ -11,34 +11,33 @@ namespace CGAL {
  * the supporting lines of the line segments are of type `Kernel::Line_2`.
  * Thus, the coordinates of the center of supporting circles, and its squared
  * radius are of type `Kernel::FT`, which should be an exact rational
- * number-type; similarly, the coefficients of each supporting line \f$ ax + by
+ * number-type; similarly, the coefficients of each supporting line
- * + c = 0\f$ are also of type `Kernel::FT`. Note however that the intersection
+ * \f$ax + by + c = 0\f$ are also of type `Kernel::FT`. Note however that the
- * point between two such arcs do not have rational coordinates in general. For
+ * intersection point between two such arcs do not have rational coordinates in
- * this reason, we do not require the endpoints of the input arcs and segments
+ * general. For this reason, we do not require the endpoints of the input arcs
- * to have rational coordinates.
+ * and segments to have rational coordinates.
  *
  * The nested `Point_2` type defined by the traits class is therefore
  * <I>different</I> than the `Kernel::Point_2` type. Its coordinates are of type
- * `CoordNT`, which an instantiation of `Sqrt_extension<NT,ROOT>` where `NT =
+ * `CoordNT`, which an instantiation of `Sqrt_extension<NT,ROOT>` where
- * ROOT = Kernel::FT`.  Moreover, the third and fourth (hidden) template
+ * `NT` = `ROOT` = `Kernel::FT`.  Moreover, the third and fourth (hidden)
- * parameters of `Sqrt_extension<NT,ROOT>` are set to `CGAL::Tag_true`, which
+ * template parameters of `Sqrt_extension<NT,ROOT>` are set to `CGAL::Tag_true`,
- * enables efficient comparison among different extensions.
+ * which enables efficient comparison among different extensions.
  *
  * For more details see the documentation of `Sqrt_extension<NT,ROOT>`.
  *
  * While `Arr_circle_segment_traits_2` models the concept
- * `ArrangementDirectionalXMonotoneTraits_2`, the implementation of the
+ * `AosDirectionalXMonotoneTraits_2`, the implementation of the
  * `Are_mergeable_2` operation does not enforce the input curves to have the
  * same direction as a precondition. Moreover, `Arr_circle_segment_traits_2`
  * supports the merging of curves of opposite directions.
  *
- * \cgalModels{ArrangementTraits_2,ArrangementDirectionalXMonotoneTraits_2}
+ * \cgalModels{AosTraits_2,AosApproximateTraits_2,AosDirectionalXMonotoneTraits_2}
  *
  */
 template <typename Kernel>
 class Arr_circle_segment_traits_2 {
 public:
-
   /*! The `Curve_2` class nested within the traits class can represent
    * arbitrary circular arcs, full circles and line segments and support their
    * construction in various ways.  The copy and default constructor as well as
@@ -88,7 +87,7 @@ public:
      * center point with rational coordinates and whose <I>squared</I> radius is
      * rational, with the given endpoints. The orientation of the arc is the
      * same as the orientation of `circ`.
-
+     *
      * \pre Both endpoints must lie on the given supporting circle.
      */
     Curve_2(const typename Kernel::Circle_2& circ,
@@ -111,9 +110,9 @@ public:
      *
      * \pre The three points must not be collinear.
      */
-    Curve_2 (const typename Kernel::Point_2& source,
+    Curve_2(const typename Kernel::Point_2& source,
-             const typename Kernel::Point_2& mid,
+            const typename Kernel::Point_2& mid,
-             const typename Kernel::Point_2& target);
+            const typename Kernel::Point_2& target);
 
     /// @}
 
@@ -162,7 +161,6 @@ public:
     typename Kernel::Circle_2 supporting_circle() const;
 
     /// @}
-
   }; /* end Arr_circle_segment_traits_2::Curve_2 */
 
 
@@ -172,16 +170,13 @@ public:
    */
   class Point_2 {
   public:
-
     /// \name Types
     /// @{
 
-    /*! the `Kernel::FT` type.
+    /// the `Kernel::FT` type.
-     */
     typedef unspecified_type Rational;
 
-    /*! the algebraic number-type.
+    /// the algebraic number-type.
-     */
     typedef unspecified_type CoordNT;
 
     /// @}
@@ -193,11 +188,11 @@ public:
      */
     Point_2();
 
-    /*! creates the point \f$ (x,y)\f$.
+    /*! creates the point \f$(x,y)\f$.
      */
     Point_2(const Rational& x, const Rational& y);
 
-    /*! creates the point \f$ (x,y)\f$.
+    /*! creates the point \f$(x,y)\f$.
      */
     Point_2(const CoordNT& x, const CoordNT& y);
 
@@ -206,36 +201,34 @@ public:
     /// \name Access Functions
     /// @{
 
-    /*! returns the \f$ x\f$-coordinate.
+    /*! returns the \f$x\f$-coordinate.
      */
     CoordNT x() const;
 
-    /*! returns the \f$ y\f$-coordinate.
+    /*! returns the \f$y\f$-coordinate.
      */
     CoordNT y() const;
 
     /// @}
-
   }; /* end Arr_circle_segment_traits_2::Point_2 */
 
 
   /*! The `X_monotone_curve_2` class nested within the traits class can
-   * represent \f$ x\f$-monotone and line segments (which are always weakly
+   * represent \f$x\f$-monotone and line segments (which are always weakly
    * \f$x\f$-monotone).  The copy and default constructor as well as the
    * assignment operator are provided. In addition, an `operator<<` for the
    * curves is defined for standard output streams.
    */
   class X_monotone_curve_2 {
   public:
-
     /// \name Creation
     /// @{
 
     /*! constructs an curve corresponding to the line segment directed
      * from `source` to `target`, both having rational coordinates.
      */
-    X_monotone_curve_2 (const typename Kernel::Point_2& source,
+    X_monotone_curve_2(const typename Kernel::Point_2& source,
-                        const typename Kernel::Point_2& target);
+                       const typename Kernel::Point_2& target);
 
     /*! constructs an curve corresponding to the line segment supported by
      * the given line, directed from `source` to `target`.  Note that the two
@@ -254,7 +247,7 @@ public:
      *
      * \pre Both endpoints must lie on the given supporting circle.
      *
-     * \pre The circular arc is \f$ x\f$-monotone.
+     * \pre The circular arc is \f$x\f$-monotone.
      */
     X_monotone_curve_2(const typename Kernel::Circle_2& circ,
                        const Point_2& source, const Point_2& target,
@@ -275,7 +268,7 @@ public:
 
     /*! returns true if `xcv` is directed right, false otherwise.
      */
-    bool is_directed_right () const;
+    bool is_directed_right() const;
 
     /*! returns the left (lexicographically smaller) endpoint of `xcv`.
      */
@@ -292,11 +285,11 @@ public:
 
     /*! determines whether `xcv` is a line segment.
      */
-    bool is_linear () const;
+    bool is_linear() const;
 
     /*! determines whether `xcv` is a circular arc.
      */
-    bool is_circular () const;
+    bool is_circular() const;
 
     /*! returns the supporting line of `xcv`.
      *
@@ -315,7 +308,6 @@ public:
     Bbox_2 bbox() const;
 
     /// @}
-
   }; /* end Arr_circle_segment_traits_2::X_monotone_curve_2 */
 
   class Trim_2 {
@@ -323,16 +315,15 @@ public:
     /// \name Creation
     /// @{
 
-    /*! trims the given x-monotone curve to an from src to tgt.
+    /*! trims the given \f$x\f$-monotone curve to an from `src` to `tgt`.
      * \ pre `src` and `tgt` lies on the curve
      */
-
     X_monotone_curve_2(const X_monotone_curve_2& xcv,
                        const Point_2& src,
                        const Point_2& tgt) const
+
     /// @}
   } /* end Arr_circle_segment_traits_2::Trim_2 */
-
 }; /* end Arr_circle_segment_traits_2 */
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_circular_arc_traits_2.h

@@ -1,19 +1,14 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2TraitsClasses
-\ingroup PkgArrangementOnSurface2TraitsClasses
+ *
+ * This class is a traits class for \cgal arrangements, built on top of a model
+ * of concept `CircularKernel`.
+ * It provides curves of type `CGAL::Circular_arc_2<CircularKernel>`.
+ *
+ * \cgalModels{AosTraits_2}
+ */
+template <typename CircularKernel>
+class Arr_circular_arc_traits_2 {};
 
-This class is a traits class for \cgal arrangements, built on top of a model of
-concept `CircularKernel`.
-It provides curves of type `CGAL::Circular_arc_2<CircularKernel>`.
-
-\cgalModels{ArrangementTraits_2}
-
-*/
-template< typename CircularKernel >
-class Arr_circular_arc_traits_2 {
-public:
-
-}; /* end Arr_circular_arc_traits_2 */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_circular_line_arc_traits_2.h

@@ -1,23 +1,17 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2TraitsClasses
-\ingroup PkgArrangementOnSurface2TraitsClasses
+ *
+ * This class is a traits class for \cgal arrangements, built on top of a model
+ * of concept `CircularKernel`. It provides curves that can be of both types
+ * `CGAL::Line_arc_2<CircularKernel>` or `CGAL::Circular_arc_2<CircularKernel>`.
+ *
+ * It uses the
+ * <A HREF="https://www.boost.org/doc/html/variant.html">std::variant</A>.
+ *
+ * \cgalModels{AosTraits_2}
+ */
+template <typename CircularKernel>
+class Arr_circular_line_arc_traits_2 {};
 
-This class is a traits class for \cgal arrangements, built on top of a
-model of concept `CircularKernel`. It provides curves that can be
-of both types
-`CGAL::Line_arc_2<CircularKernel>` or
-`CGAL::Circular_arc_2<CircularKernel>`.
-
-It uses the <A HREF="https://www.boost.org/doc/html/variant.html">std::variant</A>.
-
-\cgalModels{ArrangementTraits_2}
-
-*/
-template< typename CircularKernel >
-class Arr_circular_line_arc_traits_2 {
-public:
-
-}; /* end Arr_circular_line_arc_traits_2 */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_conic_traits_2.h

@@ -2,7 +2,7 @@ namespace CGAL {
 
 /*! \ingroup PkgArrangementOnSurface2TraitsClasses
  *
- * The class `Arr_conic_traits_2` is a model of the `ArrangementTraits_2`
+ * The class `Arr_conic_traits_2` is a model of the `AosTraits_2`
  * concept and can be used to construct and maintain arrangements of bounded
  * segments of algebraic curves of degree \f$2\f$ at most, also known as
  * <I>conic curves</I>.
@@ -13,13 +13,13 @@ namespace CGAL {
  *
  * <UL>
 
- * <LI>If \f$4 r s - t^2 > 0\f$, \f$ C\f$ is an ellipse.  A special case occurs
+ * <LI>If \f$4 r s - t^2 > 0\f$, \f$C\f$ is an ellipse.  A special case occurs
- * when \f$r = s\f$ and \f$ t = 0\f$, when \f$ C\f$ becomes a circle.
+ * when \f$r = s\f$ and \f$t = 0\f$, when \f$C\f$ becomes a circle.
  *
- * <LI>If \f$4 r s - t^2 < 0\f$, \f$ C\f$ is a hyperbola.
+ * <LI>If \f$4 r s - t^2 < 0\f$, \f$C\f$ is a hyperbola.
  *
- * <LI>If \f$4 r s - t^2 = 0\f$, \f$ C\f$ is a parabola.  A degenerate case
+ * <LI>If \f$4 r s - t^2 = 0\f$, \f$C\f$ is a parabola.  A degenerate case
- * occurs when \f$r = s = t = 0\f$, when \f$ C\f$ is a line.
+ * occurs when \f$r = s = t = 0\f$, when \f$C\f$ is a line.
  *
  * </UL>
  *
@@ -27,15 +27,15 @@ namespace CGAL {
  *
  * <UL>
  *
- * <LI>A full ellipse (or a circle) \f$ C\f$.
+ * <LI>A full ellipse (or a circle) \f$C\f$.
  *
- * <LI>The tuple \f$ \langle C, p_s, p_t, o \rangle\f$, where \f$ C\f$ is the
+ * <LI>The tuple \f$\langle C, p_s, p_t, o \rangle\f$, where \f$C\f$ is the
- * supporting conic curve, with the arc endpoints being \f$ p_s\f$ and \f$
+ * supporting conic curve, with the arc endpoints being \f$p_s\f$ and
- * p_t\f$ (the source and target points, respectively). The orientation \f$ o\f$
+ * \f$p_t\f$ (the source and target points, respectively). The orientation
- * indicates whether we proceed from \f$ p_s\f$ to \f$ p_t\f$ in a clockwise or
+ * \f$o\f$ indicates whether we proceed from \f$p_s\f$ to \f$p_t\f$ in a
- * in a counterclockwise direction. Note that \f$ C\f$ may also correspond to a
+ * clockwise or in a counterclockwise direction. Note that \f$C\f$ may also
- * line or to pair of lines---in this case \f$ o\f$ may specify a `COLLINEAR`
+ * correspond to a line or to pair of lines---in this case \f$o\f$ may specify a
- * orientation.
+ * `COLLINEAR` orientation.
  *
  * </UL>
  *
@@ -54,7 +54,7 @@ namespace CGAL {
  * must be rational numbers. This guarantees that the coordinates of all
  * arrangement vertices (in particular, those representing intersection points)
  * are algebraic numbers of degree \f$4\f$ (a real number \f$\alpha\f$ is an
- * algebraic number of degree \f$d\f$ if there exist a polynomial \f$ p\f$ with
+ * algebraic number of degree \f$d\f$ if there exist a polynomial \f$p\f$ with
  * <I>integer</I> coefficient of degree \f$d\f$ such that \f$p(\alpha) = 0\f$).
  * We therefore require separate representations of the curve
  * coefficients and the point coordinates. The `NtTraits` should be substituted
@@ -75,34 +75,31 @@ namespace CGAL {
  * and defines a curve and \f$x\f$-monotone curve types, as detailed below.
  *
  * While the `Arr_conic_traits_2` models the concept
- * `ArrangementDirectionalXMonotoneTraits_2`, the implementation of
+ * `AosDirectionalXMonotoneTraits_2`, the implementation of
  * the `Are_mergeable_2` operation does not enforce the input curves
  * to have the same direction as a precondition. Moreover, `Arr_conic_traits_2`
  * supports the merging of curves of opposite directions.
  *
- * \cgalModels{ArrangementTraits_2,ArrangementLandmarkTraits_2,ArrangementDirectionalXMonotoneTraits_2}
+ * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosApproximateTraits_2,AosDirectionalXMonotoneTraits_2}
  *
  * \cgalHeading{Types}
  */
 template <typename RatKernel, typename AlgKernel, typename NtTraits>
 class Arr_conic_traits_2 {
 public:
-
   /// \name Types
   /// @{
 
-  /*! the `NtTraits::Rational` type (and also the `RatKernel::FT` type).
+  /// the `NtTraits::Rational` type (and also the `RatKernel::FT` type).
-   */
   typedef unspecified_type      Rational;
 
-  /*! the `NtTraits::Algebraic` type (and also the `AlgKernel::FT` type).
+  /// the `NtTraits::Algebraic` type (and also the `AlgKernel::FT` type).
-   */
   typedef unspecified_type      Algebraic;
 
   /// @}
 
   /*! The `Curve_2` class nested within the conic-arc traits can represent
-   * arbitrary conic arcs and support their construction in various ways.  The
+   * arbitrary conic arcs and support their construction in various ways. The
    * copy and default constructor as well as the assignment operator are
    * provided for conic arcs. In addition, an `operator<<` for the curves is
    * defined for standard output streams.
@@ -211,7 +208,6 @@ public:
     void set_target(const Point_2 & pt);
 
     /// @}
-
   }; /* end Arr_conic_traits_2::Curve_2 */
 
   /*! \class X_monotone_curve_2
@@ -227,7 +223,6 @@ public:
    */
   class X_monotone_curve_2 {
   public:
-
     /// \name Creation
     /// @{
 
@@ -249,7 +244,6 @@ public:
     const Point_2& right() const;
 
     /// @}
-
   }; /* end Arr_conic_traits_2::X_monotone_curve_2 */
 
   /*! The `Point_2` class nested within the conic-arc traits is
@@ -366,7 +360,8 @@ public:
      * respectively) is available, and their exact locations are given
      * implicitly, specified by the intersections of the supporting conic curve
      * with \f$r_1 x^2 + s_1 y^2 + t_1 x y + u_1 x + v_1 y + w_1 = 0\f$ and
-     * \f$r_2 x^2 + s_2 y^2 + t_2 x y + u_2 x + v_2 y + w_2 = 0\f$, respectively.
+     * \f$r_2 x^2 + s_2 y^2 + t_2 x y + u_2 x + v_2 y + w_2 = 0\f$,
+     * respectively.
      *
      * \pre The two auxiliary curves specifying the endpoints really intersect
      * with the supporting conic curve, such that the arc endpoints define a
@@ -407,11 +402,13 @@ public:
      * \pre `source` and `target` must not be the same.
      * \return A segment connecting `source` and `target`.
      */
-    X_monotone_curve_2 operator()(const Point_2& source, const Point_2& target) const;
+    X_monotone_curve_2 operator()(const Point_2& source,
+                                  const Point_2& target) const;
 
     /*! constructs a special segment of a given line connecting to given
      * endpoints.
-     * \param a, b, c The coefficients of the supporting line (\f$ax + by + c = 0\f$).
+     * \param a, b, c The coefficients of the supporting line
+     *        (\f$ax + by + c = 0\f$).
      * \param source The source point.
      * \param target The target point.
      * \pre `source` and `target` must not be the same.
@@ -419,7 +416,8 @@ public:
      */
     X_monotone_curve_2 operator()(const Algebraic& a, const Algebraic& b,
                                   const Algebraic& c,
-                                  const Point_2& source, const Point_2& target) const;
+                                  const Point_2& source,
+                                  const Point_2& target) const;
   };
 
   /*! \class Construct_bbox_2
@@ -440,56 +438,14 @@ public:
     Bbox_2 operator()(const X_monotone_curve_2& xcv) const { return bbox(xcv); }
   };
 
-  /*! \name Auxiliary Functor definitions, used gor, e.g., the landmarks
+  /*! \name Auxiliary Functor definitions, used for, e.g., the landmarks \
    * point-location strategy and the drawing function.
    */
-  //@{
+  /// @{
   typedef double                                        Approximate_number_type;
   typedef CGAL::Cartesian<Approximate_number_type>      Approximate_kernel;
   typedef Approximate_kernel::Point_2                   Approximate_point_2;
-
+  /// @}
-  /*! \class Approximate_2
-   * A functor that approximates a point and an \f$x\f$-monotone curve.
-   */
-  class Approximate_2 {
-  public:
-    /*! obtains an approximation of a point coordinate.
-     * \param p The exact point.
-     * \param i The coordinate index (either 0 or 1).
-     * \pre `i` is either 0 or 1.
-     * \return An approximation of p's \f$x\f$-coordinate (if `i` == 0), or an
-     *         approximation of p's \f$y\f$-coordinate (if `i` == 1).
-     */
-    Approximate_number_type operator()(const Point_2& p, int i) const;
-
-    /*! obtains an approximation of a point.
-     * \param p The exact point.
-     */
-    Approximate_point_2 operator()(const Point_2& p) const;
-
-    /*! approximates a given \f$x\f$-monotone curve. It computes a sequence of
-     * approximate points that represent an approximate polyline, and inserts
-     * them into an output container given through an output iterator.  The
-     * first and last points in the sequence are always approximations of the
-     * endpoints of the given arc.
-     *
-     * \param oi An output iterator for the output container.
-     * \param error The error bound of the polyline approximation. This is the
-     *        Hausdorff distance between the arc and the polyline that
-     *        approximates the arc.
-     * \param xcv The exact \f$x\f$-monotone arc.
-     * \param l2r A Boolean flag that indicates whether the arc direction is
-     *        left to right.
-     * \return The past-the-end iterator of the output container.
-     *
-     * \pre Dereferencing `oi` must yield an object of type
-     *      `Arr_conic_traits_2::Approximate_point_2`.
-     */
-    template <typename OutputIterator>
-    OutputIterator operator()(OutputIterator oi, double error,
-                              const X_monotone_curve_2& xcv,
-                              bool l2r = true) const;
-  };
 
   /*! \class Trim_2
    * A functor that trims a conic arc.
@@ -522,11 +478,7 @@ public:
   /*! obtains a `Trim_2` functor. */
   Trim_2 trim_2_object() const;
 
-  /*! obtains an `Approximate_2` functor. */
-  Approximate_2 approximate_2_object() const;
-
   /// @}
-
 }; /* end Arr_conic_traits_2 */
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_consolidated_curve_data_traits_2.h

@@ -1,10 +1,9 @@
-
 namespace CGAL {
 
 /*! \ingroup PkgArrangementOnSurface2TraitsClasses
  *
  * The class `Arr_consolidated_curve_data_traits_2` is a model of the concept
- * `ArrangementTraits_2`, and serves as a decorator class that enables the
+ * `AosTraits_2`, and serves as a decorator class that enables the
  * extension of the curve type defined by the `Traits` parameter. The traits
  * class inherits its point type from `Traits::Point_2`, and defines the types
  * `Curve_2` and `X_monotone_curve_2` extended with extraneous data fields of
@@ -12,24 +11,21 @@ namespace CGAL {
  *
  * Each `Curve_2` object is associated with a single data field of type `Data`,
  * and each `X_monotone_curve_2` object is associated with a set of unique data
- * objects. When a curve is subdivided into \f$ x\f$-monotone subcurves, all
+ * objects. When a curve is subdivided into \f$x\f$-monotone subcurves, all
  * resulting subcurves are associated with a list containing a single data
- * object, copied from the inducing curve. When an \f$ x\f$-monotone curve is
+ * object, copied from the inducing curve. When an \f$x\f$-monotone curve is
  * split, its data set is duplicated, and inserted into the sets of both
- * resulting subcurves. In case two (or more) \f$ x\f$-monotone curves overlap,
+ * resulting subcurves. In case two (or more) \f$x\f$-monotone curves overlap,
- * their data sets are consolidated, and are inserted into the set of the \f$
+ * their data sets are consolidated, and are inserted into the set of the
- * x\f$-monotone curve that represents the overlap.
+ * \f$x\f$-monotone curve that represents the overlap.
  *
- * \cgalModels{ArrangementTraits_2}
+ * \cgalModels{AosTraits_2}
  */
 template <typename Traits, typename Data>
-class Arr_consolidated_curve_data_traits_2
+class Arr_consolidated_curve_data_traits_2 :
-  : public Arr_curve_data_traits_2<Traits, _Unique_list<Data>,
+    public Arr_curve_data_traits_2<Traits, _Unique_list<Data>,
-                                   _Consolidate_unique_lists<Data>,
+                                   _Consolidate_unique_lists<Data>, Data> {
-                                   Data>
-{
 public:
-
   /// \name Types
   /// @{
 
@@ -39,10 +35,10 @@ public:
   //! the base curve.
   typedef typename Base_traits_2::Curve_2 Base_curve_2;
 
-  //! the base \f$ x\f$-monotone curve curve.
+  //! the base \f$x\f$-monotone curve curve.
   typedef typename Base_traits_2::X_monotone_curve_2 Base_x_monotone_curve_2;
 
-  //! a set of data objects that is associated with an \f$ x\f$-monotone curve.
+  //! a set of data objects that is associated with an \f$x\f$-monotone curve.
   typedef unspecified_type typedef Data_container;
 
   //! a non-mutable iterator for the data objects in the data container.
@@ -59,14 +55,15 @@ public:
    */
   class Data_container {
   public:
-
     /// \name Creation
     /// @{
 
-    /*! constructs default */
+    /*! constructs default.
+     */
     Data_container();
 
-    /*! constructs set containing a single `data` object. */
+    /*! constructs set containing a single `data` object.
+     */
     Data_container(const Data& data);
 
     /// @}
@@ -74,22 +71,27 @@ public:
     /// \name Access Functions
     /// @{
 
-    /*! returns the number of data objects in the set. */
+    /*! returns the number of data objects in the set.
+     */
     std::size_t size() const;
 
-    /*! returns an iterator pointing to the first data object. */
+    /*! returns an iterator pointing to the first data object.
+     */
     Data_iterator begin() const;
 
-    /*! returns a past-the-end iterator for the data objects. */
+    /*! returns a past-the-end iterator for the data objects.
+     */
     Data_iterator end() const;
 
     /*! returns the first data object inserted into the set.
-     * \pre The number of data objects is not \f$ 0\f$.
+     *
+     * \pre The number of data objects is not \f$0\f$.
      */
     const Data& front() const;
 
     /*! returns the last data object inserted into the set.
-     *  \pre The number of data objects is not \f$ 0\f$.
+     *
+     *  \pre The number of data objects is not \f$0\f$.
      */
     const Data& back() const;
 
@@ -123,13 +125,12 @@ public:
      */
     bool erase(const Data& data);
 
-    /*! clears the set. */
+    /*! clears the set.
+     */
     void clear();
 
     /// @}
-
   }; /* end Arr_consolidated_curve_data_traits_2::Data_container */
-
 }; /* end Arr_consolidated_curve_data_traits_2 */
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_curve_data_traits_2.h

@@ -2,10 +2,10 @@ namespace CGAL {
 
 /*! \ingroup PkgArrangementOnSurface2TraitsClasses
  *
- * The class `Arr_curve_data_traits_2` is a model of the `ArrangementTraits_2`
+ * The class `Arr_curve_data_traits_2` is a model of the `AosTraits_2`
  * concept and serves as a decorator class that allows the extension of the
- * curves defined by the base traits-class (the `Tr` parameter), which serves as
+ * curves defined by the base traits-class (the `Tr` parameter), which serves
- * a geometric traits-class (a model of the `ArrangementTraits_2` concept), with
+ * as a geometric traits-class (a model of the `AosTraits_2` concept), with
  * extraneous (non-geometric) data fields.
  *
  * The traits class inherits its point type from `Traits::Point_2`, and defines
@@ -13,7 +13,7 @@ namespace CGAL {
  *
  * Each `Curve_2` object is associated with a single data field of type `CData`,
  * and each `X_monotone_curve_2` object is associated with a single data field
- * of type `XData`. When a curve is subdivided into \f$ x\f$-monotone subcurves,
+ * of type `XData`. When a curve is subdivided into \f$x\f$-monotone subcurves,
  * its data field is converted using the conversion functor, which is specified
  * by the `Cnv` template-parameter, and the resulting objects is copied to all
  * `X_monotone_curve_2` objects induced by this curve. The conversion functor
@@ -24,21 +24,18 @@ namespace CGAL {
  * By default, the two data types are the same, so the conversion operator
  * is trivial:
  *
- * <TABLE><TR><TD>
+ * <TABLE>
- * `CData` =
+ * <TR>
- * </TD>
+ * <TD>`CData` = </TD>
- * <TD>
+ * <TD>`XData`</TD>
- * `XData`
+ * </TR>
- * </TD></TR>
+ * <TR>
- * <TR><TD>
+ * <TD>`Cnv` =</TD>
- * `Cnv` =
+ * <TD>`_Default_convert_functor<CData,XData>`</TD>
- * </TD>
+ * </TR>
- * <TD>
- * `_Default_convert_functor<CData,XData>`
- * </TD></TR>
  * </TABLE>
  *
- * In case two (or more) \f$ x\f$-monotone curves overlap, their data fields are
+ * In case two (or more) \f$x\f$-monotone curves overlap, their data fields are
  * merged to a single field, using the merge functor functor, which is specified
  * by the `Mrg` template-parameter. This functor should provide an operator with
  * the following prototype:
@@ -46,48 +43,39 @@ namespace CGAL {
  * `XData operator() (const XData& d1, const XData& d2) const;`
  *
  * which returns a single data object that represents the merged data field of
- * `d1` and `d2`. The \f$ x\f$-monotone curve that represents the overlap is
+ * `d1` and `d2`. The \f$x\f$-monotone curve that represents the overlap is
  * associated with the output of this functor.
  *
- * \cgalModels{ArrangementTraits_2}
+ * \cgalModels{AosTraits_2}
  */
 template <typename Tr, typename XData, typename Mrg, typename CData, typename Cnv>
 class Arr_curve_data_traits_2 : public Tr {
 public:
-
   /// \name Types
   /// @{
 
-  /*! the base traits-class.
+  /// the base traits-class.
-   */
   typedef Tr                                            Base_traits_2;
 
-  /*! the base curve.
+  /// the base curve.
-   */
   typedef typename Base_traits_2::Curve_2               Base_curve_2;
 
-  /*! the base \f$ x\f$-monotone curve curve.
+  /// the base \f$x\f$-monotone curve curve.
-   */
   typedef typename Base_traits_2::X_monotone_curve_2    Base_x_monotone_curve_2;
 
-  /*! the point type.
+  /// the point type.
-   */
   typedef typename Base_traits_2::Point_2               Point_2;
 
-  /*! the merge functor.
+  /// the merge functor.
-   */
   typedef Mrg                                           Merge;
 
-  /*! the conversion functor.
+  /// the conversion functor.
-   */
   typedef Cnv                                           Convert;
 
-  /*! the type of data associated with curves.
+  /// the type of data associated with curves.
-   */
   typedef CData                                         Curve_data;
 
-  /*! the type of data associated with \f$ x\f$-monotone curves.
+  /// the type of data associated with \f$x\f$-monotone curves.
-   */
   typedef XData                                         X_monotone_curve_data;
 
   /// @}
@@ -97,7 +85,6 @@ public:
    */
   class Curve_2 : public Base_curve_2 {
   public:
-
     /// \name Creation
     /// @{
 
@@ -129,7 +116,6 @@ public:
     void set_data(const Curve_data& data);
 
     /// @}
-
   }; /* end Arr_curve_data_traits_2::Curve_2 */
 
   /*! The `X_monotone_curve_2` class nested within the curve-data traits extends
@@ -137,20 +123,19 @@ public:
    */
   class X_monotone_curve_2 : public Base_x_monotone_curve_2 {
   public:
-
     /// \name Creation
     /// @{
 
     /*! constructs default */
     X_monotone_curve_2();
 
-    /*! constructs an \f$ x\f$-monotone curve from the given `base` curve with
+    /*! constructs an \f$x\f$-monotone curve from the given `base` curve with
      * uninitialized data field.
      */
     X_monotone_curve_2(const Base_x_monotone_curve_2& base);
 
-    /*! constructs an \f$ x\f$-monotone curve from the given `base` \f$
+    /*! constructs an \f$x\f$-monotone curve from the given `base`
-     * x\f$-monotone curve with an attached `data` field.
+     * \f$x\f$-monotone curve with an attached `data` field.
      */
     X_monotone_curve_2(const Base_x_monotone_curve_2& base,
                        const X_monotone_curve_data& data);
@@ -170,9 +155,7 @@ public:
     void set_data(const X_monotone_curve_data& data);
 
     /// @}
-
   }; /* end Arr_curve_data_traits_2::X_monotone_curve_2 */
-
 }; /* end Arr_curve_data_traits_2 */
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_dcel.h

@@ -7,8 +7,8 @@ namespace CGAL {
  * class templates and other templates.  It is parameterized by a geometry
  * traits type and optionally by a vertex, halfedge, or face types. By default,
  * the `Arr_dcel` class template uses the \link
- * ArrangementBasicTraits_2::Point_2 `Point_2`\endlink and \link
+ * AosBasicTraits_2::Point_2 `Point_2`\endlink and \link
- * ArrangementBasicTraits_2::X_monotone_curve_2 `X_monotone_curve_2`\endlink
+ * AosBasicTraits_2::X_monotone_curve_2 `X_monotone_curve_2`\endlink
  * types nested in the traits type to instantiate the vertex and base halfedge
  * types, respectively. Thus, by default the \dcel only stores the topological
  * incidence relations and the geometric data attached to vertices and
@@ -16,15 +16,15 @@ namespace CGAL {
  * overridden. Notice that if the vertex and halfedge types are overridden, the
  * traits type is ignored.
  *
- * \cgalModels{ArrangementDcelWithRebind}
+ * \cgalModels{AosDcelWithRebind}
  *
  * \tparam Traits a geometry traits type, which is a model of the
- *                `ArrangementBasicTraits_2` concept.
+ *                `AosBasicTraits_2` concept.
- * \tparam V the vertex type, which is a model of the `ArrangementDcelVertex`
+ * \tparam V the vertex type, which is a model of the `AosDcelVertex`
  *           concept.
  * \tparam H the halfedge type, which is a model of the
- *            `ArrangementDcelHalfedge` concept.
+ *            `AosDcelHalfedge` concept.
- * \tparam F the face type, which is a model of the `ArrangementDcelFace`
+ * \tparam F the face type, which is a model of the `AosDcelFace`
  *           concept.
  *
  * \sa `Arr_dcel_base<V, H, F>`
@@ -33,7 +33,6 @@ template <typename Traits,
           typename V = Arr_vertex_base<typename Traits::Point_2>,
           typename H = Arr_halfedge_base<typename Traits::X_monotone_curve_2>,
           typename F = Arr_face_base>
-class Arr_dcel : public Arr_dcel_base<V, H, F> {
+class Arr_dcel : public Arr_dcel_base<V, H, F> {};
-};
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_dcel_base.h

@@ -1,71 +1,46 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2DCEL
-\ingroup PkgArrangementOnSurface2DCEL
+ *
-
+ * \anchor arr_refarr_dcel_base
-\anchor arr_refarr_dcel_base
+ *
-
+ * The `Arr_dcel_base` class is an important ingredient in the definition of
-The `Arr_dcel_base` class is an important ingredient in the
+ * \dcel data structures. It serves as a basis class for any instance of the
-definition of \dcel data structures. It serves as a basis class for
+ * `Dcel` template parameter of the `Arrangement_2` template. In particular it
-any instance of the `Dcel` template parameter of the
+ * is the basis class of the default `Dcel` template parameter, and the basis
-`Arrangement_2` template. In particular it is the basis class of
+ * class of any extended \dcel. The template parameters `V`, `H`, and `F` must
-the default `Dcel` template parameter, and the basis class of any
+ * be instantiated with models of the concepts `AosVertex`, `AosHalfedge`, and
-extended \dcel. The template parameters `V`, `H`, and `F`
+ * `AosFace` respectively.
-must be instantiated with models of the concepts
+ *
-`ArrangementDcelVertex`, `ArrangementDcelHalfedge`,
+ * \cgalModels{Aos}
-and `ArrangementDcelFace` respectively.
+ */
-
+template <typename V, typename H, typename F>
-\cgalModels{ArrangementDcel}
-
-*/
-template< typename V, typename H, typename F >
 class Arr_dcel_base {
 public:
+  /*! The basic \dcel face type. Serves as a basis class for an extended
+   * face record with auxiliary data fields.
+   *
+   * \cgalModels{AosFace}
+   */
+  class Arr_face_base {};
 
+  /*! The basic \dcel halfedge type. Serves as a basis class for an extended
+   * halfedge record with auxiliary data fields. The `Curve` parameter is the
+   * type of \f$x\f$-monotone curves associated with the vertices.
+   *
+   * \cgalModels{AosHalfedge}
+   */
+  template <typename Curve>
+  class Arr_halfedge_base {};
 
-/*!
+  /*! The basic \dcel vertex type. Serves as a basis class for an extended
-
+   * vertex record with auxiliary data fields. The `Point` parameter is the
-The basic \dcel face type. Serves as a basis class for an extended
+   * type of points associated with the vertices.
-face record with auxiliary data fields.
+   *
-
+   * \cgalModels{AosVertex}
-\cgalModels{ArrangementDcelFace}
+   */
-
+  template <typename Point>
-*/
+  class Arr_vertex_base {};
-class Arr_face_base {
-
-}; /* end Arr_dcel_base::Arr_face_base */
-
-/*!
-
-
-The basic \dcel halfedge type. Serves as a basis class for an
-extended halfedge record with auxiliary data fields. The `Curve`
-parameter is the type of \f$ x\f$-monotone curves associated with the vertices.
-
-\cgalModels{ArrangementDcelHalfedge}
-
-*/
-template< typename Curve >
-class Arr_halfedge_base {
-
-}; /* end Arr_dcel_base::Arr_halfedge_base */
-
-/*!
-
-
-The basic \dcel vertex type. Serves as a basis class for an extended
-vertex record with auxiliary data fields. The `Point` parameter is
-the type of points associated with the vertices.
-
-\cgalModels{ArrangementDcelVertex}
-
-*/
-template< typename Point >
-class Arr_vertex_base {
-
-}; /* end Arr_dcel_base::Arr_vertex_base */
-
-
 }; /* end Arr_dcel_base */
+
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_default_dcel.h

@@ -5,17 +5,17 @@ namespace CGAL {
  * The default \dcel class used by the `Arrangement_2`,
  * `Arr_bounded_planar_topology_traits_2`, `Arr_unb_planar_topology_traits_2`
  * class templates and other templates.  It is parameterized by a geometry
- * traits type. It uses the \link ArrangementBasicTraits_2::Point_2
+ * traits type. It uses the \link AosBasicTraits_2::Point_2
- * `Point_2`\endlink and \link ArrangementBasicTraits_2::X_monotone_curve_2
+ * `Point_2`\endlink and \link AosBasicTraits_2::X_monotone_curve_2
  * `X_monotone_curve_2`\endlink types nested in the traits type to instantiate
  * the vertex and base halfedge types, respectively. Thus, by default the \dcel
  * only stores the topological incidence relations and the geometric data
  * attached to vertices and edges.
  *
- * \cgalModels{ArrangementDcelWithRebind}
+ * \cgalModels{AosDcelWithRebind}
  *
  * \tparam Traits a geometry traits type, which is a model of the
- *                `ArrangementBasicTraits_2` concept.
+ *                `AosBasicTraits_2` concept.
  *
  * \sa `Arr_dcel<Traits, V, H, F>`
  * \sa `Arr_dcel_base<V, H, F>`

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_default_overlay_traits.h

@@ -1,57 +1,45 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2TraitsClasses
-\ingroup PkgArrangementOnSurface2TraitsClasses
+ * \ingroup PkgArrangementOnSurface2Overlay
-\ingroup PkgArrangementOnSurface2Overlay
+ *
+ * An instance of `Arr_default_overlay_traits` should be used for overlaying two
+ * arrangements of type `Arrangement` that store no auxiliary data with their
+ * \dcel records, where the resulting overlaid arrangement stores no auxiliary
+ * \dcel data as well. This class simply gives empty implementation for all
+ * traits-class functions.
+ *
+ * \cgalModels{OverlayTraits}
+ *
+ * \sa `overlay`
+ */
+template <typename Arrangement>
+class Arr_default_overlay_traits {};
 
-An instance of `Arr_default_overlay_traits` should be used for overlaying two arrangements
+/*! \ingroup PkgArrangementOnSurface2TraitsClasses
-of type `Arrangement` that store no auxiliary data with their \dcel records, where the resulting overlaid arrangement stores no auxiliary
+ * \ingroup PkgArrangementOnSurface2Overlay
-\dcel data as well. This class simply gives empty implementation for all
+ *
-traits-class functions.
+ * An instance of `Arr_face_overlay_traits` should be used for overlaying two
+ * arrangements of types `Arr_A` and `Arr_B`, which are instantiated using the
+ * same geometric traits-class and with the \dcel classes `Dcel_A` and `Dcel_B`
+ * respectively, in order to store their overlay in an arrangement of type
+ * `Arr_R`, which is instantiated using a third \dcel class `Dcel_R`. All three
+ * \dcel classes are assumed to be instantiations of the
+ * `Arr_face_extended_dcel` template with types `FaceData_A`, `FaceData_B` and
+ * `FaceData_R`, respectively.
+ *
+ * This class gives empty implementation for all overlay traits-class functions,
+ * except the function that computes the overlay of two faces. In this case, it
+ * uses the functor `OvlFaceData`, which accepts a `FaceData_A` object and a
+ * `FaceData_B` object and computes a corresponding `FaceData_R` object, in
+ * order to set the auxiliary data of the overlay face.
+ *
+ * \cgalModels{OverlayTraits}
+ *
+ * \sa `overlay`
+ * \sa `CGAL::Arr_face_extended_dcel<Traits,FData,V,H,F>`
+ */
+template <typename Arr_A, typename Arr_B, typename Arr_R, typename OvlFaceData>
+class Arr_face_overlay_traits {};
 
-\cgalModels{OverlayTraits}
-
-\sa `overlay`
-
-*/
-template< typename Arrangement >
-class Arr_default_overlay_traits {
-public:
-
-}; /* end Arr_default_overlay_traits */
-} /* end namespace CGAL */
-
-namespace CGAL {
-
-/*!
-\ingroup PkgArrangementOnSurface2TraitsClasses
-\ingroup PkgArrangementOnSurface2Overlay
-
-An instance of `Arr_face_overlay_traits` should be used for overlaying two arrangements
-of types `Arr_A` and `Arr_B`, which are instantiated using the same
-geometric traits-class and with the \dcel classes `Dcel_A` and
-`Dcel_B` respectively, in order to store their overlay in an arrangement
-of type `Arr_R`, which is instantiated using a third \dcel class
-`Dcel_R`. All three \dcel classes are assumed to be instantiations of the
-`Arr_face_extended_dcel` template with types `FaceData_A`,
-`FaceData_B` and `FaceData_R`, respectively.
-
-This class gives empty implementation for all overlay traits-class functions,
-except the function that computes the overlay of two faces. In this case,
-it uses the functor `OvlFaceData`, which accepts a `FaceData_A` object
-and a `FaceData_B` object and computes a corresponding `FaceData_R`
-object, in order to set the auxiliary data of the overlay face.
-
-\cgalModels{OverlayTraits}
-
-\sa `overlay`
-\sa `CGAL::Arr_face_extended_dcel<Traits,FData,V,H,F>`
-
-*/
-template< typename Arr_A, typename Arr_B, typename Arr_R, typename OvlFaceData >
-class Arr_face_overlay_traits {
-public:
-
-}; /* end Arr_face_overlay_traits */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_enums.h

@@ -6,7 +6,7 @@ namespace CGAL {
  * \f$x\f$-monotone curve. It is used by models geometry traits concept that
  * handle boundary conditions.
  *
- * \sa `ArrangementOpenBoundaryTraits_2`
+ * \sa `AosOpenBoundaryTraits_2`
  */
 enum Arr_curve_end { ARR_MIN_END, ARR_MAX_END };
 

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_extended_dcel.h

@@ -1,246 +1,208 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2DCEL
-\ingroup PkgArrangementOnSurface2DCEL
+ *
+ * The `Arr_extended_dcel` class-template extends the topological-features of
+ * the \dcel namely the vertex, halfedge, and face types. While it is possible
+ * to maintain extra (non-geometric) data with the curves or points of the
+ * arrangement by extending their types respectively, it is also possible to
+ * extend the vertex, halfedge, or face types of the \dcel through
+ * inheritance. As the technique to extend these types is somewhat cumbersome
+ * and difficult for inexperienced users, the `Arr_extended_dcel` class-template
+ * provides a convenient way to do that.  Each one of the three features is
+ * extended with a corresponding data type provided as parameters. This class
+ * template is also parameterized with a traits class used to extract default
+ * values for the vertex, halfedge, and face base classes, which are the
+ * remaining three template parameters respectively.  The default values follow:
+ *
+ * <TABLE><TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ *
+ * `V` =
+ * <TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ * `Arr_vertex_base<typename Traits::Point_2>`
+ * <TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ * `H` =
+ * <TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ * `Arr_halfedge_base<typename Traits::X_monotone_curve_2>`
+ * <TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ * `F` =
+ * <TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ * `Arr_face_base`
+ *
+ * </TABLE>
+ *
+ * \cgalModels{AosDcelWithRebind}
+ *
+ * \sa `Arr_dcel_base<V,H,F>`
+ */
+template <typename Traits, typename VData, typename HData, typename FData,
+          typename V, typename H, typename F>
+class Arr_extended_dcel : public Arr_dcel_base<Arr_extended_vertex<V, VData>,
+                                               Arr_extended_halfedge<H, HData>,
+                                               Arr_extended_face<F, FData>>
+{};
 
-The `Arr_extended_dcel` class-template extends the topological-features of the \dcel
+/*! \ingroup PkgArrangementOnSurface2DCEL
-namely the vertex, halfedge, and face types. While it is possible to maintain
+ *
-extra (non-geometric) data with the curves or points of the arrangement by
+ * The `Arr_extended_face` class-template extends the face topological-features
-extending their types respectively, it is also possible to extend the vertex,
+ * of the \dcel. It is parameterized by a face base-type `FaceBase` and a data
-halfedge, or face types of the \dcel through inheritance. As the technique to
+ * type `FData` used to extend the face base-type.
-extend these types is somewhat cumbersome and difficult for inexperienced
+ *
-users, the `Arr_extended_dcel` class-template provides a convenient way to do that.
+ * \cgalModels{AosDcelFace}
-Each one of the three features is extended with a corresponding data type
+ *
-provided as parameters. This class template is also parameterized with a
+ * \sa `Arr_dcel_base<V,H,F>`
-traits class used to extract default values for the vertex, halfedge, and face
+ */
-base classes, which are the remaining three template parameters respectively.
+template <typename FaceBase, typename FData>
-The default values follow:
-
-<TABLE><TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-
-`V` =
-<TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-`Arr_vertex_base<typename Traits::Point_2>`
-<TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-`H` =
-<TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-`Arr_halfedge_base<typename Traits::X_monotone_curve_2>`
-<TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-`F` =
-<TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-`Arr_face_base`
-
-</TABLE>
-
-\cgalModels{ArrangementDcelWithRebind}
-
-\sa `Arr_dcel_base<V,H,F>`
-
-*/
-template< typename Traits, typename VData, typename HData, typename FData, typename V, typename H, typename F >
-class Arr_extended_dcel
-  : public Arr_dcel_base<Arr_extended_vertex<V, VData>,
-                         Arr_extended_halfedge<H, HData>,
-                         Arr_extended_face<F, FData> >
-{
-
-}; /* end Arr_extended_dcel */
-} /* end namespace CGAL */
-
-namespace CGAL {
-
-/*!
-\ingroup PkgArrangementOnSurface2DCEL
-
-The `Arr_extended_face` class-template extends the face topological-features of the
-\dcel. It is parameterized by a face base-type `FaceBase` and a data type
-`FData` used to extend the face base-type.
-
-\cgalModels{ArrangementDcelFace}
-
-\sa `Arr_dcel_base<V,H,F>`
-
-*/
-template< typename FaceBase, typename FData >
 class Arr_extended_face : FaceBase {
 public:
+  /// \name Creation
+  /// @{
 
-/// \name Creation
+  /*! assigns `f` with the contents of the `other` vertex.
-/// @{
+   */
+  void assign(const Self & other);
 
-/*!
+  /// @}
-assigns `f` with the contents of the `other` vertex.
-*/
-void assign (const Self & other);
 
-/// @}
+  /// \name Access Functions
+  /// @{
 
-/// \name Access Functions
+  /*! obtains the auxiliary data (a non-const version, returning a reference
-/// @{
+   * to a mutable data object is also available).
+   */
+  const FData & data() const;
 
-/*!
+  /// @}
-obtains the auxiliary data (a non-const version, returning a reference
-to a mutable data object is also available).
-*/
-const FData & data () const;
 
-/// @}
+  /// \name Modifiers
+  /// @{
 
-/// \name Modifiers
+  /*! sets the auxiliary data.
-/// @{
+   */
-
+  void set_data(const FData & data);
-/*!
-sets the auxiliary data.
-*/
-void set_data (const FData & data);
-
-/// @}
 
+  /// @}
 }; /* end Arr_extended_face */
-} /* end namespace CGAL */
 
-namespace CGAL {
+/*! \ingroup PkgArrangementOnSurface2DCEL
-
+ *
-/*!
+ * The `Arr_extended_halfedge` class-template extends the halfedge
-\ingroup PkgArrangementOnSurface2DCEL
+ * topological-features of the \dcel. It is parameterized by a halfedge
-
+ * base-type `HalfedgeBase` and a data type `HData` used to extend the halfedge
-The `Arr_extended_halfedge` class-template extends the halfedge topological-features of
+ * base-type.
-the \dcel. It is parameterized by a halfedge base-type `HalfedgeBase`
+ *
-and a data type `HData` used to extend the halfedge base-type.
+ * \cgalModels{AosDcelHalfedge}
-
+ *
-\cgalModels{ArrangementDcelHalfedge}
+ * \sa `Arr_dcel_base<V,H,F>`
-
+ */
-\sa `Arr_dcel_base<V,H,F>`
+template <typename HalfedgeBase, typename HData>
-
-*/
-template< typename HalfedgeBase, typename HData >
 class Arr_extended_halfedge : public HalfedgeBase {
 public:
+  /// \name Creation
+  /// @{
 
-/// \name Creation
+  /*! assigns `he` with the contents of the `other` vertex.
-/// @{
+   */
+  void assign(const Self & other);
 
-/*!
+  /// @}
-assigns `he` with the contents of the `other` vertex.
-*/
-void assign (const Self & other);
 
-/// @}
+  /// \name Access Functions
+  /// @{
 
-/// \name Access Functions
+  /*! obtains the auxiliary data (a non-const version, returning a reference
-/// @{
+   * to a mutable data object is also available).
+   */
+  const HData & data() const;
 
-/*!
+  /// @}
-obtains the auxiliary data (a non-const version, returning a reference
-to a mutable data object is also available).
-*/
-const HData & data () const;
 
-/// @}
+  /// \name Modifiers
+  /// @{
 
-/// \name Modifiers
+  /*! sets the auxiliary data.
-/// @{
+   */
-
+  void set_data(const HData & data);
-/*!
-sets the auxiliary data.
-*/
-void set_data (const HData & data);
-
-/// @}
 
+  /// @}
 }; /* end Arr_extended_halfedge */
-} /* end namespace CGAL */
 
-namespace CGAL {
+/*! \ingroup PkgArrangementOnSurface2DCEL
-
+ *
-/*!
+ * The `Arr_extended_vertex` class-template extends the vertex
-\ingroup PkgArrangementOnSurface2DCEL
+ * topological-features of the \dcel. It is parameterized by a
-
+ * vertex base-type `VertexBase` and a data type `VData` used to extend
-The `Arr_extended_vertex` class-template extends the vertex
+ * the vertex base-type.
-topological-features of the \dcel. It is parameterized by a
+ *
-vertex base-type `VertexBase` and a data type `VData` used to extend
+ * \cgalModels{AosDcelVertex}
-the vertex base-type.
+ *
-
+ * \sa `Arr_dcel_base<V,H,F>`
-\cgalModels{ArrangementDcelVertex}
+ */
-
+template <typename VertexBase, typename VData>
-\sa `Arr_dcel_base<V,H,F>`
-
-*/
-template< typename VertexBase, typename VData >
 class Arr_extended_vertex : public VertexBase {
 public:
+  /// \name Creation
+  /// @{
 
-/// \name Creation
+  /*! assigns `v` with the contents of the `other` vertex.
-/// @{
+   */
+  void assign(const Self & other);
 
-/*!
+  /// @}
-assigns `v` with the contents of the `other` vertex.
-*/
-void assign (const Self & other);
 
-/// @}
+  /// \name Access Functions
+  /// @{
 
-/// \name Access Functions
+  /*! obtains the auxiliary data (a non-const version, returning a reference
-/// @{
+   * to a mutable data object is also available).
+   */
+  const VData & data() const;
 
-/*!
+  /// @}
-obtains the auxiliary data (a non-const version, returning a reference
-to a mutable data object is also available).
-*/
-const VData & data () const;
 
-/// @}
+  /// \name Modifiers
+  /// @{
 
-/// \name Modifiers
+  /*! sets the auxiliary data.
-/// @{
+   */
-
+  void set_data(const VData & data);
-/*!
-sets the auxiliary data.
-*/
-void set_data (const VData & data);
-
-/// @}
 
+  /// @}
 }; /* end Arr_extended_vertex */
-} /* end namespace CGAL */
+
-
+/*! \ingroup PkgArrangementOnSurface2DCEL
-namespace CGAL {
+ *
-
+ * The `Arr_face_extended_dcel` class-template extends the \dcel face-records,
-/*!
+ * making it possible to store extra (non-geometric) data with the arrangement
-\ingroup PkgArrangementOnSurface2DCEL
+ * faces.  The class should be instantiated by an `FData` type which represents
-
+ * the extra data stored with each face.
-The `Arr_face_extended_dcel` class-template extends the \dcel face-records, making it
+ *
-possible to store extra (non-geometric) data with the arrangement faces.
+ * Note that all types of \dcel features (namely vertex, halfedge and face)
-The class should be instantiated by an `FData` type which represents the
+ * are provided as template parameters. However, by default they are defined
-extra data stored with each face.
+ * as follows:
-
+ *
-Note that all types of \dcel features (namely vertex, halfedge and face)
+ * <TABLE><TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-are provided as template parameters. However, by default they are defined
+ *
-as follows:
+ * `V` =
-
+ * <TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-<TABLE><TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ * `Arr_vertex_base<typename Traits::Point_2>`
-
+ * <TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-`V` =
+ * `H` =
-<TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ * <TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-`Arr_vertex_base<typename Traits::Point_2>`
+ * `Arr_halfedge_base<typename Traits::X_monotone_curve_2>`
-<TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ * <TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-`H` =
+ * `F` =
-<TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ * <TD ALIGN=LEFT VALIGN=TOP NOWRAP>
-`Arr_halfedge_base<typename Traits::X_monotone_curve_2>`
+ * `Arr_face_base`
-<TR><TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ *
-`F` =
+ * </TABLE>
-<TD ALIGN=LEFT VALIGN=TOP NOWRAP>
+ *
-`Arr_face_base`
+ * \cgalModels{AosDcelWithRebind}
-
+ *
-</TABLE>
+ * \sa `Arr_dcel_base<V,H,F>`
-
+ */
-\cgalModels{ArrangementDcelWithRebind}
+template <typename Traits, typename FData, typename V, typename H, typename F>
-
+class Arr_face_extended_dcel :
-\sa `Arr_dcel_base<V,H,F>`
+    public Arr_dcel_base<V, H, Arr_extended_face<F, FData>> {};
-
+
-*/
-template< typename Traits, typename FData, typename V, typename H, typename F >
-class Arr_face_extended_dcel : public Arr_dcel_base<V, H, Arr_extended_face<F, FData> > {
-}; /* end Arr_face_extended_dcel */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_face_index_map.h

@@ -1,69 +1,64 @@
 namespace CGAL {
 
-  /*! \ingroup PkgArrangementOnSurface2Ref
+/*! \ingroup PkgArrangementOnSurface2Ref
-   *
+ *
-   * `Arr_face_index_map` maintains a mapping of face handles of an attached
+ * `Arr_face_index_map` maintains a mapping of face handles of an attached
-   * arrangement object to indices (of type `unsigned int`).  This class template
+ * arrangement object to indices (of type `unsigned int`).  This class template
-   * is a model of the concept `ReadablePropertyMap`. A mapping between face
+ * is a model of the concept `ReadablePropertyMap`. A mapping between face
-   * handles and indices enables convenient usage of property-map classes supplied
+ * handles and indices enables convenient usage of property-map classes supplied
-   * by `boost`.  For example, the property-map class templates
+ * by `boost`.  For example, the property-map class templates
-   * `boost::vector_property_map`, which is based on `std::vector`, and
+ * `boost::vector_property_map`, which is based on `std::vector`, and
-   * `boost::iterator_property_map`, which can be used to implement a property map
+ * `boost::iterator_property_map`, which can be used to implement a property map
-   * based on a native \CC array, require the user to supply a mapping such as
+ * based on a native \CC array, require the user to supply a mapping such as
-   * `Arr_face_index_map`.
+ * `Arr_face_index_map`.
-   *
+ *
-   * As new faces might be inserted into the attached arrangement, and
+ * As new faces might be inserted into the attached arrangement, and
-   * existing faces might be removed, the notification mechanism is used
+ * existing faces might be removed, the notification mechanism is used
-   * to dynamically maintain the mapping of face handles to indices.
+ * to dynamically maintain the mapping of face handles to indices.
-   *
+ *
-   * \cgalModels{DefaultConstructible,CopyConstructible,Assignable,ReadablePropertyMap}
+ * \cgalModels{DefaultConstructible,CopyConstructible,Assignable,ReadablePropertyMap}
-   *
+ *
-   * \sa `Arr_vertex_index_map<Arrangement>`
+ * \sa `Arr_vertex_index_map<Arrangement>`
+ */
+template <typename Arrangement_>
+class Arr_face_index_map: public Arrangement_::Observer {
+public:
+  /// \name Types
+  /// @{
+
+  /// the type of the attached arrangement.
+  typedef Arrangement_                                Arrangement_2;
+
+  typedef typename Arrangement_2::Base_aos            Base_aos;
+
+  typedef boost::readable_property_map_tag            category;
+
+  typedef unsigned int                                value_type;
+
+  typedef unsigned int                                reference;
+
+  typedef Face_handle                                 key_type;
+
+  /// The face handle type.
+  typedef typename Base_aos::Face_handle              Face_handle;
+
+  /// The type of mapping of faces to indices.
+  typedef Unique_hash_map<Face_handle, value_type>    Index_map;
+
+  /// @}
+
+  /// \name Creation
+  /// @{
+
+  /*! constructs a map that is unattached to any arrangement instance.
    */
+  Arr_face_index_map();
 
-  template <typename Arrangement_>
+  /*! constructs a map and attaches it to the given arrangement `arr`.
-  class Arr_face_index_map: public Arrangement_::Observer {
+   */
-  public:
+  Arr_face_index_map(Base_aos& arr);
 
-    /// \name Types
+  /// @}
-    /// @{
+}; /* end Arr_accessor */
-
-    /*! the type of the attached arrangement.
-     */
-    typedef Arrangement_                                Arrangement_2;
-    typedef typename Arrangement_2::Base_aos            Base_aos;
-
-    typedef boost::readable_property_map_tag            category;
-
-    typedef unsigned int                                value_type;
-
-    typedef unsigned int                                reference;
-
-    typedef Face_handle                                 key_type;
-
-    /*! The face handle type.
-     */
-    typedef typename Base_aos::Face_handle              Face_handle;
-
-    /*! The type of mapping of faces to indices.
-     */
-    typedef Unique_hash_map<Face_handle, value_type>    Index_map;
-
-    /// @}
-
-    /// \name Creation
-    /// @{
-
-    /*! constructs a map that is unattached to any arrangement instance.
-     */
-    Arr_face_index_map();
-
-    /*! constructs a map and attaches it to the given arrangement `arr`.
-     */
-    Arr_face_index_map(Base_aos& arr);
-
-    /// @}
-
-  }; /* end Arr_accessor */
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h

@@ -1,451 +1,452 @@
 namespace CGAL {
 
-  /*! \ingroup PkgArrangementOnSurface2TraitsClasses
+/*! \ingroup PkgArrangementOnSurface2TraitsClasses
-   *
+ *
-   * The traits class `Arr_geodesic_arc_on_sphere_traits_2` is a model of the
+ * The traits class `Arr_geodesic_arc_on_sphere_traits_2` is a model of the
-   * `ArrangementTraits_2` concept. It enables the construction and
+ * `AosTraits_2` concept. It enables the construction and
-   * maintenance of arrangements of arcs of great circles (also known as
+ * maintenance of arrangements of arcs of great circles (also known as
-   * geodesic arcs) that lie on the sphere (centered at the origin). Almost
+ * geodesic arcs) that lie on the sphere (centered at the origin). Almost
-   * all operations on arrangements require a kernel that supports exact
+ * all operations on arrangements require a kernel that supports exact
-   * predicates. Most operations also require a kernel that supports exact
+ * predicates. Most operations also require a kernel that supports exact
-   * constructions. However, all operations on such arrangements can be
+ * constructions. However, all operations on such arrangements can be
-   * computed efficiently, since all calculations are performed with
+ * computed efficiently, since all calculations are performed with
-   * rational arithmetic.
+ * rational arithmetic.
-   *
+ *
-   * There is an analogy between this class of arrangements and the class of
+ * There is an analogy between this class of arrangements and the class of
-   * planar arrangements induced by linear curves (i.e., segments, rays, and
+ * planar arrangements induced by linear curves (i.e., segments, rays, and
-   * lines), as properties of linear curves in the plane often, but not always,
+ * lines), as properties of linear curves in the plane often, but not always,
-   * hold for geodesic arcs on the sphere. For example, given any two
+ * hold for geodesic arcs on the sphere. For example, given any two
-   * non-antipodal points on the sphere there exists a unique great circle
+ * non-antipodal points on the sphere there exists a unique great circle
-   * connecting the two points.
+ * connecting the two points.
-   *
+ *
-   * We use the following parameterization of the unit sphere \f$S =
+ * We use the following parameterization of the unit sphere \f$S =
-   * \phi_S(\Phi)\f$: \f$\Phi = [\alpha, 2\pi + \alpha] \times [-\frac{\pi}{2},
+ * \phi_S(\Phi)\f$: \f$\Phi = [\alpha, 2\pi + \alpha] \times [-\frac{\pi}{2},
-   * \frac{\pi}{2}]\f$, \f$\phi_S(x, y) = (\cos y \cos x, \sin y \cos x, \sin
+ * \frac{\pi}{2}]\f$, \f$\phi_S(x, y) = (\cos y \cos x, \sin y \cos x, \sin
-   * x)\f$, where \f$\alpha = \arctan(X, Y)\f$. By default, \f$X = -1, Y = 0\f$,
+ * x)\f$, where \f$\alpha = \arctan(X, Y)\f$. By default, \f$X = -1, Y = 0\f$,
-   * which implies \f$\alpha = \pi\f$, and a default parameterization \f$\Phi =
+ * which implies \f$\alpha = \pi\f$, and a default parameterization \f$\Phi =
-   * [-\pi, \pi] \times [-\frac{\pi}{2}, \frac{\pi}{2}]\f$. The equator curve,
+ * [-\pi, \pi] \times [-\frac{\pi}{2}, \frac{\pi}{2}]\f$. The equator curve,
-   * for example, is given by \f$\gamma(t) = (\pi(2t - 1) + \alpha, 0)\f$, for
+ * for example, is given by \f$\gamma(t) = (\pi(2t - 1) + \alpha, 0)\f$, for
-   * \f$t \in [0,1]\f$.  This parameterization induces two contraction points
+ * \f$t \in [0,1]\f$.  This parameterization induces two contraction points
-   * \f$p_s = (0, 0, -1) = \phi_S(y,-\frac{\pi}{2})\f$ and \f$p_n = (0, 0, 1) =
+ * \f$p_s = (0, 0, -1) = \phi_S(y,-\frac{\pi}{2})\f$ and \f$p_n = (0, 0, 1) =
-   * \phi_S(y,\frac{\pi}{2})\f$, referred to as the south and north poles,
+ * \phi_S(y,\frac{\pi}{2})\f$, referred to as the south and north poles,
-   * respectively, and an identification curve \f$\{\phi_S(\pi +
+ * respectively, and an identification curve \f$\{\phi_S(\pi +
-   * \alpha,x)\,|\,-\frac{\pi}{2} \leq v \leq \frac{\pi}{2}\}\f$, as
+ * \alpha,x)\,|\,-\frac{\pi}{2} \leq v \leq \frac{\pi}{2}\}\f$, as
-   * \f$\phi_S(-\pi + \alpha,v) = \phi_S(+\pi + \alpha,v)\f$ for all \f$x\f$
+ * \f$\phi_S(-\pi + \alpha,v) = \phi_S(+\pi + \alpha,v)\f$ for all \f$x\f$
-   * (which coincides with the opposite Prime (Greenwich) Meridian when
+ * (which coincides with the opposite Prime (Greenwich) Meridian when
-   * \f$\alpha = \pi\f$).  The elements that substitutes the template parameters
+ * \f$\alpha = \pi\f$).  The elements that substitutes the template parameters
-   * `X` and `Y` when `Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>` is
+ * `X` and `Y` when `Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>` is
-   * instantiated must be integral values that define a not necessarily
+ * instantiated must be integral values that define a not necessarily
-   * normalized vector \f$(x,y)\f$ in the \f$xy\f$-plane that bisects the
+ * normalized vector \f$(x,y)\f$ in the \f$xy\f$-plane that bisects the
-   * identification curve.
+ * identification curve.
 
-   * \cgalModels{ArrangementTraits_2,ArrangementLandmarkTraits_2,ArrangementSphericalBoundaryTraits_2}
+ * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosApproximateTraits_2,AosSphericalBoundaryTraits_2}
+ */
+template <typename Kernel, typename X, typename Y>
+class Arr_geodesic_arc_on_sphere_traits_2 {
+public:
+  /*! The `Point_2` class nested within the traits is used to represent a
+   * point on a sphere centered at the origin. The point is in fact a
+   * not-necessarily normalized 3D direction extended with information that
+   * specifies the location of the point pre-image in the parameter space.
+   *
+   * \cgalModels{Assignable,DefaultConstructible,CopyConstructible}
    */
-
+  class Point_2 {
-  template <typename Kernel, typename X, typename Y>
-  class Arr_geodesic_arc_on_sphere_traits_2 {
   public:
-    /*! The `Point_2` class nested within the traits is used to represent a
+    /// \name Enumeration types
-     * point on a sphere centered at the origin. The point is in fact a
+    /// @{
-     * not-necessarily normalized 3D direction extended with information that
+
-     * specifies the location of the point pre-image in the parameter space.
+    /*! The location type indicates a location in the parameter space.
-     *
-     * \cgalModels{Assignable,DefaultConstructible,CopyConstructible}
      */
-    class Point_2 {
+    enum Location_type {
-    public:
+      /// Internal to the parameter space.
-      /// \name Enumeration types
+      NO_BOUNDARY_LOC = 0,
-      /// @{
 
-      /*! The location type indicates a location in the parameter space.
+      /// The bottom side boundary of the parameter space (the south pole).
-       */
+      MIN_BOUNDARY_LOC,
-      enum Location_type {
-        /// Internal to the parameter space.
-        NO_BOUNDARY_LOC = 0,
 
-        /// The bottom side boundary of the parameter space (the south pole).
+      /// The identified left and right side boundaries of the parameter space.
-        MIN_BOUNDARY_LOC,
+      MID_BOUNDARY_LOC,
 
-        /// The identified left and right side boundaries of the parameter space.
+      /// The top side boundary of the parameter space (the north pole).
-        MID_BOUNDARY_LOC,
+      MAX_BOUNDARY_LOC
-
-        /// The top side boundary of the parameter space (the north pole).
-        MAX_BOUNDARY_LOC
-      };
-      /// @}
-
-      /// \name Types
-      /// @{
-      typedef Kernel::Direction_3 Direction_3;
-      /// @}
-
-      /// \name Creation
-      /// @{
-
-      /*! constructs a point from a direction and a location.
-       * \param[in] dir the direction.
-       * \param[in] location indicates the location of the point pre-image
-       *            in the parameter space.
-       */
-      Point_2(const Direction_3& dir, Location_type location);
-
-      /// @}
-
-      /// \name Operations
-      /// @{
-
-      /*! sets the location of the point pre-image in the parameter space.
-       * \param[in] location the updated location of the point pre-image in
-       *            the parameter space.
-       */
-      void set_location(Location_type location);
-
-      /*! obtains the location of the point.
-       * \return the location of the point pre-image in the parameter space.
-       */
-      Location_type location() const;
-
-      /// @}
     };
+    /// @}
 
-    /*! The `X_monotone_curve_2` class nested within the traits is used to
+    /// \name Types
-     * represent an \f$x\f$-monotone geodesic arc on the a sphere centered at
+    /// @{
-     * the origin. The pre-image of an \f$x\f$-monotone geodesic arc does not
+    typedef Kernel::Direction_3 Direction_3;
-     * intersect the identified left and right sides of the boundary of the
+    /// @}
-     * parameter space.
+
-     *
+    /// \name Creation
-     * \cgalModels{Assignable,DefaultConstructible,CopyConstructible}
+    /// @{
+
+    /*! constructs a point from a direction and a location.
+     * \param[in] dir the direction.
+     * \param[in] location indicates the location of the point pre-image
+     *            in the parameter space.
      */
-    class X_monotone_curve_2 {
+    Point_2(const Direction_3& dir, Location_type location);
-    public:
-      /// \name Types
-      /// @{
-      typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
-      /// @}
 
-      /// \name Creation
+    /// @}
-      /// @{
 
-      /*! constructs an \f$x\f$-monotone geodesic arc.
+    /// \name Operations
-       * \param[in] source the source point of the arc.
+    /// @{
-       * \param[in] target the target point of the arc.
-       * \param[in] normal the normal of the plane that contains the arc.
-       * \param[in] is_vertical is the arc vertical ?
-       * \param[in] is_directed_right is the arc directed from left to right?
-       * \param[in] is_full is the arc a full great circle?
-       * \param[in] is_degenerate is the arc degenerate (single point)?
-       * \param[in] is_empty is the arc empty?
-       * \pre Both endpoints lie on the given plane.
-       */
-      X_monotone_curve_2(const Point_2& source,
-                         const Point_2& target,
-                         const Direction_3& normal,
-                         bool is_vertical,
-                         bool is_directed_right,
-                         bool is_full = false,
-                         bool is_degenerate = false,
-                         bool is_empty = false);
 
-      /*! construct an \f$x\f$-monotone geodesic arc.
+    /*! sets the location of the point pre-image in the parameter space.
-       * \param[in] normal the normal of the plane containing the arc.
+     * \param[in] location the updated location of the point pre-image in
-       * \param[in] source the source-point direction.
+     *            the parameter space.
-       * \param[in] target the target-point direction.
-       * \pre Both endpoints lie on the given plane.
-       */
-      X_monotone_curve_2(const Point_2& source,
-                         const Point_2& target,
-                         const Direction_3& normal);
-
-      /*! construct a full great-circle.
-       * \param[in] point the endpoint of the full great-circle.
-       * \param[in] normal the normal of the plane containing the arc.
-       * \pre the point lies on the given plane.
-       * \pre the point pre-image lies on the identified left and right sides
-       *      of the boundary of the parameter space.
-       */
-      X_monotone_curve_2(const Point_2& point,
-                         const Direction_3& normal);
-
-      /// @}
-
-      /// \name Operations
-      /// @{
-
-      /*! sets the source endpoint.
-       * \param[in] source the updated source endpoint.
-       */
-      void set_source(const Point_2& source);
-
-      /*! sets the target endpoint.
-       * \param[in] target the updated target endpoint.
-       */
-      void set_target(const Point_2& target);
-
-      /*! sets the normal of the underlying plane.
-       * \param[in] normal the updated normal of the underlying plane.
-       */
-      void set_normal(const Direction_3& normal);
-
-      /*! sets the flag that indicates whether the arc is vertical.
-       * \param[in] flag indicates whether the arc pre-image in the parameter
-       *            space is vertical.
-       */
-      void set_is_vertical(bool flag);
-
-      /*! sets the flag that indicates whether the direction of the arc
-       * pre-image in the parameter space is from left to right.
-       * \param flag indicates whether the arc pre-image in the parameter
-       *             space is from left to right.
-       */
-      void set_is_directed_right(bool flag);
-
-      /*! sets the flag that indicates whether the arc is a full great circle.
-       * \param[in] flag indicates whether the arc is a full great circle.
-       */
-      void set_is_full(bool flag);
-
-      /*! sets the flag that indicates whether the arc degenerates to a point.
-       * \param[in] flag indicates whether the arc degenerates to a point.
-       */
-      void set_is_degenerate(bool flag);
-
-      /*! sets the flag that indicates whether the arc is empty.
-       * \param[in] flag indicates whether the arc is empty.
-       */
-      void set_is_empty(bool flag);
-
-      /*! obtains the source point.
-       */
-      const Point_2& source() const;
-
-      /*! obtains the target point.
-       */
-      const Point_2& target() const;
-
-      /*! obtains the normal to the containing plane.
-       */
-      const Direction_3& normal() const;
-
-      /*! obtains the (lexicographically) left endpoint direction.
-       */
-      const Point_2& left() const;
-
-      /*! obtains the (lexicographically) right endpoint.
-       */
-      const Point_2& right() const;
-
-      /*! determines whether the arc is vertical.
-       */
-      bool is_vertical() const;
-
-      /*! determines whether the arc is directed lexicographically from left to
-       * right.
-       */
-      bool is_directed_right() const;
-
-      /*! determines whether the arc is a great circle.
-       */
-      bool is_full() const;
-
-      /*! determines whether the arc is degenerate.
-       */
-      bool is_degenerate() const;
-
-      /*! determines whether the arc is empty. */
-      bool is_empty() const;
-
-      /*! determines whether the arc is a meridian.
-       */
-      bool is_meridian() const;
-
-      /// @}
-    };
-
-    /*!
      */
-    class Curve_2 {
+    void set_location(Location_type location);
-    public:
-      /// \name Types
-      /// @{
-      typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
-      /// @}
 
-      /// \name Creation
+     /*! obtains the location of the point.
-      /// @{
+     * \return the location of the point pre-image in the parameter space.
-      /// @}
-
-      /// \name Operations
-      /// @{
-      /// @}
-    };
-
-    /*! Construction functor of a point.
-     *
-     * \cgalModels{Assignable,CopyConstructible,AdaptableUnaryFunction,AdaptableTernaryFunction}
      */
+    Location_type location() const;
 
-    /*!
+    /// @}
-     */
-    class Construct_point_2 {
-    public:
-      /// \name Types
-      /// @{
-      typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 result_type;
-      typedef typename Kernel::FT                                FT;
-      typedef typename Kernel::Direction_3                       Direction_3;
-      /// @}
-
-      /// \name Operations
-      /// @{
-
-      /*! constructs a point on the sphere from three coordinates, which define
-       * a (not necessarily normalized) direction.
-       * \param[in] x the x coordinate
-       * \param[in] y the y coordinate
-       * \param[in] z the z coordinate
-       */
-      Point_2 operator()(const FT& x, const FT& y, const FT& z);
-
-      /*! constructs a point on the sphere from a (not necessarily normalized)
-       * direction.
-       * \param other the other direction
-       */
-      Point_2 operator()(const Direction_3& other);
-
-      /// @}
-    };
-
-    /*! Construction functor of \f$x\f$-monotone geodesic arcs.
-     *
-     * \cgalModels{Assignable,CopyConstructible,AdaptableUnaryFunction,AdaptableBinaryFunction,AdaptableTernaryFunction}
-     */
-    class Construct_x_monotone_curve_2 {
-    public:
-      /// \name Types
-      /// @{
-      typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
-      typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::X_monotone_curve_2 result_type;
-      typedef Kernel::Direction_3 Direction_3;
-      typedef Direction_3 argument_type;
-      /// @}
-
-      /// \name Operations
-      /// @{
-
-      /*! constructs the minor geodesic arc from two endpoints. The minor arc
-       * is the one with the smaller angle among the two geodesic arcs with
-       * the given endpoints.
-       * 1. Find out whether the arc is x-monotone.
-       * 2. If it is x-monotone,
-       *    2.1 Find out whether it is vertical, and
-       *    2.2 whether the target is larger than the source (directed right).
-       *
-       * An arc is vertical, iff
-       * 1. one of its endpoint direction pierces a pole, or
-       * 2. the projections of the endpoint directions onto the xy-plane coincide.
-       * \param[in] p the first endpoint.
-       * \param[in] q the second endpoint.
-       * \pre p and q must not coincide.
-       * \pre p and q cannot be antipodal.
-       * \pre The constructed minor arc does not intersect the identification
-       *      curve in its interior.
-       */
-      X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q);
-
-      /*! constructs a full great circle from a normal to a plane.
-       * Observe that the constructed arc has one endpoint that lies on
-       * the identification curve. This point is considered both the source and
-       * target (and also the left and right) point of the arc.
-       * \param normal the normal to the plane containing the great circle.
-       * \pre the plane is not vertical.
-       */
-      X_monotone_curve_2 operator()(const Direction_3& normal);
-
-      /*! constructs a geodesic arc from two endpoints and a normal to the plane
-       * containing the arc. The two endpoints determine the plane. The normal
-       * determines the orientation of the plane and the final arc (whether its
-       * the minor arc or the major arc). The right-hand rule can be used
-       * to select the appropriate normal.
-       * \param[in] p the first endpoint.
-       * \param[in] q the second endpoint.
-       * \param[in] normal the normal to the oriented plane containing the arc.
-       * \pre Both endpoints lie on the given oriented plane.
-       * \pre The constructed arc does not intersect the identification curve
-       *      in its interior.
-       */
-      X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q,
-                                    const Direction_3& normal);
-
-      /// @} /* end of operations */
-    };
-
-    /*! Construction functor of geodesic arcs.
-     *
-     * \cgalModels{Assignable,CopyConstructible,AdaptableUnaryFunction,AdaptableBinaryFunction,AdaptableTernaryFunction}
-     */
-    class Construct_curve_2 {
-    public:
-      /// \name Types
-      /// @{
-      typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
-      typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Curve_2 result_type;
-      typedef Kernel::Direction_3 Direction_3;
-      typedef Direction_3 argument_type;
-      /// @}
-
-      /// \name Operations
-      /// @{
-
-      /*! constructs a full great circle from a normal to a plane.
-       * \param normal the normal to the plane containing the great circle.
-       */
-      X_monotone_curve_2 operator()(const Direction_3& normal);
-
-      /*! constructs the minor geodesic arc from two endpoints. The minor arc
-       * is the one with the smaller angle among the two geodesic arcs with
-       * the given endpoints.
-       * 1. Find out whether the arc is x-monotone.
-       * 2. If it is x-monotone,
-       *     1. Find out whether it is vertical, and
-       *     2. whether the target is larger than the source (directed right).
-       *
-       * An arc is vertical, iff
-       * 1. one of its endpoint direction pierces a pole, or
-       * 2. the projections of the endpoint directions onto the xy-plane coincide.
-       *
-       * \param[in] p the first endpoint.
-       * \param[in] q the second endpoint.
-       * \pre p and q must not coincide.
-       * \pre p and q cannot be antipodal.
-       */
-      Curve_2 operator()(const Point_2& p, const Point_2& q);
-
-      /*! constructs a geodesic arc from two endpoints and a normal to the plane
-       * containing the arc. The two endpoints determine the plane. The normal
-       * determines the orientation of the plane and the final arc (whether its
-       * the minor arc or the major arc). The right-hand rule can be used
-       * to select the appropriate normal.
-       * \param[in] p the first endpoint.
-       * \param[in] q the second endpoint.
-       * \param[in] normal the normal to the oriented plane containing the arc.
-       * \pre Both endpoints lie on the given oriented plane.
-       */
-      Curve_2 operator()(const Point_2& p, const Point_2& q,
-                         const Direction_3& normal);
-      /// @}
-    };
-
-    /*! returns an instance of `Construct_point_2`.
-     */
-    Construct_point_2 construct_point_2_object() const;
-
-    /*! returns an instance of `Construct_x_monotone_curve_2`.
-     */
-    Construct_x_monotone_curve_2 construct_x_monotone_curve_2_object() const;
-
-    /*! returns an instance of `Construct_curve_2`.
-     */
-    Construct_curve_2 construct_curve_2_object() const;
   };
 
+  /*! The `X_monotone_curve_2` class nested within the traits is used to
+   * represent an \f$x\f$-monotone geodesic arc on the a sphere centered at
+   * the origin. The pre-image of an \f$x\f$-monotone geodesic arc does not
+   * intersect the identified left and right sides of the boundary of the
+   * parameter space.
+   *
+   * \cgalModels{Assignable,DefaultConstructible,CopyConstructible}
+   */
+  class X_monotone_curve_2 {
+  public:
+    /// \name Types
+    /// @{
+    typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
+    /// @}
+
+    /// \name Creation
+    /// @{
+
+    /*! constructs an \f$x\f$-monotone geodesic arc.
+     * \param[in] source the source point of the arc.
+     * \param[in] target the target point of the arc.
+     * \param[in] normal the normal of the plane that contains the arc.
+     * \param[in] is_vertical is the arc vertical ?
+     * \param[in] is_directed_right is the arc directed from left to right?
+     * \param[in] is_full is the arc a full great circle?
+     * \param[in] is_degenerate is the arc degenerate (single point)?
+     * \param[in] is_empty is the arc empty?
+     *
+     * \pre Both endpoints lie on the given plane.
+     */
+    X_monotone_curve_2(const Point_2& source,
+                       const Point_2& target,
+                       const Direction_3& normal,
+                       bool is_vertical,
+                       bool is_directed_right,
+                       bool is_full = false,
+                       bool is_degenerate = false,
+                       bool is_empty = false);
+
+    /*! constructs an \f$x\f$-monotone geodesic arc.
+     * \param[in] normal the normal of the plane containing the arc.
+     * \param[in] source the source-point direction.
+     * \param[in] target the target-point direction.
+     *
+     * \pre Both endpoints lie on the given plane.
+     */
+    X_monotone_curve_2(const Point_2& source,
+                       const Point_2& target,
+                       const Direction_3& normal);
+
+    /*! constructs a full great-circle.
+     * \param[in] point the endpoint of the full great-circle.
+     * \param[in] normal the normal of the plane containing the arc.
+     *
+     * \pre the point lies on the given plane.
+     * \pre the point pre-image lies on the identified left and right sides
+     *      of the boundary of the parameter space.
+     */
+    X_monotone_curve_2(const Point_2& point,
+                       const Direction_3& normal);
+
+    /// @}
+
+    /// \name Operations
+    /// @{
+
+    /*! sets the source endpoint.
+     * \param[in] source the updated source endpoint.
+     */
+    void set_source(const Point_2& source);
+
+    /*! sets the target endpoint.
+     * \param[in] target the updated target endpoint.
+     */
+    void set_target(const Point_2& target);
+
+    /*! sets the normal of the underlying plane.
+     * \param[in] normal the updated normal of the underlying plane.
+     */
+    void set_normal(const Direction_3& normal);
+
+    /*! sets the flag that indicates whether the arc is vertical.
+     * \param[in] flag indicates whether the arc pre-image in the parameter
+     *            space is vertical.
+     */
+    void set_is_vertical(bool flag);
+
+    /*! sets the flag that indicates whether the direction of the arc
+     * pre-image in the parameter space is from left to right.
+     * \param flag indicates whether the arc pre-image in the parameter
+     *             space is from left to right.
+     */
+    void set_is_directed_right(bool flag);
+
+    /*! sets the flag that indicates whether the arc is a full great circle.
+     * \param[in] flag indicates whether the arc is a full great circle.
+     */
+    void set_is_full(bool flag);
+
+    /*! sets the flag that indicates whether the arc degenerates to a point.
+     * \param[in] flag indicates whether the arc degenerates to a point.
+     */
+    void set_is_degenerate(bool flag);
+
+    /*! sets the flag that indicates whether the arc is empty.
+     * \param[in] flag indicates whether the arc is empty.
+     */
+    void set_is_empty(bool flag);
+
+    /*! obtains the source point.
+     */
+    const Point_2& source() const;
+
+    /*! obtains the target point.
+     */
+    const Point_2& target() const;
+
+    /*! obtains the normal to the containing plane.
+     */
+    const Direction_3& normal() const;
+
+    /*! obtains the (lexicographically) left endpoint direction.
+     */
+    const Point_2& left() const;
+
+    /*! obtains the (lexicographically) right endpoint.
+     */
+    const Point_2& right() const;
+
+    /*! Determines whether the arc is vertical.
+     */
+    bool is_vertical() const;
+
+    /*! determines whether the arc is directed lexicographically from left to right.
+     */
+    bool is_directed_right() const;
+
+    /*! determines whether the arc is a great circle.
+     */
+    bool is_full() const;
+
+    /*! determines whether the arc is degenerate.
+     */
+    bool is_degenerate() const;
+
+    /*! determines whether the arc is empty. */
+    bool is_empty() const;
+
+    /*! determines whether the arc is a meridian.
+     */
+    bool is_meridian() const;
+
+    /// @}
+  };
+
+  /*!
+   */
+  class Curve_2 {
+  public:
+    /// \name Types
+    /// @{
+    typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
+    /// @}
+
+    /// \name Creation
+    /// @{
+    /// @}
+
+    /// \name Operations
+    /// @{
+    /// @}
+  };
+
+  /*! Construction functor of a point.
+   *
+   * \cgalModels{Assignable,CopyConstructible,AdaptableUnaryFunction,AdaptableTernaryFunction}
+   */
+  /*!
+   */
+  class Construct_point_2 {
+  public:
+    /// \name Types
+    /// @{
+    typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 result_type;
+    typedef typename Kernel::FT                                FT;
+    typedef typename Kernel::Direction_3                       Direction_3;
+    /// @}
+
+    /// \name Operations
+    /// @{
+
+    /*! constructs a point on the sphere from three coordinates, which define
+     * a (not necessarily normalized) direction.
+     * \param[in] x the x coordinate
+     * \param[in] y the y coordinate
+     * \param[in] z the z coordinate
+     */
+    Point_2 operator()(const FT& x, const FT& y, const FT& z);
+
+    /*! constructs a point on the sphere from a (not necessarily normalized)
+     * direction.
+     * \param other the other direction
+     */
+    Point_2 operator()(const Direction_3& other);
+
+    /// @}
+  };
+
+  /*! Construction functor of \f$x\f$-monotone geodesic arcs.
+   *
+   * \cgalModels{Assignable,CopyConstructible,AdaptableUnaryFunction,AdaptableBinaryFunction,AdaptableTernaryFunction}
+   */
+  class Construct_x_monotone_curve_2 {
+  public:
+    /// \name Types
+    /// @{
+    typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
+    typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::X_monotone_curve_2 result_type;
+    typedef Kernel::Direction_3 Direction_3;
+    typedef Direction_3 argument_type;
+    /// @}
+
+    /// \name Operations
+    /// @{
+
+    /*! constructs the minor geodesic arc from two endpoints. The minor arc
+     * is the one with the smaller angle among the two geodesic arcs with
+     * the given endpoints.
+     * 1. Find out whether the arc is \f$x\f$-monotone.
+     * 2. If it is \f$x\f$-monotone,
+     *    2.1 Find out whether it is vertical, and
+     *    2.2 whether the target is larger than the source (directed right).
+     *
+     * An arc is vertical, iff
+     * 1. one of its endpoint direction pierces a pole, or
+     * 2. the projections of the endpoint directions onto the \f$xy\f$-plane coincide.
+     * \param[in] p the first endpoint.
+     * \param[in] q the second endpoint.
+     * \pre p and q must not coincide.
+     * \pre p and q cannot be antipodal.
+     * \pre The constructed minor arc does not intersect the identification
+     *      curve in its interior.
+     */
+    X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q);
+
+    /*! constructs a full great circle from a normal to a plane.
+     * Observe that the constructed arc has one endpoint that lies on
+     * the identification curve. This point is considered both the source and
+     * target (and also the left and right) point of the arc.
+     * \param normal the normal to the plane containing the great circle.
+     * \pre the plane is not vertical.
+     */
+    X_monotone_curve_2 operator()(const Direction_3& normal);
+
+    /*! constructs a geodesic arc from two endpoints and a normal to the plane
+     * containing the arc. The two endpoints determine the plane. The normal
+     * determines the orientation of the plane and the final arc (whether its
+     * the minor arc or the major arc). The right-hand rule can be used
+     * to select the appropriate normal.
+     * \param[in] p the first endpoint.
+     * \param[in] q the second endpoint.
+     * \param[in] normal the normal to the oriented plane containing the arc.
+     * \pre Both endpoints lie on the given oriented plane.
+     * \pre The constructed arc does not intersect the identification curve
+     *      in its interior.
+     */
+    X_monotone_curve_2 operator()(const Point_2& p, const Point_2& q,
+                                  const Direction_3& normal);
+
+    /// @} /* end of operations */
+  };
+
+  /*! Construction functor of geodesic arcs.
+   *
+   * \cgalModels{Assignable,CopyConstructible,AdaptableUnaryFunction,AdaptableBinaryFunction,AdaptableTernaryFunction}
+   */
+  class Construct_curve_2 {
+  public:
+    /// \name Types
+    /// @{
+    typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Point_2 Point_2;
+    typedef Arr_geodesic_arc_on_sphere_traits_2<Kernel, X, Y>::Curve_2 result_type;
+    typedef Kernel::Direction_3 Direction_3;
+    typedef Direction_3 argument_type;
+    /// @}
+
+    /// \name Operations
+    /// @{
+
+    /*! constructs a full great circle from a normal to a plane.
+     * \param normal the normal to the plane containing the great circle.
+     */
+    X_monotone_curve_2 operator()(const Direction_3& normal);
+
+    /*! constructs the minor geodesic arc from two endpoints. The minor arc
+     * is the one with the smaller angle among the two geodesic arcs with
+     * the given endpoints.
+     * 1. Find out whether the arc is \f$x\f$-monotone.
+     * 2. If it is \f$x\f$-monotone,
+     *     1. Find out whether it is vertical, and
+     *     2. whether the target is larger than the source (directed right).
+     *
+     * An arc is vertical, iff
+     * 1. one of its endpoint direction pierces a pole, or
+     * 2. the projections of the endpoint directions onto the \f$xy\f$-plane coincide.
+     *
+     * \param[in] p the first endpoint.
+     * \param[in] q the second endpoint.
+     * \pre p and q must not coincide.
+     * \pre p and q cannot be antipodal.
+     */
+    Curve_2 operator()(const Point_2& p, const Point_2& q);
+
+    /*! constructs a geodesic arc from two endpoints and a normal to the plane
+     * containing the arc. The two endpoints determine the plane. The normal
+     * determines the orientation of the plane and the final arc (whether its
+     * the minor arc or the major arc). The right-hand rule can be used
+     * to select the appropriate normal.
+     * \param[in] p the first endpoint.
+     * \param[in] q the second endpoint.
+     * \param[in] normal the normal to the oriented plane containing the arc.
+     *
+     * \pre Both endpoints lie on the given oriented plane.
+     */
+    Curve_2 operator()(const Point_2& p, const Point_2& q,
+                       const Direction_3& normal);
+    /// @}
+  };
+
+  /*! returns an instance of `Construct_point_2`.
+   */
+  Construct_point_2 construct_point_2_object() const;
+
+  /*! returns an instance of `Construct_x_monotone_curve_2`.
+   */
+  Construct_x_monotone_curve_2 construct_x_monotone_curve_2_object() const;
+
+  /*! returns an instance of `Construct_curve_2`.
+   */
+  Construct_curve_2 construct_curve_2_object() const;
+};
+
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_landmarks_point_location.h

@@ -1,62 +1,58 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2PointLocation
-\ingroup PkgArrangementOnSurface2PointLocation
+ *
+ * \anchor arr_reflm_pl
+ *
+ * The `Arr_landmarks_point_location` class implements a Jump & Walk algorithm,
+ * where special points, referred to as "landmarks", are chosen in a
+ * preprocessing stage, their place in the arrangement is found, and they are
+ * inserted into a data-structure that enables efficient nearest-neighbor search
+ * (a <span class="textsc">Kd</span>-tree). Given a query point, the nearest
+ * landmark is located and a "walk" strategy is applied from the landmark to the
+ * query point.
+ *
+ * There are various strategies to select the landmark set in the
+ * arrangement, where the strategy is determined by the
+ * `Generator` template parameter. The following landmark-generator
+ * classes are available:
+ * <DL>
+ * <DT><B>`Arr_landmarks_vertices_generator`</B><DD>
+ * The arrangement vertices are used as the landmarks set.
+ *
+ * <DT><B>`Arr_random_landmarks_generator`</B><DD>
+ * \f$n\f$ random points in the bounding box of the arrangement are chosen
+ * as the landmarks set.
+ *
+ * <DT><B>`Arr_halton_landmarks_generator`</B><DD>
+ * \f$n\f$ Halton points in the bounding box of the arrangement are chosen
+ * as the landmarks set.
+ *
+ * <DT><B>`Arr_middle_edges_landmarks_generator`</B><DD>
+ * The midpoint of each arrangement edge is computed, and the resulting
+ * set of points is used as the landmarks set. This generator can be applied
+ * only for arrangements of line segments.
+ *
+ * <DT><B>`Arr_grid_landmarks_generator`</B><DD>
+ * A set of \f$n\f$ landmarks are chosen on a
+ * \f$\lceil \sqrt{n} \rceil \times \lceil \sqrt{n} \rceil\f$
+ * grid that covers the bounding box of the arrangement.
+ * </DL>
+ * The `Arr_landmarks_vertices_generator` class is the default generator
+ * and used if no `Generator` parameter is specified.
+ *
+ * It is recommended to use the landmarks point-location strategy
+ * when the application frequently issues point-location queries on a
+ * rather static arrangement that the changes applied to it are mainly
+ * insertions of curves and not deletions of them.
+ *
+ * \cgalModels{AosPointLocation_2,AosVerticalRayShoot_2}
+ *
+ * \sa `AosPointLocation_2`
+ * \sa `AosVerticalRayShoot_2`
+ * \sa `CGAL::Arr_point_location_result<Arrangement>`
+ */
+template <typename Arrangement, typename Generator>
+class Arr_landmarks_point_location {};
 
-\anchor arr_reflm_pl
-
-The `Arr_landmarks_point_location` class implements a Jump & Walk algorithm, where special
-points, referred to as "landmarks", are chosen in a preprocessing stage,
-their place in the arrangement is found, and they are inserted into a
-data-structure that enables efficient nearest-neighbor search (a
-<span class="textsc">Kd</span>-tree). Given a query point, the nearest landmark is located and a
-"walk" strategy is applied from the landmark to the query point.
-
-There are various strategies to select the landmark set in the
-arrangement, where the strategy is determined by the
-`Generator` template parameter. The following landmark-generator
-classes are available:
-<DL>
-<DT><B>`Arr_landmarks_vertices_generator` - </B><DD>
-The arrangement vertices are used as the landmarks set.
-
-<DT><B>`Arr_random_landmarks_generator` - </B><DD>
-\f$ n\f$ random points in the bounding box of the arrangement are chosen
-as the landmarks set.
-
-<DT><B>`Arr_halton_landmarks_generator` - </B><DD>
-\f$ n\f$ Halton points in the bounding box of the arrangement are chosen
-as the landmarks set.
-
-<DT><B>`Arr_middle_edges_landmarks_generator` - </B><DD>
-The midpoint of each arrangement edge is computed, and the resulting
-set of points is used as the landmarks set. This generator can be applied
-only for arrangements of line segments.
-
-<DT><B>`Arr_grid_landmarks_generator` - </B><DD>
-A set of \f$ n\f$ landmarks are chosen on a
-\f$ \lceil \sqrt{n} \rceil \times \lceil \sqrt{n} \rceil\f$
-grid that covers the bounding box of the arrangement.
-</DL>
-The `Arr_landmarks_vertices_generator` class is the default generator
-and used if no `Generator` parameter is specified.
-
-It is recommended to use the landmarks point-location strategy
-when the application frequently issues point-location queries on a
-rather static arrangement that the changes applied to it are mainly
-insertions of curves and not deletions of them.
-
-\cgalModels{ArrangementPointLocation_2,ArrangementVerticalRayShoot_2}
-
-\sa `ArrangementPointLocation_2`
-\sa `ArrangementVerticalRayShoot_2`
-\sa `CGAL::Arr_point_location_result<Arrangement>`
-
-*/
-template< typename Arrangement, typename Generator >
-class Arr_landmarks_point_location {
-public:
-
-}; /* end Arr_landmarks_point_location */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_line_arc_traits_2.h

@@ -1,19 +1,14 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2TraitsClasses
-\ingroup PkgArrangementOnSurface2TraitsClasses
+ *
+ * This class is a traits class for \cgal arrangements, built on top of a
+ * model of concept `CircularKernel`. It provides curves of type
+ * `CGAL::Line_arc_2<CircularKernel>`.
+ *
+ * \cgalModels{AosTraits_2}
+ */
+template <typename CircularKernel>
+class Arr_line_arc_traits_2 {};
 
-This class is a traits class for \cgal arrangements, built on top of a
-model of concept `CircularKernel`. It provides curves of type
-`CGAL::Line_arc_2<CircularKernel>`.
-
-\cgalModels{ArrangementTraits_2}
-
-*/
-template< typename CircularKernel >
-class Arr_line_arc_traits_2 {
-public:
-
-}; /* end Arr_line_arc_traits_2 */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_linear_traits_2.h

@@ -3,10 +3,10 @@ namespace CGAL {
 /*! \ingroup PkgArrangementOnSurface2TraitsClasses
  *
  * The traits class `Arr_linear_traits_2` is a model of the
- * `ArrangementTraits_2` concept, which enables the construction and maintenance
+ * `AosTraits_2` concept, which enables the construction and maintenance
  * of arrangements of linear objects. The linear objects may be bounded (line
  * segments) or unbounded (rays and lines). Thus, it is also a model of the
- * concept `ArrangementOpenBoundaryTraits_2`. The traits class is parameterized
+ * concept `AosOpenBoundaryTraits_2`. The traits class is parameterized
  * parameterized with a \cgal-kernel model; see the reference page of
  * `Arr_segment_traits_2<Kernel>` for further explanations and recommendations
  * on choosing a kernel.
@@ -14,35 +14,34 @@ namespace CGAL {
  * `Arr_linear_traits_2` defines `Kernel::Point_2` as its point type. The nested
  * `X_monotone_curve_2` and `Curve_2` types defined by the traits class (as is
  * the case with the various segment-traits classes, both types refer to the
- * same class, as <I>every</I> linear object is (weakly) \f$ x\f$-monotone), are
+ * same class, as <I>every</I> linear object is (weakly) \f$x\f$-monotone), are
  * constructible from a point, a line segment, a ray and from a line (objects of
  * types `Kernel::Point_2`, `Kernel::Segment_2`, `Kernel::Ray_2` and
  * `Kernel::Line_2`, respectively). On the other hand, when we are given a curve
  * we can find out its actual type and convert it to the respective kernel
  * object (say, to a `Kernel::Ray_2`).
  *
- * \cgalModels{ArrangementTraits_2,ArrangementLandmarkTraits_2,ArrangementOpenBoundaryTraits_2}
+ * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosOpenBoundaryTraits_2}
  */
 template <typename Kernel>
 class Arr_linear_traits_2 {
 public:
-
   /// \name Types
   /// @{
 
-  //!
+  ///
   typedef typename Kernel::Segment_2 Segment_2;
 
-  //!
+  ///
   typedef typename Kernel::Ray_2 Ray_2;
 
-  //!
+  ///
   typedef typename Kernel::Line_2 Line_2;
 
-  //!
+  ///
   typedef typename Kernel::Point_2 Point_2;
 
-  //!
+  ///
   typedef typename X_monotone_curve_2 Curve_2;
 
   /// @}
@@ -57,20 +56,19 @@ public:
    */
   class X_monotone_curve_2 {
   public:
-
     /// \name Types
     /// @{
 
-    //!
+    ///
     typedef typename Kernel::Point_2 Point_2;
 
-    //!
+    ///
     typedef typename Kernel::Segment_2 Segment_2;
 
-    //!
+    ///
     typedef typename Kernel::Ray_2 Ray_2;
 
-    //!
+    ///
     typedef typename Kernel::Line_2 Line_2;
 
     /// @}
@@ -139,7 +137,6 @@ public:
     Point_2 target() const;
 
     /// @}
-
   }; /* end Arr_linear_traits_2::X_monotone_curve_2 */
 
   class Trim_2 {
@@ -147,7 +144,7 @@ public:
     /// \name Creation
     /// @{
 
-    /*! trims the given x-monotone curve to an from src to tgt.
+    /*! trims the given \f$x\f$-monotone curve to an from `src` to `tgt`.
      * \ pre `src` and `tgt` lies on the curve
      */
     X_monotone_curve_2 operator()(const X_monotone_curve_2& xcv,
@@ -157,7 +154,6 @@ public:
   } /* end Arr_linear_traits_2::Trim_2 */
 
   Trim_2 trim_2_object() const;
-
 }; /* end Arr_linear_traits_2 */
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_naive_point_location.h

@@ -1,28 +1,22 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2PointLocation
-\ingroup PkgArrangementOnSurface2PointLocation
+ *
+ * \anchor arr_refnaive_pl
+ *
+ * The `Arr_naive_point_location` class implements a naive algorithm that
+ * traverses all the vertices and halfedges in the arrangement in search for an
+ * answer to a point-location query.  The query time is therefore linear in the
+ * complexity of the arrangement.  Naturally, this point-location strategy could
+ * turn into a heavy time-consuming process when applied to dense arrangements.
+ *
+ * \cgalModels{AosPointLocation_2,AosVerticalRayShoot_2}
+ *
+ * \sa `AosPointLocation_2`
+ * \sa `AosVerticalRayShoot_2`
+ * \sa `CGAL::Arr_point_location_result<Arrangement>`
+ */
+template <typename Arrangement>
+class Arr_naive_point_location {};
 
-\anchor arr_refnaive_pl
-
-The `Arr_naive_point_location` class implements a naive algorithm that traverses
-all the vertices and halfedges in the arrangement in search for an
-answer to a point-location query.
-The query time is therefore linear in the complexity of the arrangement.
-Naturally, this point-location strategy could turn into a heavy
-time-consuming process when applied to dense arrangements.
-
-\cgalModels{ArrangementPointLocation_2,ArrangementVerticalRayShoot_2}
-
-\sa `ArrangementPointLocation_2`
-\sa `ArrangementVerticalRayShoot_2`
-\sa `CGAL::Arr_point_location_result<Arrangement>`
-
-*/
-template< typename Arrangement >
-class Arr_naive_point_location {
-public:
-
-}; /* end Arr_naive_point_location */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_non_caching_segment_basic_traits_2.h

@@ -1,32 +1,26 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2TraitsClasses
-\ingroup PkgArrangementOnSurface2TraitsClasses
+ *
+ * The traits class `Arr_non_caching_segment_basic_traits_2` is a model of the
+ * `AosTraits_2` concept that allow the construction and maintenance of
+ * arrangements of sets of pairwise interior-disjoint line segments. It is
+ * templated with a \cgal-Kernel model, and it is derived from it. This traits
+ * class is a thin layer above the parameterized kernel. It inherits the
+ * `Point_2` from the kernel and its `X_monotone_curve_2` type is defined as
+ * `Kernel::Segment_2`. Most traits-class functor are inherited from the kernel
+ * functor, and the traits class only supplies the necessary functors that are
+ * not provided by the kernel. The kernel is parameterized with a number type,
+ * which should support the arithmetic operations \f$+\f$, \f$-\f$ and
+ * \f$\times\f$ in an exact manner in order to avoid robustness problems.  Using
+ * `Cartesian<MP_Float>` or `Cartesian<Gmpz>` are possible substitutions for the
+ * kernel. Using other (inexact) number types (for example, instantiating the
+ * template with `Simple_cartesian<double>`) is also possible, at the user's own
+ * risk.
+ *
+ * \cgalModels{AosLandmarkTraits_2}
+ */
+template <typename Kernel>
+class Arr_non_caching_segment_basic_traits_2 {};
 
-The traits class `Arr_non_caching_segment_basic_traits_2` is a model of the `ArrangementTraits_2`
-concept that allow the construction and maintenance of arrangements of
-sets of pairwise interior-disjoint line segments. It is templated with a
-\cgal-Kernel model, and it is derived from it. This traits class is a
-thin layer above the parameterized kernel. It inherits the `Point_2`
-from the kernel and its `X_monotone_curve_2` type is defined as
-`Kernel::Segment_2`. Most traits-class functor are inherited from the
-kernel functor, and the traits class only supplies the necessary functors
-that are not provided by the kernel. The kernel is parameterized with a
-number type, which should support the arithmetic operations \f$ +\f$, \f$ -\f$ and
-\f$ \times\f$ in an exact manner in order to avoid robustness problems.
-Using `Cartesian<MP_Float>` or `Cartesian<Gmpz>` are possible
-substitutions for the kernel. Using other (inexact) number types
-(for example, instantiating the template with
-`Simple_cartesian<double>`) is also possible, at the user's own
-risk.
-
-\cgalModels{ArrangementLandmarkTraits_2}
-
-*/
-template< typename Kernel >
-class Arr_non_caching_segment_basic_traits_2 {
-public:
-
-}; /* end Arr_non_caching_segment_basic_traits_2 */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_non_caching_segment_traits_2.h

@@ -1,47 +1,41 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2TraitsClasses
-\ingroup PkgArrangementOnSurface2TraitsClasses
+ *
+ * The traits class `Arr_non_caching_segment_traits_2` is a model of the
+ * `AosTraits_2` concept that allows the construction and maintenance of
+ * arrangements of line segments. It is parameterized with a \cgal-Kernel type,
+ * and it is derived from it. This traits class is a thin layer above the
+ * parameterized kernel. It inherits the `Point_2` from the kernel and its
+ * `X_monotone_curve_2` and `Curve_2` types are both defined as
+ * `Kernel::Segment_2`. Most traits-class functor are inherited from the kernel
+ * functor, and the traits class only supplies the necessary functors that are
+ * not provided by the kernel. The kernel is parameterized with a number type,
+ * which should support exact rational arithmetic in order to avoid robustness
+ * problems, although other number types could be used at the user's own risk.
+ *
+ * The traits-class implementation is very simple, yet may lead to a cascaded
+ * representation of intersection points with exponentially long bit-lengths,
+ * especially if the kernel is parameterized with a number type that does not
+ * perform normalization (e.g. `Quotient<MP_Float>`).  The
+ * `Arr_segment_traits_2` traits class avoids this cascading problem, and should
+ * be the default choice for implementing arrangements of line segments. It is
+ * recommended to use `Arr_non_caching_segment_traits_2` only for very sparse
+ * arrangements of huge sets of input segments.
+ *
+ * While `Arr_non_caching_segment_traits_2` models the concept
+ * `AosDirectionalXMonotoneTraits_2`, the implementation of the
+ * `Are_mergeable_2` operation does not enforce the input curves to have the
+ * same direction as a precondition. Moreover,
+ * `Arr_non_caching_segment_traits_2` supports the merging of curves of opposite
+ * directions.
+ *
+ * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosDirectionalXMonotoneTraits_2}
+ *
+ * \sa `Arr_segment_traits_2<Kernel>`
+ */
+template <typename Kernel>
+class Arr_non_caching_segment_traits_2 :
+    public Arr_non_caching_segment_basic_traits_2<Kernel> {};
 
-The traits class `Arr_non_caching_segment_traits_2` is a model of the `ArrangementTraits_2`
-concept that allows the construction and maintenance of arrangements of
-line segments. It is parameterized with a \cgal-Kernel type, and it
-is derived from it. This traits class is a thin layer above the
-parameterized kernel. It inherits the `Point_2` from the kernel and its
-`X_monotone_curve_2` and `Curve_2` types are both defined as
-`Kernel::Segment_2`. Most traits-class functor are inherited from the
-kernel functor, and the traits class only supplies the necessary functors
-that are not provided by the kernel. The kernel is parameterized with a
-number type, which should support exact rational arithmetic in order to
-avoid robustness problems, although other number types could be used at the
-user's own risk.
-
-The traits-class implementation is very simple, yet may lead to
-a cascaded representation of intersection points with exponentially long
-bit-lengths, especially if the kernel is parameterized with a number type
-that does not perform normalization (e.g. `Quotient<MP_Float>`).
-The `Arr_segment_traits_2` traits class avoids this cascading
-problem, and should be the default choice for implementing arrangements of
-line segments. It is recommended to use `Arr_non_caching_segment_traits_2` only for very sparse
-arrangements of huge sets of input segments.
-
-While `Arr_non_caching_segment_traits_2` models the concept
-`ArrangementDirectionalXMonotoneTraits_2`, the implementation of
-the `Are_mergeable_2` operation does not enforce the input curves
-to have the same direction as a precondition. Moreover, `Arr_non_caching_segment_traits_2`
-supports the merging of curves of opposite directions.
-
-\cgalModels{ArrangementTraits_2,ArrangementLandmarkTraits_2,ArrangementDirectionalXMonotoneTraits_2}
-
-\sa `Arr_segment_traits_2<Kernel>`
-
-*/
-template< typename Kernel >
-class Arr_non_caching_segment_traits_2
-  : public Arr_non_caching_segment_basic_traits_2<Kernel>
- {
-public:
-
-}; /* end Arr_non_caching_segment_traits_2 */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_overlay_2.h

@@ -1,75 +1,72 @@
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2Funcs
-\ingroup PkgArrangementOnSurface2Funcs
+ * \brief Computes the overlay of two arrangements `arr1` and `arr2`, and sets
-\brief Computes the overlay of two arrangements `arr1` and `arr2`, and sets
+ * the output arrangement `res` to represent the overlaid arrangement.
-the output arrangement `res` to represent the overlaid arrangement.
+ *
+ * \details
+ * Computes the overlay of two input arrangement
+ * objects, and returns the overlaid arrangement. All three arrangements
+ * can be instantiated with different geometric traits classes and different
+ * \dcel classes (encapsulated in the various topology-traits classes).
+ * The geometry traits of the resulting arrangement is used to construct the
+ * resulting arrangement. This means that all the types (e.g.,
+ * `Traits::Point_2`, `Traits::Curve_2`, and `Traits::Point_2`)
+ * of both input arrangements have to be convertible to the types in the
+ * resulting arrangement. A given overlay-traits object is used to properly
+ * construct the overlaid \dcel that represents the resulting arrangement.
+ *
+ * \pre `res` does not refer to either `arr1` or `arr2` (that is,
+ * "self overlay" is not supported).
+ *
+ * \pre The overlay-traits object `ovl_tr` must model the `OverlayTraits`
+ *   concept, which is able to construct records of the `ResDcel` class on
+ *   the basis of the `Dcel1` and `Dcel2` records that induce them.
+ *
+ * \sa `OverlayTraits`
+ */
+template <typename GeomTraitsA, typename GeomTraitsB,
+          typename GeomTraitsRes, typename TopTraitsA,
+          typename TopTraitsB, typename TopTraitsRes,
+          typename OverlayTraits>
+void overlay(const Arrangement_2<GeomTraitsA, TopTraitsA>& arr1,
+             const Arrangement_2<GeomTraitsB, TopTraitsB>& arr2,
+             Arrangement_2<GeomTraitsRes, TopTraitsRes>& arr_res,
+             OverlayTraits& ovl_tr);
 
-\details
+/*! \ingroup PkgArrangementOnSurface2Funcs
-Computes the overlay of two input arrangement
+ * \brief
-objects, and returns the overlaid arrangement. All three arrangements
+ * Computes the overlay of two arrangements with history `arr1` and
-can be instantiated with different geometric traits classes and different
+ * `arr2`, and sets the output arrangement with history `res` to
-\dcel classes (encapsulated in the various topology-traits classes).
+ * represent the overlaid arrangement. The function also constructs a
-The geometry traits of the resulting arrangement is used to construct the
+ * consolidated set of curves that induce `res`.
-resulting arrangement. This means that all the types (e.g.,
+ *
-`Traits::Point_2`, `Traits::Curve_2`, and `Traits::Point_2`)
+ * \details
-of both input arrangements have to be convertible to the types in the
+ * Computes the overlay of two input arrangement
-resulting arrangement. A given overlay-traits object is used to properly
+ * objects, and returns the overlaid arrangement. All three arrangements
-construct the overlaid \dcel that represents the resulting arrangement.
+ * can be instantiated with different geometric traits classes and different
-
+ * \dcel classes (encapsulated in the various topology-traits classes).
-\pre `res` does not refer to either `arr1` or `arr2` (that is, "self overlay" is not supported).
+ * The geometry traits of the resulting arrangement is used to construct the
-
+ * resulting arrangement. This means that all the types (e.g.,
-\pre The overlay-traits object `ovl_tr` must model the `OverlayTraits`
+ * `Traits::Point_2`, `Traits::Curve_2`, and `Traits::Point_2`)
-  concept, which is able to construct records of the `ResDcel` class on
+ * of both input arrangements have to be convertible to the types in the
-  the basis of the `Dcel1` and `Dcel2` records that induce them.
+ * resulting arrangement. A given overlay-traits object is used to properly
-
+ * construct the overlaid \dcel that represents the resulting arrangement.
-\sa `OverlayTraits`
+ *
-*/
+ * \pre `res` does not refer to either `arr1` or `arr2` (that is,
-template <class GeomTraitsA, class GeomTraitsB,
+ * "self overlay" is not supported).
-          class GeomTraitsRes, class TopTraitsA,
+ *
-          class TopTraitsB, class TopTraitsRes,
+ * \pre The overlay-traits object `ovl_tr` must model the `OverlayTraits`
-          class OverlayTraits>
+ *   concept, which is able to construct records of the `ResDcel` class on
-void overlay (const Arrangement_2<GeomTraitsA, TopTraitsA>& arr1,
+ *   the basis of the `Dcel1` and `Dcel2` records that induce them.
-              const Arrangement_2<GeomTraitsB, TopTraitsB>& arr2,
+ *
-              Arrangement_2<GeomTraitsRes, TopTraitsRes>& arr_res,
+ * \sa `OverlayTraits`
-              OverlayTraits& ovl_tr);
+ */
-
+template <typename Traits, typename Dcel1, typename Dcel2,
-/*!
-\ingroup PkgArrangementOnSurface2Funcs
-\brief Computes the overlay of two arrangements with history `arr1` and
-`arr2`, and sets the output arrangement with history `res` to
-represent the overlaid arrangement. The function also constructs a
-consolidated set of curves that induce `res`.
-
-\details
-Computes the overlay of two input arrangement
-objects, and returns the overlaid arrangement. All three arrangements
-can be instantiated with different geometric traits classes and different
-\dcel classes (encapsulated in the various topology-traits classes).
-The geometry traits of the resulting arrangement is used to construct the
-resulting arrangement. This means that all the types (e.g.,
-`Traits::Point_2`, `Traits::Curve_2`, and `Traits::Point_2`)
-of both input arrangements have to be convertible to the types in the
-resulting arrangement. A given overlay-traits object is used to properly
-construct the overlaid \dcel that represents the resulting arrangement.
-
-\pre `res` does not refer to either `arr1` or `arr2` (that is, "self overlay" is not supported).
-
-\pre The overlay-traits object `ovl_tr` must model the `OverlayTraits`
-  concept, which is able to construct records of the `ResDcel` class on
-  the basis of the `Dcel1` and `Dcel2` records that induce them.
-
-\sa `OverlayTraits`
-
-*/
-template<typename Traits, typename Dcel1, typename Dcel2,
          typename ResDcel, typename OverlayTraits>
-void overlay (const Arrangement_with_history_2<Traits,Dcel1>& arr1,
+void overlay(const Arrangement_with_history_2<Traits,Dcel1>& arr1,
-              const Arrangement_with_history_2<Traits,Dcel2>& arr2,
+             const Arrangement_with_history_2<Traits,Dcel2>& arr2,
-              Arrangement_with_history_2<Traits,ResDcel>& res,
+             Arrangement_with_history_2<Traits,ResDcel>& res,
-              OverlayTraits& ovl_tr);
+             OverlayTraits& ovl_tr);
-
-
-
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_point_location_result.h

@@ -8,16 +8,15 @@ namespace CGAL {
  * \tparam Arrangement must be an instance of the
  * `CGAL::Arrangement_on_surface_2<GeometryTraits,Topology>` class template.
  *
- * \sa `ArrangementPointLocation_2`
+ * \sa `AosPointLocation_2`
- * \sa `ArrangementVerticalRayShoot_2`
+ * \sa `AosVerticalRayShoot_2`
  * \sa `CGAL::Arr_naive_point_location<Arrangement>`
  * \sa `CGAL::Arr_walk_along_line_point_location<Arrangement>`
  * \sa `CGAL::Arr_landmarks_point_location<Arrangement,Generator>`
  * \sa `CGAL::Arr_trapezoid_ric_point_location<Arrangement>`
  */
 template <typename Arrangement>
-struct Arr_point_location_result
+struct Arr_point_location_result {
-{
   /*! The type of the arrangement feature that is the result of a
    * point-location query or a vertical ray-shoot query, namely,
    * `std::variant<Arrangement_on_surface_2::Vertex_const_handle, Arrangement_on_surface_2::Halfedge_const_handle, Arrangement_on_surface_2::Face_const_handle>`

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_polyline_traits_2.h

@@ -30,15 +30,15 @@ namespace CGAL {
  * The type substituting the template parameter `SegmentTraits_2` when
  * the template Arr_polyline_traits_2 is instantiated must be a model
  * of the concepts
- *   - `ArrangementTraits_2`,
+ *   - `AosTraits_2`,
- *   - `ArrangementDirectionalXMonotoneTraits_2`,
+ *   - `AosDirectionalXMonotoneTraits_2`,
- *   - `ArrangementConstructXMonotoneCurveTraits_2`,
+ *   - `AosConstructXMonotoneCurveTraits_2`,
- *   - `ArrangementConstructCurveTraits_2`.
+ *   - `AosConstructCurveTraits_2`.
  *
  * If, in addition, the GeometryTraits_2 models the concept
- * `ArrangementApproximateTraits_2` then `Arr_polycurve_traits_2` models
+ * `AosApproximateTraits_2` (or `AosApproximatePointTraits_2`) then
- * this concept as well. The same holds for the concept
+ * `Arr_polycurve_traits_2` models this concept as well. The same holds for the
- * `ArrangementOpenBoundaryTraits_2`. If no type is provided, then
+ * concept `AosOpenBoundaryTraits_2`. If no type is provided, then
  * `Arr_segment_traits_2` (instantiated with
  * `Exact_predicates_exact_constructions_kernel` as the kernel) is used.
  * Otherwise,
@@ -52,17 +52,17 @@ namespace CGAL {
  *
  * The number type used by the injected segment traits should support exact
  * rational arithmetic (that is, the number type should support the arithmetic
- * operations \f$ +\f$, \f$ -\f$, \f$ \times\f$ and \f$ \div\f$ carried out
+ * operations \f$+\f$, \f$-\f$, \f$\times\f$ and \f$\div\f$ carried out
  * without loss of precision), in order to avoid robustness problems, although
  * other inexact number types could be used at the user's own risk.
  *
- * A polyline that comprises \f$n > 0\f$ segments has \f$ n+1 \f$ points, and
+ * A polyline that comprises \f$n > 0\f$ segments has \f$n+1\f$ points, and
- * they are represented as objects of type `SegmentTraits_2::Point_2`. Since the
+ * they are represented as objects of type `SegmentTraits_2::Point_2`. Since
- * notion of a \a vertex is reserved to 0-dimensional elements of an
+ * the notion of a \a vertex is reserved to 0-dimensional elements of an
  * arrangement, we use, in this context, the notion of \a points in order to
- * refer to the vertices of a polyline. For example, an arrangement induced by a
+ * refer to the vertices of a polyline. For example, an arrangement induced by
- * single non-self intersecting polyline has exactly two vertices regardless of
+ * a single non-self intersecting polyline has exactly two vertices regardless
- * the number of points. Finally, the types `Segment_2` and
+ * of the number of points. Finally, the types `Segment_2` and
  * `X_monotone_segment_2` nested in `Arr_polyline_traits_2` are nothing but
  * `SegmentTraits_2::Curve_2` and `SegmentTraits_2::X_monotone_curve_2`,
  * respectively.
@@ -77,9 +77,9 @@ namespace CGAL {
  * the macro `CGAL_ALWAYS_LEFT_TO_RIGHT` to 1 before any \cgal header is
  * included.
  *
- * \cgalModels{ArrangementTraits_2,ArrangementDirectionalXMonotoneTraits_2,`ArrangementConstructXMonotoneCurveTraits_2`
+ * \cgalModels{AosTraits_2,AosDirectionalXMonotoneTraits_2,AosConstructXMonotoneCurveTraits_2,AosConstructCurveTraits_2,AosApproximateTraits_2
- *             ArrangementConstructCurveTraits_2,ArrangementApproximateTraits_2 (if the type that substitutes
+ * (if the type that substitutes the template parameter `SegmentTraits_2`
- *   the template parameter `SegmentTraits_2` models the concept as well)}
+ * models the concept as well)}
  *
  * \sa `Arr_polycurve_traits_2<SubcurveTraits_2>`
  * \sa `Arr_Bezier_curve_traits_2<RatKernel, AlgKernel, NtTraits>`
@@ -91,22 +91,23 @@ namespace CGAL {
  * \sa `CGAL_ALWAYS_LEFT_TO_RIGHT`
  */
 template <typename SegmentTraits_2>
-class Arr_polyline_traits_2 : public Arr_polycurve_traits_2<SegmentTraits_2>{
+class Arr_polyline_traits_2 : public Arr_polycurve_traits_2<SegmentTraits_2> {
 public:
-
   /// \name Types
   /// @{
-  /*!
+
-   */
+  ///
   typedef SegmentTraits_2                             Segment_traits_2;
-  // TODO: Have to turn these into links, so whenever I mention Point_2 it
+
-  //       will point here and *not* to Kernel::Point_2 for instance.
+  ///
   typedef SegmentTraits_2::Point_2                    Point_2;
 
-  /*!
+  ///
-   */
   typedef SegmentTraits_2::Curve_2                    Segment_2;
+
+  ///
   typedef SegmentTraits_2::X_monotone_curve_2         X_monotone_segment_2;
+
   /// @}
 
   /*! The `Curve_2` type nested within the traits class respresnts
@@ -114,18 +115,18 @@ public:
    */
   class Curve_2 {
   public:
-    //! Const iterator of subcurves.
+    /// Const iterator of subcurves.
     typedef std::vector<X_monotone_segment_2>::const_iterator
       Segment_const_iterator;
 
-    //! Reverse const iterator of subcurves.
+    /// Reverse const iterator of subcurves.
     typedef std::reverse_iterator<Segment_const_iterator>
       Segment_const_reverse_iterator;
 
-    //! constructs default.
+    /// constructs default.
     Curve_2();
 
-    //! constructs from a subcurve.
+    /// constructs from a subcurve.
     Curve_2(const Segment_2& seg);
 
     /*! constructs a polyline from a range of subcurves.
@@ -137,16 +138,16 @@ public:
     template <typename InputIterator>
     void Curve_2(InputIterator begin, InputIterator end);
 
-    //! obtains an iterator for the polycurve subcurves.
+    /// obtains an iterator for the polycurve subcurves.
     Segment_const_iterator begin_segments() const;
 
-    //! obtains a past-the-end iterator for the polycurve subcurves.
+    /// obtains a past-the-end iterator for the polycurve subcurves.
     Segment_const_iterator end_segments() const;
 
-    //! obtains the first reverse iterator of the polyline subcurves.
+    /// obtains the first reverse iterator of the polyline subcurves.
     Segment_const_reverse_iterator rbegin_segments() const;
 
-    //! obtains the past-the-end reverse iterator for the polyline points.
+    /// obtains the past-the-end reverse iterator for the polyline points.
     Segment_const_reverse_iterator rend_segments() const;
 
     /*! obtains the number of subcurves that comprise the poyline.
@@ -161,11 +162,11 @@ public:
   class X_monotone_curve_2 {
   public:
 
-    //! Const iterator of subcurves.
+    /// Const iterator of subcurves.
     typedef std::vector<X_monotone_segment_2>::const_iterator
       Segment_const_iterator;
 
-    //! Reverse const iterator of subcurves.
+    /// Reverse const iterator of subcurves.
     typedef std::reverse_iterator<Segment_const_iterator>
       Segment_const_reverse_iterator;
 
@@ -177,8 +178,8 @@ public:
 
     /*! constructs from a range.  Similar to the constructor of a general
      * polycurve.  Like in the case of general polycurve, for the sake of
-     * backwards compatibility we have to keep an implementation of construction
+     * backwards compatibility we have to keep an implementation of
-     * from a range of points. DO NOT USE THIS CONSTRUCTION.
+     * construction from a range of points. DO NOT USE THIS CONSTRUCTION.
      */
     template <typename InputIterator>
     X_monotone_curve_2(InputIterator begin, InputIterator end);
@@ -222,15 +223,15 @@ public:
     /*! obtains a polyline connecting the two given endpoints.
      * \param p The first point.
      * \param q The second point.
-     * \pre `p` and `q` are distinct.
      * \return A segment connecting `p` and `q`.
+     * \pre `p` and `q` are distinct.
      */
     Curve_2 operator()(const Point_2& p, const Point_2& q) const;
 
     /*! obtains a polyline that comprises of one given segment.
      * \param seg input segment
-     * \pre `seg` is not degenerated (not tested)
      * \return A polyline with one segment, namely `seg`.
+     * \pre `seg` is not degenerated (not tested)
      */
     Curve_2 operator()(const Segment_2& seg) const;
 
@@ -239,10 +240,10 @@ public:
      *
      * \param begin iterator pointing to the first element in the range.
      * \param end iterator pointing to the past-the-end element in the range.
+     * \return A polyline using the corresponding construction implementation.
      * \pre The given range form a continuous and well-oriented polyline
      *      (not tested).
      * \pre Contains no degenerated segments (not tested)
-     * \return A polyline using the corresponding construction implementation.
      */
     template <typename ForwardIterator>
     Curve_2 operator()(ForwardIterator begin, ForwardIterator end) const;
@@ -272,7 +273,7 @@ public:
 
     /*! appends a point `p` to an existing polyline `cv` at the back.
      * \param cv a polyline. Note, `cv` is not (necessarily)
-     *        \f$ x\f$-monotone.
+     *        \f$x\f$-monotone.
      * \param p a point to be appended to `cv` at the back.
      * \pre `cv` contains at least one segment.
      */
@@ -322,7 +323,7 @@ public:
 
     /*! appends a point `p` to an existing polyline `cv` at the front.
      * \param cv a polyline. Note, `cv` is not (necessarily)
-     *        \f$ x\f$-monotone.
+     *        \f$x\f$-monotone.
      * \param p a point to be appended to `cv` at the back.
      * \pre `cv` contains at least one segment.
      */
@@ -382,7 +383,6 @@ public:
   Push_front_2 push_front_2_object() const;
 
   /// @} /* End Accessing Functor Objects */
-
 }; /* end Arr_polyline_traits_2 */
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_rational_function_traits_2.h

@@ -1,30 +1,28 @@
-
 namespace CGAL {
 
 /*! \ingroup PkgArrangementOnSurface2TraitsClasses
  *
  * The traits class `Arr_rational_function_traits_2` is a model of the
- * `ArrangementTraits_2` concept. It handles bounded and unbounded arcs of
+ * `AosTraits_2` concept. It handles bounded and unbounded arcs of
  * rational functions, referred to as <i>rational arcs</i> (in particular, such
  * an arc may correspond to the entire graph of a rational function). It
  * supports bounded and unbounded arcs. Thus, it is also a model of the concept
- * `ArrangementOpenBoundaryTraits_2`. The traits class enables the construction
+ * `AosOpenBoundaryTraits_2`. The traits class enables the construction
  * and maintenance of arrangements of such arcs.
  *
  * A rational function \f$y = \frac{P(x)}{Q(x)}\f$ is defined by two polynomials
  * \f$P\f$ and \f$Q\f$ of arbitrary degrees.  If \f$Q(x) = 1\f$ then the
  * function is a simple polynomial function.  Usually the domain is
  * \f$\mathbb{R}\f$ but the function may also be restricted to a bounded
- * interval \f$[x_{\rm min}, x_{\rm max}]\f$ or defined over a ray \f$(-\infty,
+ * interval \f$[x_{\rm min}, x_{\rm max}]\f$ or defined over a ray
- * x_{\rm max}]\f$ or over \f$[x_{\rm min}, \infty)\f$.  Rational functions are
+ * \f$(-\infty,x_{\rm max}]\f$ or over \f$[x_{\rm min}, \infty)\f$.  Rational
- * represented by the nested type `Curve_2`.  Note that a rational function may
+ * functions are represented by the nested type `Curve_2`.  Note that a rational
- * be not continuous since roots of \f$Q\f$ induce vertical asymptotes, which
+ * function may be not continuous since roots of \f$Q\f$ induce vertical asymptotes,
- * would contradict the notion of an \f$x\f$-monotone curve as it is introduced
+ * which would contradict the notion of an \f$x\f$-monotone curve as it is introduced
- * by the `ArrangementTraits_2` concept.  Thus, continuous portions of rational
+ * by the `AosTraits_2` concept.  Thus, continuous portions of rational functions are
- * functions are represented by the nested type `X_monotone_curve_2`, which is
+ * represented by the nested type `X_monotone_curve_2`, which is different from
- * different from `Curve_2`.  Constructors for both classes are provided by the
+ * `Curve_2`.  Constructors for both classes are provided by the traits.  A `Curve_2`
- * traits.  A `Curve_2` may be split up into several `X_monotone_curve_2` using
+ * may be split up into several `X_monotone_curve_2` using `Make_x_monotone_2`.
- * `Make_x_monotone_2`.
  *
  * The template parameter of the traits must be a model of the concept
  * `AlgebraicKernel_d_1`.  A rational function is then represented by two
@@ -44,12 +42,12 @@ namespace CGAL {
  * cleans up the cache on demand.
  *
  * While `Arr_rational_function_traits_2` models the concept
- * `ArrangementDirectionalXMonotoneTraits_2`, the implementation of the
+ * `AosDirectionalXMonotoneTraits_2`, the implementation of the
  * `Are_mergeable_2` operation does not enforce the input curves to have the
  * same direction as a precondition. Moreover, `Arr_rational_function_traits_2`
  * supports the merging of curves of opposite directions.
  *
- * \cgalModels{ArrangementTraits_2,ArrangementDirectionalXMonotoneTraits_2,ArrangementOpenBoundaryTraits_2}
+ * \cgalModels{AosTraits_2,AosDirectionalXMonotoneTraits_2,AosOpenBoundaryTraits_2}
  */
 template <typename AlgebraicKernel_d_1>
 class Arr_rational_function_traits_2 {
@@ -57,24 +55,19 @@ public:
   /// \name Types
   /// @{
 
-  /*!
+  ///
-   */
   typedef AlgebraicKernel_d_1 Algebraic_kernel_d_1;
 
-  /*!
+  ///
-   */
   typedef AlgebraicKernel_d_1::Coefficient Coefficient;
 
-  /*!
+  ///
-   */
   typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;
 
-  /*!
+  ///
-   */
   typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;
 
-  /*!
+  ///
-   */
   typedef AlgebraicKernel_d_1::Bound Bound;
 
   /// @}
@@ -83,7 +76,7 @@ public:
   /// @{
 
   /*! constructs an empty traits that uses the kernel pointed by `kernel`
-   *  for performing algebraic operations.
+   * for performing algebraic operations.
    */
   Arr_rational_function_traits_2<AlgebraicKernel_d_1>(const Algebraic_kernel_d_1* kernel);
 
@@ -116,34 +109,27 @@ public:
    *
    * \cgalModels{Assignable,CopyConstructible,AdaptableBinaryFunction,AdaptableUnaryFunction}
    */
-
   class Construct_curve_2 {
   public:
     /// \name Types
     /// @{
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;
 
-    /*!
+    ///
-     */
     typedef Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Curve_2 result_type;
 
-    /*!
+    ///
-     */
     typedef Polynomial_1 argument_type;
 
-    /*!
+    ///
-     */
     typedef Polynomial_1 first_argument_type;
 
-    /*!
+    ///
-     */
     typedef Polynomial_1 second_argument_type;
 
     /// @}
@@ -156,7 +142,7 @@ public:
     Curve_2 operator()(Polynomial_1 P) const;
 
     /*! constructs a curve representing the polynomial function \f$y = P(x)\f$.
-     * The function is defined over the interval \f$[x,+\infty)\f$ if \f$ right\f$
+     * The function is defined over the interval \f$[x,+\infty)\f$ if \f$right\f$
      * is true and \f$(-\infty,x]\f$ otherwise.
      */
     Curve_2 operator()(Polynomial_1 P, const Algebraic_real_1& x,
@@ -174,8 +160,8 @@ public:
 
     /*! constructs a curve representing the rational function \f$y = P(x)/Q(x)\f$.
      * The function is defined over the interval
-     * \f$ I=[x,+\infty)\f$ if \f$ right\f$ is true and
+     * \f$I=[x,+\infty)\f$ if \f$right\f$ is true and
-     * \f$ I=(-\infty,x]\f$ otherwise.
+     * \f$I=(-\infty,x]\f$ otherwise.
      */
     Curve_2 operator()(Polynomial_1 P, Polynomial_1 Q,
                        const Algebraic_real_1& x, bool right) const;
@@ -196,8 +182,7 @@ public:
     /*! constructs a curve representing the polynomial function \f$y = P(x)\f$,
      * where the coefficients of \f$P\f$ are given in the range `[begin,end)`.
      * The function is defined over the interval
-     * \f$[x,+\infty)\f$ if \f$ right\f$ is true and \f$(-\infty,x]\f$
+     * \f$[x,+\infty)\f$ if \f$right\f$ is true and \f$(-\infty,x]\f$ otherwise.
-     * otherwise.
      */
     template <typename InputIterator>
     Curve_2 operator()(InputIterator begin, InputIterator end,
@@ -221,7 +206,7 @@ public:
                        InputIterator begin_denom, InputIterator end_denom) const;
 
     /*! constructs a curve representing the rational function \f$y = P(x)/Q(x)\f$,
-     * where the coefficients of \f$P\f$ and \f$ Q\f$ are given in the ranges
+     * where the coefficients of \f$P\f$ and \f$Q\f$ are given in the ranges
      * `[begin_numer,end_numer)` and `[begin_denom,end_denom)`, respectively.
      * The function is defined over the interval \f$I=[x,+\infty)\f$
      * if \f$right\f$ is true and \f$I=(-\infty,x]\f$ otherwise.
@@ -243,7 +228,6 @@ public:
                        const Algebraic_real_1& upper) const;
 
     /// @}
-
   }; /* end Arr_rational_function_traits_2::Construct_curve_2 */
 
   /*! Functor to construct a `X_monotone_curve_2`. To enable caching the class is
@@ -254,32 +238,25 @@ public:
    */
   class Construct_x_monotone_curve_2 {
   public:
-
     /// \name Types
     /// @{
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;
 
-    /*!
+    ///
-     */
     typedef Arr_rational_function_traits_2<AlgebraicKernel_d_1>::X_monotone_curve_2 result_type;
 
-    /*!
+    ///
-     */
     typedef Polynomial_1 argument_type;
 
-    /*!
+    ///
-     */
     typedef Polynomial_1 first_argument_type;
 
-    /*!
+    ///
-     */
     typedef Polynomial_1 second_argument_type;
 
     /// @}
@@ -287,14 +264,14 @@ public:
     /// \name Operations
     /// @{
 
-    /*! constructs an \f$ x\f$-monotone curve supported by the polynomial function
+    /*! constructs an \f$x\f$-monotone curve supported by the polynomial function
-     * \f$ y = P(x)\f$.
+     * \f$y = P(x)\f$.
      */
     X_monotone_curve_2 operator()(Polynomial_1 P) const;
 
     /*! constructs an \f$x\f$-monotone curve supported by the polynomial function
      * \f$y = P(x)\f$. The function is defined over the interval
-     * \f$[x,+\infty)\f$ if \f$ right\f$ is true and \f$(-\infty,x]\f$
+     * \f$[x,+\infty)\f$ if \f$right\f$ is true and \f$(-\infty,x]\f$
      * otherwise.
      */
     X_monotone_curve_2 operator()(Polynomial_1 P,
@@ -311,14 +288,16 @@ public:
 
     /*! constructs an \f$x\f$-monotone curve supported by the rational function
      * \f$y = P(x)/Q(x)\f$.
+     *
      * \pre \f$Q\f$ has no real roots.
      */
     X_monotone_curve_2 operator()(Polynomial_1 P, Polynomial_1 Q) const;
 
     /*! constructs an \f$x\f$-monotone curve supported by the rational function
      * \f$y = P(x)/Q(x)\f$. The function is defined over the interval
-     * \f$I=[x,+\infty)\f$ if \f$ right\f$ is true and \f$I=(-\infty,x]\f$
+     * \f$I=[x,+\infty)\f$ if \f$right\f$ is true and \f$I=(-\infty,x]\f$
      * otherwise.
+     *
      * \pre \f$Q\f$ has no real roots in the interior of \f$I\f$.
      */
     X_monotone_curve_2 operator()(Polynomial_1 P, Polynomial_1 Q,
@@ -334,8 +313,8 @@ public:
                                   const Algebraic_real_1& lower,
                                   const Algebraic_real_1& upper) const;
 
-    /*! constructs an \f$ x\f$-monotone curve supported by the polynomial function
+    /*! constructs an \f$x\f$-monotone curve supported by the polynomial function
-     * \f$ y = P(x)\f$, where the coefficients of \f$P\f$ are given in the range
+     * \f$y = P(x)\f$, where the coefficients of \f$P\f$ are given in the range
      * `[begin,end)`.
      */
     template <typename InputIterator>
@@ -376,9 +355,10 @@ public:
      * \f$y = P(x)/Q(x)\f$, where the coefficients of \f$P\f$ and \f$Q\f$ are
      * given in the ranges `[begin_numer,end_numer)` and
      * `[begin_denom,end_denom)`, respectively. The function is defined over the
-     * interval \f$ I=[x,+\infty)\f$ if \f$ right\f$ is true and
+     * interval \f$I=[x,+\infty)\f$ if \f$right\f$ is true and
-     * \f$ I=(-\infty,x]\f$ otherwise.
+     * \f$I=(-\infty,x]\f$ otherwise.
-     * \pre \f$ Q\f$ has no real roots in the interior of \f$ I\f$.
+     *
+     * \pre \f$Q\f$ has no real roots in the interior of \f$I\f$.
      */
     template <typename InputIterator>
     X_monotone_curve_2 operator()(InputIterator begin_numer,
@@ -388,7 +368,7 @@ public:
                                   const Algebraic_real_1& x, bool right) const;
 
     /*! constructs an \f$x\f$-monotone curve supported by the rational function
-     * \f$y = P(x)/Q(x)\f$, where the coefficients of \f$ P\f$ and \f$Q\f$ are
+     * \f$y = P(x)/Q(x)\f$, where the coefficients of \f$P\f$ and \f$Q\f$ are
      * given in the ranges `[begin_numer,end_numer)` and
      * `[begin_denom,end_denom)`, respectively. The function is defined over the
      * interval \f$I=[lower,upper]\f$.
@@ -403,7 +383,6 @@ public:
                                   const Algebraic_real_1& upper) const;
 
     /// @}
-
   }; /* end Arr_rational_function_traits_2::Construct_x_monotone_curve_2 */
 
   /*! The `Curve_2` class nested within the traits is used to represent rational
@@ -413,16 +392,13 @@ public:
    */
   class Curve_2 {
   public:
-
     /// \name Types
     /// @{
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;
 
     /// @}
@@ -432,11 +408,11 @@ public:
 
     /*! returns the numerator of the supporting rational function.
      */
-    const Polynomial_1& numerator () const;
+    const Polynomial_1& numerator() const;
 
     /*! returns the denominator of the supporting rational function.
      */
-    const Polynomial_1& denominator () const;
+    const Polynomial_1& denominator() const;
 
     /*! returns whether &ccedil;urve is continuous, namely whether it does not
      * contains any vertical asymptotes in its interior.
@@ -446,19 +422,21 @@ public:
     /*! returns whether the \f$x\f$-coordinate of &ccedil;urve's left end is
      * finite or whether it is \f$\pm\infty\f$.
      */
-    Arr_parameter_space left_parameter_space_in_x () const;
+    Arr_parameter_space left_parameter_space_in_x() const;
 
     /*! returns whether the \f$x\f$-coordinate of &ccedil;urve's right end is
      * finite or whether it is \f$\pm\infty\f$.
      */
-    Arr_parameter_space right_parameter_space_in_x () const;
+    Arr_parameter_space right_parameter_space_in_x() const;
 
     /*! returns the \f$x\f$-coordinate of the left end.
+     *
      * \pre `left_boundary_in_x()` == `ARR_INTERIOR`
      */
     Algebraic_real_1 left_x() const;
 
     /*! returns the \f$x\f$-coordinate of the right end.
+     *
      * \pre `right_boundary_in_x()` == `ARR_INTERIOR`
      */
     Algebraic_real_1 right_x() const;
@@ -475,16 +453,13 @@ public:
     /// \name Types
     /// @{
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Bound Bound;
 
     /// @}
@@ -494,22 +469,22 @@ public:
 
     /*! returns the numerator of the supporting rational function.
      */
-    Polynomial_1 numerator () const;
+    Polynomial_1 numerator() const;
 
     /*! returns the denominator of the supporting rational function.
      */
-    Polynomial_1 denominator () const;
+    Polynomial_1 denominator() const;
 
     /*! returns double-approximations of the x- and y-coordinates.
      */
     std::pair<double,double> to_double() const;
 
-    /*! returns the \f$ x\f$-coordinate of the point.
+    /*! returns the \f$x\f$-coordinate of the point.
      */
     Algebraic_real_1 x() const;
 
     /*! obtains the \f$y\f$-coordinates of the point. <B>Attention:</B> As
-     * described above, points are not stored by their y-coordinate in
+     * described above, points are not stored by their \f$y\f$-coordinate in
      * `Algebraic_real_1` representation. In fact, this representation must be
      * computed on demand, and might become quite costly for points defined by
      * high-degree polynomials.  Therefore, it is recommended to avoid calls to
@@ -519,27 +494,31 @@ public:
 
     /*! Computes a pair \f$p\f$ approximating the \f$x\f$-coordinate with
      * respect to the given absolute precision \f$a\f$.
+     *
      * \post \f$p.first \leq x \leq p.second\f$
-     * \post \f$p.second - p.first \leq2^{-a}\f$
+     * \post \f$p.second - p.first \leq 2^{-a}\f$
      */
     std::pair<Bound,Bound> approximate_absolute_x(int a) const;
 
     /*! Computes a pair \f$p\f$ approximating the \f$y\f$-coordinate with
      * respect to the given absolute precision \f$a\f$.
+     *
      * \post \f$p.first \leq y \leq p.second\f$
-     * \post \f$p.second - p.first \leq2^{-a}\f$
+     * \post \f$p.second - p.first \leq 2^{-a}\f$
      */
     std::pair<Bound,Bound> approximate_absolute_y(int a) const;
 
     /*! Computes a pair \f$p\f$ approximating the \f$x\f$-coordinate with
      * respect to the given relative precision \f$r\f$.
+     *
      * \post \f$p.first \leq x \leq p.second\f$
      * \post \f$p.second - p.first \leq2^{-r}|x|\f$
      */
     std::pair<Bound,Bound> approximate_relative_x(int r) const;
 
-    /*! Computes a pair \f$p\f$ approximating the \f$ y\f$-coordinate with
+    /*! computes a pair \f$p\f$ approximating the \f$y\f$-coordinate with
      * respect to the given relative precision \f$r\f$.
+     *
      * \post \f$p.first \leq y \leq p.second\f$
      * \post \f$p.second - p.first \leq2^{-r}|y|\f$
      */
@@ -550,7 +529,7 @@ public:
   }; /* end Arr_rational_function_traits_2::Point_2 */
 
   /*! The `X_monotone_curve_2` class nested within the traits is used to represent
-   * \f$ x\f$-monotone parts of rational functions. In particular, such an
+   * \f$x\f$-monotone parts of rational functions. In particular, such as
    * \f$x\f$-monotone curve may not contain a vertical asymptote in its interior
    * \f$x\f$-range.
    *
@@ -558,20 +537,16 @@ public:
    */
   class X_monotone_curve_2 {
   public:
-
     /// \name Types
     /// @{
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1;
 
-    /*!
+    ///
-     */
     typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1;
 
-    /*!
+    ///
-     */
     typedef Arr_rational_function_traits_2<AlgebraicKernel_d_1>::Point_2 Point_2;
 
     /// @}
@@ -581,21 +556,21 @@ public:
 
     /*! returns the numerator of the supporting rational function.
      */
-    const Polynomial_1& numerator () const;
+    const Polynomial_1& numerator() const;
 
     /*! returns the denominator of the supporting rational function.
      */
-    const Polynomial_1& denominator () const;
+    const Polynomial_1& denominator() const;
 
     /*! returns whether the \f$x\f$-coordinate of the source is finite or
      * whether it is \f$\pm\infty\f$.
      */
-    Arr_parameter_space source_parameter_space_in_x () const;
+    Arr_parameter_space source_parameter_space_in_x() const;
 
     /*! returns whether the \f$y\f$-coordinate of the source is finite or
      * whether it is \f$\pm\infty\f$.
      */
-    Arr_parameter_space source_parameter_space_in_y () const;
+    Arr_parameter_space source_parameter_space_in_y() const;
 
     /*! returns the source point of the arc.
      * \pre Both the \f$x\f$- and \f$y\f$-coordinates of the source point is
@@ -604,6 +579,7 @@ public:
     const Point_2& source() const;
 
     /*! returns the \f$x\f$-coordinate of the source point.
+     *
      * \pre The \f$x\f$-coordinate of the source point is finite.
      */
     Algebraic_real_1 source_x() const;
@@ -611,12 +587,12 @@ public:
     /*! returns whether the \f$x\f$-coordinate of the target is finite or
      * whether it is \f$\pm\infty\f$.
      */
-    Arr_parameter_space target_parameter_space_in_x () const;
+    Arr_parameter_space target_parameter_space_in_x() const;
 
     /*! returns whether the \f$y\f$-coordinate of the target is finite or
      * whether it is \f$\pm\infty\f$.
      */
-    Arr_parameter_space target_parameter_space_in_y () const;
+    Arr_parameter_space target_parameter_space_in_y() const;
 
     /*! returns the target point of the arc.
      * \pre Both the \f$x\f$- and \f$y\f$-coordinates of the target point is
@@ -625,6 +601,7 @@ public:
     const Point_2& target() const;
 
     /*! returns the \f$x\f$-coordinate of the target point.
+     *
      * \pre The \f$x\f$-coordinate of the target point is finite.
      */
     Algebraic_real_1 target_x() const;
@@ -632,19 +609,21 @@ public:
     /*! returns whether the \f$x\f$-coordinate of the left curve end is finite or
      * whether it is \f$\pm\infty\f$.
      */
-    Arr_parameter_space left_parameter_space_in_x () const;
+    Arr_parameter_space left_parameter_space_in_x() const;
 
     /*! returns whether the \f$y\f$-coordinate of the left curve end is finite or
      * whether it is \f$\pm\infty\f$.
      */
-    Arr_parameter_space left_parameter_space_in_y () const;
+    Arr_parameter_space left_parameter_space_in_y() const;
 
     /*! returns the left point of the arc.
+     *
      * \pre Both the \f$x\f$- and \f$y\f$-coordinates of the left point is finite.
      */
     const Point_2& left() const;
 
     /*! returns the \f$x\f$-coordinate of the left point.
+     *
      * \pre The \f$x\f$-coordinate of the left point is finite.
      */
     Algebraic_real_1 left_x() const;
@@ -666,18 +645,18 @@ public:
     const Point_2& right() const;
 
     /*! returns the \f$x\f$-coordinate of the right point.
+     *
      * \pre The \f$x\f$-coordinate of the right point is finite.
      */
     Algebraic_real_1 right_x() const;
 
     /*! returns whether the curve is oriented from left to right.
      */
-    bool is_left_to_right () const;
+    bool is_left_to_right() const;
 
     /// @}
 
   }; /* end Arr_rational_function_traits_2::X_monotone_curve_2 */
-
 }; /* end Arr_rational_function_traits_2 */
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_segment_traits_2.h

@@ -3,12 +3,12 @@ namespace CGAL {
 /*! \ingroup PkgArrangementOnSurface2TraitsClasses
  *
  * The traits class `Arr_segment_traits_2` is a model of the
- * `ArrangementTraits_2` concept, which allows the construction and maintenance
+ * `AosTraits_2` concept, which allows the construction and maintenance
  * of arrangements of line segments. It is parameterized with a
  * \cgal-kernel model that is templated in turn with a number type. To avoid
  * numerical errors and robustness problems, the number type should support
  * exact rational arithmetic; that is, the number type should support the
- * arithmetic operations \f$ +\f$, \f$ -\f$, \f$ \times\f$ and \f$ \div\f$
+ * arithmetic operations \f$+\f$, \f$-\f$, \f$\times\f$ and \f$\div\f$
  * carried out without loss of precision.
  *
  * For example, instantiating the traits template with kernels that support
@@ -30,7 +30,7 @@ namespace CGAL {
  * endpoints only, while the traits class needs to store extra data with its
  * segments, in order to efficiently operate on them. Nevertheless, the nested
  * `X_monotone_curve_2` and `Curve_2` types (in this case both types refer to
- * the same class, as <I>every</I> line segment is (weakly) \f$ x\f$-monotone)
+ * the same class, as <I>every</I> line segment is (weakly) \f$x\f$-monotone)
  * can however be converted to the type `Kernel::Segment_2`.
  *
  * `Arr_segment_traits_2` achieves faster running times than the
@@ -47,81 +47,82 @@ namespace CGAL {
  * `Arr_non_caching_segment_traits_2` traits-class.
  *
  * While `Arr_segment_traits_2` models the concept
- * `ArrangementDirectionalXMonotoneTraits_2`, the implementation of the
+ * `AosDirectionalXMonotoneTraits_2`, the implementation of the
  * `Are_mergeable_2` operation does not enforce the input curves to have the
  * same direction as a precondition. Moreover, `Arr_segment_traits_2` supports
  * the merging of curves of opposite directions.
  *
- * \cgalModels{ArrangementTraits_2,ArrangementLandmarkTraits_2,ArrangementDirectionalXMonotoneTraits_2}
+ * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosApproximateTraits_2,AosDirectionalXMonotoneTraits_2}
  */
 template <typename Kernel>
 class Arr_segment_traits_2 : public Kernel {
 public:
+  /// \name Types
+  /// @{
 
-  //! \name Types
+  /// the segment type.
-  //! @{
-
-  //! the segment type.
   typedef typename Kernel::Segment_2            Segment_2;
 
-  //! the line type.
+  /// the line type.
   typedef typename Kernel::Line_2               Line_2;
 
-  //! the point type.
+  /// the point type.
   typedef typename Kernel::Point_2              Point_2;
 
-  //! @}
+  /// @}
 
   /*! The `X_monotone_curve_2` class nested within the traits class is
    * used to represent segments.
    */
   class X_monotone_curve_2 {
   public:
-    //! \name Creation
+    /// \name Creation
-    //! @{
+    /// @{
 
     /*! constructs default. */
     X_monotone_curve_2();
 
-    //! @}
+    /// @}
 
-    //! \name Access Functions
+    /// \name Access Functions
-    //! @{
+    /// @{
 
-    //! obtains the (lexicographically) left endpoint.
+    /// obtains the (lexicographically) left endpoint.
     const Point_2& left() const;
 
-    //! obtains the (lexicographically) right endpoint.
+    /// obtains the (lexicographically) right endpoint.
     const Point_2& right() const;
 
-    //! obtains the supporting line.
+    /// obtains the supporting line.
     const Line_2& line() const;
 
-    //! determines whether the curve is vertical.
+    /// determines whether the curve is vertical.
     bool is_vertical() const;
 
-    //! determines whether the curve is directed lexicographic from left to right
+    /// determines whether the curve is directed lexicographic from left to right
     bool is_directed_right() const;
 
-    //! @}
+    /// @}
   };
 
-  //! The curve type.
+  /// The curve type.
   typedef X_monotone_curve_2                    Curve_2;
 
-  //! A functor that trims curves.
+  /// A functor that trims curves.
   class Trim_2 {
   public:
-    //! \name Creation
+    /// \name Creation
-    //! @{
+    /// @{
 
-    /*! trims the given x-monotone curve to an from src to tgt.
+    /*! trims the given \f$x\f$-monotone curve to an from `src` to `tgt`.
+     *
      * \ pre `src` and `tgt` lies on the curve
      */
     X_monotone_curve_2(const X_monotone_curve_2& xcv,
                        const Point_2& src, const Point_2& tgt) const;
 
+    //! @}
   } /* end Arr_segment_traits_2::Trim_2 */
-
 }; /* end Arr_segment_traits_2 */
+
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_spherical_topology_traits_2.h

@@ -10,18 +10,18 @@ namespace CGAL {
  * The `Arr_spherical_topology_traits_2` template has two parameters:
  * <UL>
  * <LI>The `GeometryTraits_2` template-parameter should be substituted by
- * a model of the `ArrangementBasicTraits_2` concept. The traits
+ * a model of the `AosBasicTraits_2` concept. The traits
  * class defines the types of \f$x\f$-monotone curves and two-dimensional
- * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
+ * points, namely `AosBasicTraits_2::X_monotone_curve_2` and
- * `ArrangementBasicTraits_2::Point_2`,
+ * `AosBasicTraits_2::Point_2`,
  *   respectively, and supports basic geometric predicates on them.
  * <LI>The `Dcel` template-parameter should be substituted by
- * a class that is a model of the `ArrangementDcel` concept. The
+ * a class that is a model of the `AosDcel` concept. The
  * value of this parameter is by default
  * `Arr_default_dcel<Traits>`.
  * </UL>
  *
- * \cgalModels{ArrangementBasicTopologyTraits}
+ * \cgalModels{AosBasicTopologyTraits}
  *
  * \sa `Arr_default_dcel<Traits>`
  * \sa `CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel,x,y>`
@@ -62,10 +62,10 @@ public:
   /// \name Accessors
   /// @{
 
-  /*! obtains the DCEL (const version). */
+  /*! obtains the \dcel (const version). */
   const Dcel& dcel() const;
 
-  /*! obtains the DCEL (non-const version). */
+  /*! obtains the \dcel (non-const version). */
   Dcel& dcel();
 
   /*! obtains the spherical face (const version). */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_tags.h

@@ -17,14 +17,10 @@ namespace CGAL {
  * \sa `Arr_closed_side_tag`
  * \sa `Arr_contracted_side_tag`
  * \sa `Arr_identified_side_tag`
- * \sa `ArrangementBasicTraits_2`
+ * \sa `AosBasicTraits_2`
  */
 struct Arr_oblivious_side_tag {};
 
-}
-
-namespace CGAL {
-
 /*! \ingroup PkgArrangementOnSurface2Tags
  *
  * This type tag is used to indicate that a side of the parameter space, either
@@ -35,7 +31,7 @@ namespace CGAL {
  * `Bottom_side_category`, and `Top_side_category`, nested in every geometry
  * traits class, must be convertible to the type `Arr_open_side_tag`. For
  * example, all categories above, nested in every model of the
- * `ArrangementOpenBoundaryTraits_2` concept, must be convertible to
+ * `AosOpenBoundaryTraits_2` concept, must be convertible to
  * `Arr_open_side_tag`, as curves are expected to approach all the four boundary
  * sides of the parameter space (i.e., left, right, bottom, and top).
  *
@@ -46,14 +42,10 @@ namespace CGAL {
  * \sa `Arr_closed_side_tag`
  * \sa `Arr_contracted_side_tag`
  * \sa `Arr_identified_side_tag`
- * \sa `ArrangementOpenBoundaryTraits_2`
+ * \sa `AosOpenBoundaryTraits_2`
  */
 struct Arr_open_side_tag : {};
 
-}
-
-namespace CGAL {
-
 /*! \ingroup PkgArrangementOnSurface2Tags
  *
  * This type tag is used to indicate that a side of the parameter space, either
@@ -73,14 +65,10 @@ namespace CGAL {
  * \sa `Arr_open_side_tag`
  * \sa `Arr_contracted_side_tag`
  * \sa `Arr_identified_side_tag`
- * \sa `ArrangementOpenBoundaryTraits_2`
+ * \sa `AosOpenBoundaryTraits_2`
  */
 struct Arr_closed_side_tag {};
 
-}
-
-namespace CGAL {
-
 /*! \ingroup PkgArrangementOnSurface2Tags
  *
  * This type tag is used to indicate that a side of the parameter space, either
@@ -92,7 +80,7 @@ namespace CGAL {
  * nested in every geometry traits class, must be convertible to the type
  * `Arr_contracted_side_tag`. For example, the `Bottom_side_category` and
  * `Top_side_category` category types, nested in every model of the
- * `ArrangementSphericalBoundaryTraits_2 concept` (such as any instance of the
+ * `AosSphericalBoundaryTraits_2 concept` (such as any instance of the
  * `Arr_geodesic_arc_on_sphere_traits_2` class template) must be convertible to
  * `Arr_contracted_side_tag`
  *
@@ -103,14 +91,10 @@ namespace CGAL {
  * \sa `Arr_open_side_tag`
  * \sa `Arr_closed_side_tag`
  * \sa `Arr_identified_side_tag`
- * \sa `ArrangementOpenBoundaryTraits_2`
+ * \sa `AosOpenBoundaryTraits_2`
  */
 struct Arr_contracted_side_tag {};
 
-}
-
-namespace CGAL {
-
 /*! \ingroup PkgArrangementOnSurface2Tags
  *
  * This type tag is used to indicate that a side of the parameter space, either
@@ -122,7 +106,7 @@ namespace CGAL {
  * nested in every geometry traits class, must be convertible to the type
  * `Arr_identified_side_tag`. For example, the `Left_side_category` and
  * `Right_side_category` category types, nested in every model of the
- * `ArrangementSphericalBoundaryTraits_2 concept` (such as any instance of the
+ * `AosSphericalBoundaryTraits_2 concept` (such as any instance of the
  * `Arr_geodesic_arc_on_sphere_traits_2` class template) must be convertible to
  * `Arr_identified_side_tag`
  *
@@ -133,7 +117,7 @@ namespace CGAL {
  * \sa `Arr_open_side_tag`
  * \sa `Arr_closed_side_tag`
  * \sa `Arr_contracted_side_tag`
- * \sa `ArrangementOpenBoundaryTraits_2`
+ * \sa `AosOpenBoundaryTraits_2`
  */
 struct Arr_identified_side_tag {};
 

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_trapezoid_ric_point_location.h

@@ -1,66 +1,69 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2PointLocation
-\ingroup PkgArrangementOnSurface2PointLocation
+ *
-
+ * \anchor arr_reftrap_pl
-\anchor arr_reftrap_pl
+ *
-
+ * The `Arr_trapezoid_ric_point_location` class implements the incremental
-The `Arr_trapezoid_ric_point_location` class implements the incremental randomized algorithm
+ * randomized algorithm introduced by Mulmuley \cgalCite{m-fppa-90} as presented
-introduced by Mulmuley \cgalCite{m-fppa-90} as presented by
+ * by Seidel \cgalCite{s-sfira-91} (see also [\cgalCite{bkos-cgaa-00} Chapter
-Seidel \cgalCite{s-sfira-91} (see also [\cgalCite{bkos-cgaa-00} Chapter 6).
+ * 6).  It subdivides each arrangement face to pseudo-trapezoidal cells, each of
-It subdivides each arrangement face to pseudo-trapezoidal cells, each
+ * constant complexity, and constructs and maintains a linear-size search
-of constant complexity, and constructs and maintains a linear-size search
+ * structure on top of these cells, such that each query can be answered in
-structure on top of these cells, such that each query can be answered
+ * \cgalBigO{\log n} time, where \f$n\f$ is the complexity of the arrangement.
-in \cgalBigO{\log n} time, where \f$ n\f$ is the complexity of the arrangement.
+ *
-
+ * Constructing the search structures takes \cgalBigO{n \log n} expected time
-Constructing the search structures takes \cgalBigO{n \log n} expected time
+ * and may require a small number of rebuilds
-and may require a small number of rebuilds \cgalCite{hkh-iiplgtds-12}. Therefore
+ * \cgalCite{hkh-iiplgtds-12}. Therefore attaching a trapezoidal point-location
-attaching a trapezoidal point-location object to an existing arrangement
+ * object to an existing arrangement may incur some overhead in running
-may incur some overhead in running times. In addition, the point-location
+ * times. In addition, the point-location object needs to keep its auxiliary
-object needs to keep its auxiliary data structures up-to-date as the
+ * data structures up-to-date as the arrangement goes through structural
-arrangement goes through structural changes. It is therefore recommended
+ * changes. It is therefore recommended to use this point-location strategy for
-to use this point-location strategy for static arrangements (or arrangement
+ * static arrangements (or arrangement that do not alter frequently), and when
-that do not alter frequently), and when the number of issued queries
+ * the number of issued queries is relatively large.
-is relatively large.
+ *
-
+ * This strategy supports arbitrary subdivisions, including unbounded ones.
-This strategy supports arbitrary subdivisions, including unbounded ones.
+ *
-
+ * \cgalModels{AosPointLocation_2,AosVerticalRayShoot_2}
-\cgalModels{ArrangementPointLocation_2,ArrangementVerticalRayShoot_2}
+ *
-
+ * \sa `AosPointLocation_2`
-\sa `ArrangementPointLocation_2`
+ * \sa `AosVerticalRayShoot_2`
-\sa `ArrangementVerticalRayShoot_2`
+ * \sa `CGAL::Arr_point_location_result<Arrangement>`
-\sa `CGAL::Arr_point_location_result<Arrangement>`
-
 */
-template< typename Arrangement >
+template <typename Arrangement>
 class Arr_trapezoid_ric_point_location {
 public:
+  /// \name Creation
+  /// @{
 
-/// \name Creation
+  /*! If `with_guarantees` is set to true, the construction performs rebuilds in
-/// @{
+   * order to guarantee a resulting structure with linear size and logarithmic
+   * query time. Otherwise the structure has expected linear size and expected
+   * logarithmic query time.
+   */
+  Arr_trapezoid_ric_point_location(bool with_guarantees = true);
 
-/*!
+  /*! constructs a point location search structure for the given arrangement.
-If with_guarantees is set to true, the construction performs rebuilds in order to guarantee a resulting structure with linear size and logarithmic query time. Otherwise the structure has expected linear size and expected logarithmic query time.
+   * If with_guarantees is set to true, the construction performs rebuilds in
-*/
+   * order to guarantee a resulting structure with linear size and logarithmic
-Arr_trapezoid_ric_point_location (bool with_guarantees = true);
+   * query time. Otherwise the structure has expected linear size and expected
+   * logarithmic query time.
+   */
+  Arr_trapezoid_ric_point_location(const Arrangement& arr,
+                                   bool with_guarantees = true);
 
-/*!
+  /// @}
-Constructs a point location search structure for the given arrangement. If with_guarantees is set to true, the construction performs rebuilds in order to guarantee a resulting structure with linear size and logarithmic query time. Otherwise the structure has expected linear size and expected logarithmic query time.
-*/
-Arr_trapezoid_ric_point_location (const Arrangement& arr, bool with_guarantees = true);
 
-/// @}
+  /// \name Modifiers
+  /// @{
 
-/// \name Modifiers
+  /*! If with_guarantees is set to true, the structure will guarantee linear
-/// @{
+   * size and logarithmic query time, that is, this function may cause a
-
+   * reconstruction of the data structure.
-/*!
+   */
-If with_guarantees is set to true, the structure will guarantee linear size and logarithmic query time, that is, this function may cause a reconstruction of the data structure.
+  void with_guarantees(bool with_guarantees);
-*/
-void with_guarantees (bool with_guarantees);
-
-/// @}
 
+  /// @}
 }; /* end Arr_trapezoid_ric_point_location */
+
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_triangulation_point_location.h

@@ -14,13 +14,12 @@ namespace CGAL {
  * (especially when the number of modifications applied to the arrangement is
  * high) and provided only for educational purposes.
  *
- * \cgalModels{ArrangementPointLocation_2,ArrangementVerticalRayShoot_2}
+ * \cgalModels{AosPointLocation_2,AosVerticalRayShoot_2}
  *
- * \sa `ArrangementPointLocation_2`
+ * \sa `AosPointLocation_2`
- * \sa `ArrangementVerticalRayShoot_2`
+ * \sa `AosVerticalRayShoot_2`
  * \sa `CGAL::Arr_point_location_result<Arrangement>`
  */
-
 template <typename Arrangement_>
 class Arr_triangulation_point_location : public Arrangement_::Observer {}
 

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_unb_planar_topology_traits_2.h

@@ -10,24 +10,24 @@ namespace CGAL {
  * The `Arr_unb_planar_topology_traits_2` template has two parameters:
  * <UL>
  * <LI>The `GeometryTraits_2` template-parameter should be substituted by
- * a model of the `ArrangementBasicTraits_2` concept. The traits
+ * a model of the `AosBasicTraits_2` concept. The traits
  * class defines the types of \f$x\f$-monotone curves and two-dimensional
- * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
+ * points, namely `AosBasicTraits_2::X_monotone_curve_2` and
- * `ArrangementBasicTraits_2::Point_2`,
+ * `AosBasicTraits_2::Point_2`,
  *   respectively, and supports basic geometric predicates on them.
  * <LI>The `Dcel` template-parameter should be substituted by
- * a class that is a model of the `ArrangementDcel` concept. The
+ * a class that is a model of the `AosDcel` concept. The
  * value of this parameter is by default
  * `Arr_default_dcel<Traits>`.
  * </UL>
  *
- * \cgalModels{ArrangementBasicTopologyTraits}
+ * \cgalModels{AosBasicTopologyTraits}
  *
  * \sa `Arr_default_dcel<Traits>`
  * \sa `CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel,x,y>`
  */
 template <typename GeometryTraits_2,
-          typename Dcel = Arr_default_dcel<GeometryTraits_2> >
+          typename Dcel = Arr_default_dcel<GeometryTraits_2>>
 class Arr_unb_planar_topology_traits_2 {
 public:
   /// \name Types
@@ -62,10 +62,10 @@ public:
   /// \name Accessors
   /// @{
 
-  /*! obtains the DCEL (const version). */
+  /*! obtains the \dcel (const version). */
   const Dcel& dcel() const;
 
-  /*! obtains the DCEL (non-const version). */
+  /*! obtains the \dcel (non-const version). */
   Dcel& dcel();
 
   /*! obtains the unbounded face (const version). */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_vertex_index_map.h

@@ -1,69 +1,64 @@
 namespace CGAL {
 
-  /*! \ingroup PkgArrangementOnSurface2Ref
+/*! \ingroup PkgArrangementOnSurface2Ref
-   *
+ *
-   * `Arr_vertex_index_map` maintains a mapping of vertex handles of an attached
+ * `Arr_vertex_index_map` maintains a mapping of vertex handles of an attached
-   * arrangement object to indices (of type `unsigned int`).  This class template
+ * arrangement object to indices (of type `unsigned int`).  This class template
-   * is a model of the concept `ReadablePropertyMap`. A mapping between vertex
+ * is a model of the concept `ReadablePropertyMap`. A mapping between vertex
-   * handles and indices enables convenient usage of property-map classes supplied
+ * handles and indices enables convenient usage of property-map classes supplied
-   * by `boost`.  For example, the property-map class templates
+ * by `boost`.  For example, the property-map class templates
-   * `boost::vector_property_map`, which is based on `std::vector`, and
+ * `boost::vector_property_map`, which is based on `std::vector`, and
-   * `boost::iterator_property_map`, which can be used to implement a property map
+ * `boost::iterator_property_map`, which can be used to implement a property map
-   * based on a native \CC array, require the user to supply a mapping such as
+ * based on a native \CC array, require the user to supply a mapping such as
-   * `Arr_vertex_index_map`.
+ * `Arr_vertex_index_map`.
-   *
+ *
-   * As new vertices might be inserted into the attached arrangement, and
+ * As new vertices might be inserted into the attached arrangement, and
-   * existing vertices might be removed, the notification mechanism is used
+ * existing vertices might be removed, the notification mechanism is used
-   * to dynamically maintain the mapping of vertex handles to indices.
+ * to dynamically maintain the mapping of vertex handles to indices.
-   *
+ *
-   * \cgalModels{DefaultConstructible,CopyConstructible,Assignable,ReadablePropertyMap}
+ * \cgalModels{DefaultConstructible,CopyConstructible,Assignable,ReadablePropertyMap}
-   *
+ *
-   * \sa `Arr_face_index_map<Arrangement>`
+ * \sa `Arr_face_index_map<Arrangement>`
+ */
+template <typename Arrangement_>
+class Arr_vertex_index_map: public Arrangement_::Observer {
+public:
+  /// \name Types
+  /// @{
+
+  /// the type of the attached arrangement.
+  typedef Arrangement_                                Arrangement_2;
+
+  typedef typename Arrangement_2::Base_aos            Base_aos;
+
+  typedef boost::readable_property_map_tag            category;
+
+  typedef unsigned int                                value_type;
+
+  typedef unsigned int                                reference;
+
+  typedef Vertex_handle                               key_type;
+
+  /// The vertex handle type.
+  typedef typename Base_aos::Vertex_handle            Vertex_handle;
+
+  /// The type of mapping of vertices to indices.
+  typedef Unique_hash_map<Vertex_handle, value_type>  Index_map;
+
+  /// @}
+
+  /// \name Creation
+  /// @{
+
+  /*! constructs a map that is unattached to any arrangement instance.
    */
+  Arr_vertex_index_map();
 
-  template< typename Arrangement_>
+  /*! constructs a map and attaches it to the given arrangement `arr`.
-  class Arr_vertex_index_map: public Arrangement_::Observer {
+   */
-  public:
+  Arr_vertex_index_map(Base_aos& arr);
 
-    /// \name Types
+  /// @}
-    /// @{
+}; /* end Arr_accessor */
-
-    /*! the type of the attached arrangement.
-     */
-    typedef Arrangement_                                Arrangement_2;
-    typedef typename Arrangement_2::Base_aos            Base_aos;
-
-    typedef boost::readable_property_map_tag            category;
-
-    typedef unsigned int                                value_type;
-
-    typedef unsigned int                                reference;
-
-    typedef Vertex_handle                               key_type;
-
-    /*! The vertex handle type.
-     */
-    typedef typename Base_aos::Vertex_handle            Vertex_handle;
-
-    /*! The type of mapping of vertices to indices.
-     */
-    typedef Unique_hash_map<Vertex_handle, value_type>  Index_map;
-
-    /// @}
-
-    /// \name Creation
-    /// @{
-
-    /*! constructs a map that is unattached to any arrangement instance.
-     */
-    Arr_vertex_index_map();
-
-    /*! constructs a map and attaches it to the given arrangement `arr`.
-     */
-    Arr_vertex_index_map(Base_aos& arr);
-
-    /// @}
-
-  }; /* end Arr_accessor */
 
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_walk_along_line_point_location.h

@@ -1,38 +1,31 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2PointLocation
-\ingroup PkgArrangementOnSurface2PointLocation
+ *
+ * \anchor arr_refwalk_pl
+ *
+ * The `Arr_walk_along_line_point_location` class implements a very simple
+ * point-location (and vertical ray-shooting) strategy that improves the naive
+ * one.  The algorithm considers an imaginary vertical ray emanating from the
+ * query point, and simulates a walk along the zone of this ray, starting from
+ * the unbounded face until reaching the query point.  In dense arrangements
+ * this walk can considerably reduce the number of traversed arrangement edges,
+ * with respect to the naïve algorithm.
+ *
+ * The walk-along-a-line point-location object (just like the naïve one)
+ * does not use any auxiliary data structures. Thus, attaching it to an existing
+ * arrangement takes constant time, and any ongoing updates to this arrangement
+ * do not affect the point-location object.  It is therefore recommended to use
+ * the "walk" point-location strategy for arrangements that are constantly
+ * changing, especially if the number of issued queries is not large.
+ *
+ * \cgalModels{AosPointLocation_2,AosVerticalRayShoot_2}
+ *
+ * \sa `AosPointLocation_2`
+ * \sa `AosVerticalRayShoot_2`
+ * \sa `CGAL::Arr_point_location_result<Arrangement>`
+ */
+template <typename Arrangement>
+class Arr_walk_along_line_point_location {};
 
-\anchor arr_refwalk_pl
-
-The `Arr_walk_along_line_point_location` class implements a very simple point-location (and
-vertical ray-shooting) strategy that improves the naive one.
-The algorithm considers an imaginary vertical ray emanating from the
-query point, and simulates a walk along the zone of this ray, starting
-from the unbounded face until reaching the query point.
-In dense arrangements this walk can considerably reduce the number
-of traversed arrangement edges, with respect to the na&iuml;ve
-algorithm.
-
-The walk-along-a-line point-location object (just like the na&iuml;ve one)
-does not use any auxiliary data structures. Thus, attaching it to an
-existing arrangement takes constant time, and any ongoing updates to
-this arrangement do not affect the point-location object.
-It is therefore recommended to use the "walk" point-location strategy
-for arrangements that are constantly changing, especially if the number
-of issued queries is not large.
-
-\cgalModels{ArrangementPointLocation_2,ArrangementVerticalRayShoot_2}
-
-\sa `ArrangementPointLocation_2`
-\sa `ArrangementVerticalRayShoot_2`
-\sa `CGAL::Arr_point_location_result<Arrangement>`
-
-*/
-template< typename Arrangement >
-class Arr_walk_along_line_point_location {
-public:
-
-}; /* end Arr_walk_along_line_point_location */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_2.h

@@ -5,7 +5,7 @@ namespace CGAL {
  * \anchor arr_refarr
  *
  * An object `arr` of the class `Arrangement_2` represents the planar
- * subdivision induced by a set of \f$ x\f$-monotone curves and isolated points
+ * subdivision induced by a set of \f$x\f$-monotone curves and isolated points
  * into maximally connected cells. The arrangement is represented as a
  * doubly-connected edge-list (\dcel) such that each \dcel vertex is associated
  * with a point of the plane and each edge is associated with an \f$
@@ -16,13 +16,13 @@ namespace CGAL {
  * The `Arrangement_2` template has two parameters:
  * <UL>
  * <LI>The `Traits` template-parameter should be instantiated with
- * a model of the `ArrangementBasicTraits_2` concept. The traits
+ * a model of the `AosBasicTraits_2` concept. The traits
- * class defines the types of \f$ x\f$-monotone curves and two-dimensional
+ * class defines the types of \f$x\f$-monotone curves and two-dimensional
- * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
+ * points, namely `AosBasicTraits_2::X_monotone_curve_2` and
- * `ArrangementBasicTraits_2::Point_2`,
+ * `AosBasicTraits_2::Point_2`,
  *   respectively, and supports basic geometric predicates on them.
  * <LI>The `Dcel` template-parameter should be instantiated with
- * a class that is a model of the `ArrangementDcel` concept. The
+ * a class that is a model of the `AosDcel` concept. The
  * value of this parameter is by default
  * `Arr_default_dcel<Traits>`.
  * </UL>
@@ -30,9 +30,9 @@ namespace CGAL {
  * The available traits classes and \dcel classes are
  * described below.
  *
- * \sa `ArrangementDcel`
+ * \sa `AosDcel`
  * \sa `Arr_default_dcel<Traits>`
- * \sa `ArrangementBasicTraits_2`
+ * \sa `AosBasicTraits_2`
  * \sa `CGAL::overlay()`
  * \sa `CGAL::is_valid()`
  *
@@ -156,41 +156,42 @@ public:
 
   /// @}
 }; /* end Arrangement_2 */
+
 } /* end namespace CGAL */
 
 namespace CGAL {
 
 /*! \ingroup PkgArrangementOnSurface2Insert
- * The function `%insert` inserts one or more curves or \f$ x\f$-monotone curves
+ * The function `%insert` inserts one or more curves or \f$x\f$-monotone curves
  * into a given arrangement, where no restrictions are imposed on the inserted
- * curves. If an inserted curve is not \f$ x\f$-monotone curve, it is subdivided
+ * curves. If an inserted curve is not \f$x\f$-monotone curve, it is subdivided
- * into \f$ x\f$-monotone subcurves (and perhaps isolated points), which are
+ * into \f$x\f$-monotone subcurves (and perhaps isolated points), which are
  * inserted into the arrangement.
  *
  * \cgalHeading{Requirements}
  *
  * <UL>
- * <LI>If the curve is \f$ x\f$-monotone curve then The instantiated
+ * <LI>If the curve is \f$x\f$-monotone curve then The instantiated
- *   `Traits` class must model the `ArrangementXMonotoneTraits_2`
+ *   `Traits` class must model the `AosXMonotoneTraits_2`
- *   concept. In case that the curve is not \f$ x\f$-monotone then the
+ *   concept. In case that the curve is not \f$x\f$-monotone then the
  *   instantiated `Traits` class must model the
- *   `ArrangementTraits_2` concept. That is, it should define the
+ *   `ArrtTraits_2` concept. That is, it should define the
- *   `Curve_2` type, and support its subdivision into \f$ x\f$-monotone
+ *   `Curve_2` type, and support its subdivision into \f$x\f$-monotone
  *   subcurves (and perhaps isolated points).
  * <LI>The point-location object `pl`, must model the
- *   `ArrangementPointLocation_2` concept.
+ *   `AosPointLocation_2` concept.
  * </UL>
  */
 
 /// @{
 
 /*! Inserts the given curve `c` into the arrangement `arr`.
- * `c` is subdivided into \f$ x\f$-monotone subcurves (and perhaps isolated
+ * `c` is subdivided into \f$x\f$-monotone subcurves (and perhaps isolated
  * points). Each subcurve is in turn inserted into the arrangement by locating
  * its left endpoint and computing its zone until reaching the right endpoint.
  *
  * The given point-location object `pl` is used to locate the left
- * endpoints of the \f$ x\f$-monotone curves. By default, the function uses the
+ * endpoints of the \f$x\f$-monotone curves. By default, the function uses the
  * "walk along line" point-location strategy  -  namely an instance of
  * the class `Arr_walk_along_line_point_location<Arrangement_2<Traits,Dcel> >`.
  *
@@ -200,7 +201,7 @@ template <typename Traits, typename Dcel, typename Curve, typename PointLocation
 void insert(Arrangement_2<Traits,Dcel>& arr, const Curve& c,
             const PointLocation& pl = walk_pl);
 
-/*! Inserts the<I>\f$ x\f$-monotone (only)</I> curve `xc` into the arrangement
+/*! Inserts the<I>\f$x\f$-monotone (only)</I> curve `xc` into the arrangement
  * `arr`. The object `obj`, which wraps a `Vertex_const_handle`, a
  * `Halfedge_const_handle`, or a `Face_const_handle`, represents the location of
  * `xc`'s left endpoint in the arrangement. The zone of `xc` is computed
@@ -213,7 +214,7 @@ void insert(Arrangement_2<Traits, Dcel>& arr,
             const typename Traits::X_monotone_curve_2& xc,
             typename Arr_point_location_result<Arrangement_2<Traits, Dcel> >::type obj);
 
-/*! Aggregately inserts the curves or \f$ x\f$-monotone curves in the range
+/*! Aggregately inserts the curves or \f$x\f$-monotone curves in the range
  * `[first,last)` into the arrangement `arr` using the sweep-line framework.
  * \param arr the target arrangement.
  * \param first the iterator to the first element in the range of curves.
@@ -227,7 +228,7 @@ void insert(Arrangement_2<Traits, Dcel>& arr,
 
 /*! \ingroup PkgArrangementOnSurface2Funcs
  *
- * Inserts a given \f$ x\f$-monotone curve into a given arrangement, where the
+ * Inserts a given \f$x\f$-monotone curve into a given arrangement, where the
  * interior of the given curve is disjoint from all existing arrangement
  * vertices and edges. Under this assumption, it is possible to locate the
  * endpoints of the given curve in the arrangement, and use one of the
@@ -247,9 +248,9 @@ void insert(Arrangement_2<Traits, Dcel>& arr,
  *
  * <UL>
  * <LI>The instantiated `Traits` class must model the restricted
- * `ArrangementBasicTraits_2` concept, as no intersections are computed.
+ * `AosBasicTraits_2` concept, as no intersections are computed.
  * <LI>The point-location object `pl` must model the
- * `ArrangementPointLocation_2` concept.
+ * `AosPointLocation_2` concept.
  * </UL>
  */
 template <typename Traits, typename Dcel,typename PointLocation>
@@ -260,7 +261,7 @@ insert_non_intersecting_curve(Arrangement_2<Traits,Dcel>& arr,
 
 /*! \ingroup PkgArrangementOnSurface2Funcs
  *
- * Inserts a set of \f$ x\f$-monotone curves in a given range into a given
+ * Inserts a set of \f$x\f$-monotone curves in a given range into a given
  * arrangement. The insertion is performed in an aggregated manner, using the
  * sweep-line algorithm. The input curves should be pairwise disjoint in their
  * interior and pairwise interior-disjoint from all existing arrangement
@@ -270,7 +271,7 @@ insert_non_intersecting_curve(Arrangement_2<Traits,Dcel>& arr,
  *
  * <UL>
  * <LI>The instantiated `Traits` class must model the
- * `ArrangementBasicTraits_2` concept, as no intersections are computed.
+ * `AosBasicTraits_2` concept, as no intersections are computed.
  * <LI>`InputIterator::value_type` must be `Traits::X_monotone_curve_2`
  * </UL>
  */
@@ -296,14 +297,14 @@ void insert_non_intersecting_curves(Arrangement_2<Traits,Dcel>& arr,
  *
  * <UL>
  * <LI>The instantiated `Traits` class must model the
- * `ArrangementXMonotoneTraits_2` concept. Not all expressions listed
+ * `AosXMonotoneTraits_2` concept. Not all expressions listed
  * by this concept are required. In fact the traits class must model the
- * `ArrangementBasicTraits_2` concept, and support the splitting functionality.
+ * `AosBasicTraits_2` concept, and support the splitting functionality.
  * <LI>The point-location object `pl`, must model the
- * `ArrangementPointLocation_2` concept.
+ * `AosPointLocation_2` concept.
  * </UL>
  */
-template<typename Traits, typename Dcel, typename PointLocation>
+template <typename Traits, typename Dcel, typename PointLocation>
 typename Arrangement_2<Traits,Dcel>::Vertex_handle
 insert_point(Arrangement_2<Traits,Dcel>& arr,
              const typename Traits::Point_2& p,
@@ -315,7 +316,7 @@ insert_point(Arrangement_2<Traits,Dcel>& arr,
  *
  * Invokes the member function `arr.is_valid()` to verify the topological
  * correctness of the arrangement. Then it performs additional validity
- * tests. It checks that all \f$ x\f$-monotone curves associated with
+ * tests. It checks that all \f$x\f$-monotone curves associated with
  * arrangement edges are pairwise disjoint in their interior. Then it makes sure
  * that all holes and all isolated vertices are located within the proper
  * arrangement faces. Note that the test carried out by this function may take a
@@ -327,7 +328,7 @@ insert_point(Arrangement_2<Traits,Dcel>& arr,
  * The instantiated traits class must model the concept
  * `ArranagmentXMonotoneTraits_2`.
  */
-template<typename Traits, typename Dcel>
+template <typename Traits, typename Dcel>
 bool is_valid(const Arrangement_2<Traits, Dcel>& arr);
 
 /*! \ingroup PkgArrangementOnSurface2Funcs
@@ -337,8 +338,8 @@ bool is_valid(const Arrangement_2<Traits, Dcel>& arr);
  * its endpoints become isolated, they are removed as well. The call
  * `remove_edge(arr, e)` is equivalent to the call `arr.remove_edge (e, true,
  * true)`. However, this free function requires that `Traits` be a model of the
- * refined concept `ArrangementXMonotoneTraits_2`, which requires merge
+ * refined concept `AosXMonotoneTraits_2`, which requires merge
- * operations on \f$ x\f$-monotone curves. If one of the end-vertices of the
+ * operations on \f$x\f$-monotone curves. If one of the end-vertices of the
  * given edge becomes redundant after the edge is removed (see `remove_vertex()`
  * for the definition of a redundant vertex), it is removed, and its incident
  * edges are merged.  If the edge-removal operation causes two faces to merge,
@@ -349,7 +350,7 @@ bool is_valid(const Arrangement_2<Traits, Dcel>& arr);
  *
  * <UL>
  * <LI>The instantiated traits class must model the concept
- * `ArrangementXMonotoneTraits_2`.
+ * `AosXMonotoneTraits_2`.
  * </UL>
  */
 template <typename Traits, typename Dcel>
@@ -362,17 +363,17 @@ remove_edge(Arrangement_2<Traits,Dcel>& arr,
  * Attempts to removed a given vertex from a given arrangement. The vertex can
  * be removed if it is either an isolated vertex, (and has no incident edge,) or
  * if it is a <I>redundant</I> vertex. That is, it has exactly two incident
- * edges, whose associated curves can be merged to form a single \f$
+ * edges, whose associated curves can be merged to form a single \f$x\f$-monotone
- * x\f$-monotone curve.  The function returns a boolean value that indicates
+ * curve.  The function returns a boolean value that indicates
  * whether it succeeded removing the vertex from the arrangement.
  *
  * \cgalHeading{Requirements}
  *
  * <UL>
  * <LI>The instantiated `Traits` class must model the
- * `ArrangementXMonotoneTraits_2` concept. Not all expressions listed
+ * `AosXMonotoneTraits_2` concept. Not all expressions listed
  * by this concept are required. In fact the traits class must model the
- * `ArrangementBasicTraits_2` concept and support the merging functionality.
+ * `AosBasicTraits_2` concept and support the merging functionality.
  * </UL>
  */
 template <typename Traits, typename Dcel>

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_2.h

@@ -5,11 +5,11 @@ namespace CGAL {
  * \anchor arr_refaos
  *
  * An object `aos` of the class `Arrangement_on_surface_2` represents the
- * subdivision induced by a set of \f$ x\f$-monotone curves and isolated points
+ * subdivision induced by a set of \f$x\f$-monotone curves and isolated points
  * into maximally connected cells. The arrangement is represented as a
  * doubly-connected edge-list (<span class="textsc">Dcel</span>) such that each
  * <span class="textsc">Dcel</span> vertex is associated with a point of the
- * plane and each edge is associated with an \f$ x\f$-monotone curve whose
+ * plane and each edge is associated with an \f$x\f$-monotone curve whose
  * interior is disjoint from all other edges and vertices. Recall that an
  * arrangement edge is always comprised of a pair of twin <span
  * class="textsc">Dcel</span> halfedges.
@@ -18,21 +18,21 @@ namespace CGAL {
  * <UL>
  * <LI>The `GeometryTraits` template-parameter should be substituted by
  * a model of a geometry traits. The minimal requirements are defined by the
- * `ArrangementBasicTraits_2` concept. A model of this concept defines
+ * `AosBasicTraits_2` concept. A model of this concept defines
- * the types of \f$ x\f$-monotone curves and two-dimensional points, namely
+ * the types of \f$x\f$-monotone curves and two-dimensional points, namely
- * `ArrangementBasicTraits_2::X_monotone_curve_2` and
+ * `AosBasicTraits_2::X_monotone_curve_2` and
- * `ArrangementBasicTraits_2::Point_2`, respectively, and supports basic
+ * `AosBasicTraits_2::Point_2`, respectively, and supports basic
  * geometric predicates on them.
  * <LI>The `TopologyTraits` template-parameter should be substituted by a
- * class that is a model of the `ArrangementTopologyTraits` concept.
+ * class that is a model of the `AosTopologyTraits` concept.
  * </UL>
  *
  * The available traits classes and <span class="textsc">Dcel</span> classes are
  * described below.
 
- * \sa `ArrangementDcel`
+ * \sa `AosDcel`
  * \sa `Arr_default_dcel<Traits>`
- * \sa `ArrangementBasicTraits_2`
+ * \sa `AosBasicTraits_2`
  * \sa `CGAL::overlay()`
 
  * Insertion Functions
@@ -62,10 +62,10 @@ public:
   /// \name Types
   /// @{
 
-  /*! the geometry traits class in use. */
+  /// the geometry traits class in use.
   typedef GeometryTraits                              Geometry_traits_2;
 
-  /*! the topology traits class in use. */
+  /// the topology traits class in use.
   typedef TopologyTraits                                Topology_traits;
 
   /*! a private type used as an abbreviation of the
@@ -78,18 +78,18 @@ public:
    */
   typedef typename Topology_traits::Dcel                Dcel;
 
-  /*! the point type, as defined by the traits class. */
+  /// the point type, as defined by the traits class.
   typedef typename Geometry_traits_2::Point_2           Point_2;
 
-  /*! the \f$ x\f$-monotone curve type, as defined by the traits class. */
+  /// the \f$x\f$-monotone curve type, as defined by the traits class.
   typedef typename Geometry_traits_2::X_monotone_curve_2 X_monotone_curve_2;
 
-  /*! the size type (equivalent to `size_t`). */
+  /// the size type (equivalent to `std::size_t`).
   typedef typename Dcel::Size                           Size;
 
   /*! \ingroup PkgArrangementOnSurface2DCEL
-   * An object \f$ v\f$ of the class `Vertex` represents an arrangement vertex,
+   * An object \f$v\f$ of the class `Vertex` represents an arrangement vertex,
-   * that is a \f$ 0\f$-dimensional cell, associated with a point on the
+   * that is a \f$0\f$-dimensional cell, associated with a point on the
    * ambient surface.
    */
   class Vertex : public typename Dcel::Vertex {
@@ -137,14 +137,14 @@ public:
      */
     const typename Traits::Point_2& point() const;
 
-    /*! obtains the placement of the \f$ x\f$-coordinate in the parameter space,
+    /*! obtains the placement of the \f$x\f$-coordinate in the parameter space,
      * that is, either the left boundary-side, the interior, or the right
      * boundary-side. If the vertex lies on an identified vertical side, the
      * return value is non-deterministic.
      */
     Arr_parameter_space parameter_space_in_x() const;
 
-    /*! obtains the placement of the \f$ y\f$-coordinate in the parameter space,
+    /*! obtains the placement of the \f$y\f$-coordinate in the parameter space,
      * that is, either the bottom boundary-side, the interior, or the top
      * boundary-side. If the vertex lies on an identified horizontal side, the
      * return value is non-deterministic.
@@ -152,17 +152,16 @@ public:
     Arr_parameter_space parameter_space_in_y() const;
 
     /// @}
-
   }; /* end Vertex */
 
   /*! \ingroup PkgArrangementOnSurface2DCEL
-   * An object \f$ e\f$ of the class `Halfedge` represents a halfedge in the
+   * An object \f$e\f$ of the class `Halfedge` represents a halfedge in the
    * arrangement. A halfedge is directed from its <I>source</I> vertex
    * to its <I>target</I> vertex, and has an <I>incident face</I> lying to
    * its left. Each halfedge has a <I>twin</I> halfedge directed in the
    * opposite direction, where the pair of twin halfedges form together
-   * an arrangement edge, that is, a \f$ 1\f$-dimensional cell, associated
+   * an arrangement edge, that is, a \f$1\f$-dimensional cell, associated
-   * with planar \f$ x\f$-monotone curve.
+   * with planar \f$x\f$-monotone curve.
    *
    * Halfedges are stored in doubly-connected lists and form chains. These
    * chains define the inner and outer boundaries of connected components.
@@ -221,7 +220,7 @@ public:
      */
     Ccb_halfedge_circulator ccb();
 
-    /*! obtains the \f$ x\f$-monotone curve associated with `e`.
+    /*! obtains the \f$x\f$-monotone curve associated with `e`.
      * \pre `e` is not a fictitious halfedge.
      */
     const typename Traits::X_monotone_curve_2& curve() const;
@@ -372,7 +371,7 @@ public:
   /// Mutable
   /// @{
 
-  /*! a handle to an arrangement vertex. */
+  /// a handle to an arrangement vertex.
   typedef unspecified_type Vertex_handle;
 
   /*! a handle to a halfedge.
@@ -380,7 +379,7 @@ public:
    */
   typedef unspecified_type Halfedge_handle;
 
-  /*! a handle to an arrangement face. */
+  /// a handle to an arrangement face.
   typedef unspecified_type Face_handle;
 
   /*! a bidirectional iterator over the
@@ -458,7 +457,7 @@ public:
    */
   typedef unspecified_type Halfedge_const_handle;
 
-  /*! a handle to an arrangement face. */
+  /// a handle to an arrangement face.
   typedef unspecified_type Face_const_handle;
 
   /*! a bidirectional iterator over the
@@ -791,7 +790,7 @@ public:
    * \pre `c` must not be an unbounded curve.
    * \pre `v1` and `v2` are associated with `c`'s endpoints.
    * \pre If `v1` and `v2` are already connected by an edge, this edge
-   * represents an \f$ x\f$-monotone curve that is interior-disjoint from `c`).
+   * represents an \f$x\f$-monotone curve that is interior-disjoint from `c`).
    */
   Halfedge_handle insert_at_vertices(const X_monotone_curve_2& c,
                                      Vertex_handle v1,
@@ -878,12 +877,17 @@ public:
    * fictitious halfedge that should contain the vertex at infinity that
    * corresponds to the unbounded left end of `c`.  The function returns a
    * handle for one of the new halfedges directed (lexicographically) from right
-   * to left.  \pre The interior of `c` is disjoint from all existing
+   * to left.
-   * arrangement vertices and edges. `c` must have a bounded right endpoint and
+   *
-   * an unbounded left end.  \pre `pred->target()` is associated with the right
+   * \pre The interior of `c` is disjoint from all existing arrangement vertices
-   * endpoint of `c`, and `c` should be inserted after `pred` in a clockwise
+   * and edges. `c` must have a bounded right endpoint and an unbounded left
-   * order around this vertex.  \pre `fict_pred` is a fictitious halfedge that
+   * end.
-   * contains the unbounded left end of `c`.
+   *
+   * \pre `pred->target()` is associated with the right endpoint of `c`, and `c`
+   * should be inserted after `pred` in a clockwise order around this vertex.
+   *
+   * \pre `fict_pred` is a fictitious halfedge that contains the unbounded left
+   * end of `c`.
   */
   Halfedge_handle insert_from_right_vertex(const X_monotone_curve_2& c,
                                            Halfedge_handle pred,
@@ -899,7 +903,7 @@ public:
    * vertices and edges.
    * \pre `pred1->target()` and `v2` are associated with `c`'s endpoints.
    * \pre If `pred1->target` and `v2` are already connected by an edge, this
-   * edge represents an \f$ x\f$-monotone curve that is interior-disjoint from
+   * edge represents an \f$x\f$-monotone curve that is interior-disjoint from
    * `c`).
    */
   Halfedge_handle insert_at_vertices(const X_monotone_curve_2& c,
@@ -918,7 +922,7 @@ public:
    * \pre `pred1->target()` and `pred2->target()` are associated with `c`'s
    * endpoints.
    * \pre If `pred1->target` and `pred2->target()` are already connected by an
-   * edge, this edge represents an \f$ x\f$-monotone curve that is
+   * edge, this edge represents an \f$x\f$-monotone curve that is
    * interior-disjoint from `c`).
    */
   Halfedge_handle insert_at_vertices(const X_monotone_curve_2& c,
@@ -943,7 +947,7 @@ public:
    */
   Face_handle remove_isolated_vertex(Vertex_handle v);
 
-  /*! sets `c` to be the \f$ x\f$-monotone curve associated with the edge `e`.
+  /*! sets `c` to be the \f$x\f$-monotone curve associated with the edge `e`.
    * The function obtains a handle for the modified edge (same as `e`).
    * \pre `c` is geometrically equivalent to the curve currently associated
    * with `e`.
@@ -967,12 +971,14 @@ public:
 
   /*! merges the edges represented by `e1` and `e2` into
    * a single edge, associated with the given merged curve `c`.  Denote `e1`'s
-   * end-vertices as \f$ u_1\f$ and \f$ v\f$, while `e2`'s end-vertices are
+   * end-vertices as \f$u_1\f$ and \f$v\f$, while `e2`'s end-vertices are
-   * denoted \f$ u_2\f$ and \f$ v\f$. The function removes the common vertex \f$
+   * denoted \f$u_2\f$ and \f$v\f$. The function removes the common vertex
-   * v\f$ returns a handle for one of the merged halfedges, directed from \f$
+   * \f$v\f$ returns a handle for one of the merged halfedges, directed from
-   * u_1\f$ to \f$ u_2\f$.
+   * \f$u_1\f$ to \f$u_2\f$.
+   *
    * \pre `e1` and `e2` share a common end-vertex, such that the two other
    * end-vertices of the two edges are associated with `c`'s endpoints.
+   * \pre `e1` and `e2` have the same direction.
    */
   Halfedge_handle merge_edge(Halfedge_handle e1,
                              Halfedge_handle e2,
@@ -985,7 +991,7 @@ public:
    * whether they should be left as isolated vertices in the arrangement.
    * If the operation causes two faces to merge, the merged face is returned.
    * Otherwise, the face to which the edge was incident is returned.
-  */
+   */
   Face_handle remove_edge(Halfedge_handle e,
                           bool remove_source = true,
                           bool remove_target = true);
@@ -1007,43 +1013,43 @@ public:
   bool is_valid() const;
 
   /// @}
-
 }; /* end Arrangement_on_surface_2 */
+
 } /* end namespace CGAL */
 
 namespace CGAL {
 
 /*! \ingroup PkgArrangementOnSurface2Insert
- * The function `%insert` inserts one or more curves or \f$ x\f$-monotone
+ * The function `%insert` inserts one or more curves or \f$x\f$-monotone
  * curves into a given arrangement, where no restrictions are imposed on the
- * inserted curves. If an inserted curve is not \f$ x\f$-monotone curve, it is
+ * inserted curves. If an inserted curve is not \f$x\f$-monotone curve, it is
- * subdivided into \f$ x\f$-monotone subcurves (and perhaps isolated points),
+ * subdivided into \f$x\f$-monotone subcurves (and perhaps isolated points),
  * which are inserted into the arrangement.
  *
  * \cgalHeading{Requirements}
  *
  * <UL>
- * <LI>If the curve is \f$ x\f$-monotone curve then The instantiated
+ * <LI>If the curve is \f$x\f$-monotone curve then The instantiated
- * `Traits` class must model the `ArrangementXMonotoneTraits_2`
+ * `Traits` class must model the `AosXMonotoneTraits_2`
- * concept. In case that the curve is not \f$ x\f$-monotone then the
+ * concept. In case that the curve is not \f$x\f$-monotone then the
  * instantiated `Traits` class must model the
- * `ArrangementTraits_2` concept. That is, it should define the
+ * `AosTraits_2` concept. That is, it should define the
- * `Curve_2` type, and support its subdivision into \f$ x\f$-monotone
+ * `Curve_2` type, and support its subdivision into \f$x\f$-monotone
  * subcurves (and perhaps isolated points).
  * <LI>The point-location object `pl`, must model the
- * `ArrangementPointLocation_2` concept.
+ * `AosPointLocation_2` concept.
  * </UL>
  */
 
 /// @{
 
 /*! Inserts the given curve `c` into the arrangement `arr`.  `c` is subdivided
- * into \f$ x\f$-monotone subcurves (and perhaps isolated points). Each subcurve
+ * into \f$x\f$-monotone subcurves (and perhaps isolated points). Each subcurve
  * is in turn inserted into the arrangement by locating its left endpoint and
  * computing its zone until reaching the right endpoint.
  *
  * The given point-location object `pl` is used to locate the left endpoints of
- * the \f$ x\f$-monotone curves. By default, the function uses the "walk along
+ * the \f$x\f$-monotone curves. By default, the function uses the "walk along
  * line" point-location strategy - namely an instance of the class
  * `Arr_walk_along_line_point_location<Arrangement_on_surface_2<GeometryTraits, TopologyTraits> >`.
  *
@@ -1069,7 +1075,7 @@ void insert(Arrangement_on_surface_2<GeometryTraits, TopologyTraits>& arr,
             typename Arr_point_location_result<Arrangement_on_surface_2<GeometryTraits, TopologyTraits> >::type obj);
 
 
-/*! Aggregately inserts the curves or \f$ x\f$-monotone curves in the range
+/*! Aggregately inserts the curves or \f$x\f$-monotone curves in the range
  * `[first,last)` into the arrangement `arr` using the sweep-line framework.
  * \param arr the target arrangement.
  * \param first the iterator to the first element in the range of curves.
@@ -1089,7 +1095,7 @@ void insert(Arrangement_on_surface_2<GeometryTraits, TopologyTraits>& arr,
  * arrangement's edges or vertices.
  *
  * If the give curve is not an \f$x\f$-monotone curve then the function
- * subdivides the given curve into \f$ x\f$-monotone subcurves and isolated
+ * subdivides the given curve into \f$x\f$-monotone subcurves and isolated
  * vertices . Each subcurve is in turn checked for intersection.  The function
  * uses the zone algorithm to check if the curve intersects the
  * arrangement. First, the curve's left endpoint is located. Then, its zone is
@@ -1103,7 +1109,7 @@ void insert(Arrangement_on_surface_2<GeometryTraits, TopologyTraits>& arr,
  * `Arr_walk_along_line_point_location<Arrangement_on_surface_2<GeometryTraits,
  * TopologyTraits> >`.
  *
- * Checks if the given curve or \f$ x\f$-monotone curve `c` intersects
+ * Checks if the given curve or \f$x\f$-monotone curve `c` intersects
  * edges or vertices of the existing arrangement `arr`.
  *
  * \pre If provided, `pl` must be attached to the given arrangement `arr`.
@@ -1111,14 +1117,14 @@ void insert(Arrangement_on_surface_2<GeometryTraits, TopologyTraits>& arr,
  * \cgalHeading{Requirements}
  *
  * <UL>
- * <LI>If `c` is \f$ x\f$-monotone then the instantiated `GeometryTraits`
+ * <LI>If `c` is \f$x\f$-monotone then the instantiated `GeometryTraits`
- * class must model the `ArrangementXMonotoneTraits_2` concept. If
+ * class must model the `AosXMonotoneTraits_2` concept. If
  * `c` is a curve then the instantiated `GeometryTraits` class must
- * model the `ArrangementTraits_2` concept. That is, it should
+ * model the `AosTraits_2` concept. That is, it should
  * define the `Curve_2` type, and support its subdivision into
- * \f$ x\f$-monotone subcurves (and perhaps isolated points).
+ * \f$x\f$-monotone subcurves (and perhaps isolated points).
  * <LI>The point-location object `pl`, must model the
- * `ArrangementPointLocation_2` concept.
+ * `AosPointLocation_2` concept.
  * </UL>
  */
 template <typename GeometryTraits, typename TopologyTraits, typename Curve,
@@ -1128,7 +1134,7 @@ bool do_intersect(Arrangement_on_surface_2<GeometryTraits, TopologyTraits>& arr,
 
 /*! \ingroup PkgArrangementOnSurface2Funcs
  *
- * Inserts a given \f$ x\f$-monotone curve into a given arrangement, where the
+ * Inserts a given \f$x\f$-monotone curve into a given arrangement, where the
  * given curve and the existing arrangement edges (more precisely, the curves
  * geometric mappings of the edges) must be pairwise disjoint in their
  * interiors, and the interior of the input curve must not contain existing
@@ -1152,9 +1158,9 @@ bool do_intersect(Arrangement_on_surface_2<GeometryTraits, TopologyTraits>& arr,
  *
  * <UL>
  * <LI>The instantiated `Traits` class must model the restricted
- * `ArrangementBasicTraits_2` concept, as no intersections are computed.
+ * `AosBasicTraits_2` concept, as no intersections are computed.
  * <LI>The point-location object `pl` must model the
- * `ArrangementPointLocation_2` concept.
+ * `AosPointLocation_2` concept.
  * </UL>
  */
 template <typename GeometryTraits, typename TopologyTraits,
@@ -1167,7 +1173,7 @@ insert_non_intersecting_curve
 
 /*! \ingroup PkgArrangementOnSurface2Funcs
  *
- * Inserts a set of \f$ x\f$-monotone curves in a given range into a given
+ * Inserts a set of \f$x\f$-monotone curves in a given range into a given
  * arrangement. The insertion is performed in an aggregated manner using the
  * sweep-line algorithm. The input curves and the existing arrangement edges
  * (more precisely, the curves geometric mappings of the edges) must be pairwise
@@ -1180,7 +1186,7 @@ insert_non_intersecting_curve
  *
  * <UL>
  * <LI>The instantiated `Traits` class must model the
- * `ArrangementBasicTraits_2` concept, as no intersections are computed.
+ * `AosBasicTraits_2` concept, as no intersections are computed.
  * <LI>`InputIterator::value_type` must be `Traits::X_monotone_curve_2`
  * </UL>
  */
@@ -1209,12 +1215,12 @@ void insert_non_intersecting_curves
  *
  * <UL>
  * <LI>The instantiated `Traits` class must model the
- * `ArrangementXMonotoneTraits_2` concept. Not all expressions listed
+ * `AosXMonotoneTraits_2` concept. Not all expressions listed
  * by this concept are required. In fact the traits class must model the
- * `ArrangementBasicTraits_2` concept, and support the splitting
+ * `AosBasicTraits_2` concept, and support the splitting
  * functionality.
  * <LI>The point-location object `pl`, must model the
- * `ArrangementPointLocation_2` concept.
+ * `AosPointLocation_2` concept.
  * </UL>
  */
 template <typename GeometryTraits, typename TopologyTraits,
@@ -1230,7 +1236,7 @@ insert_point(Arrangement_on_surface_2<GeometryTraits, TopologyTraits>& arr,
  *
  * Invokes the member function `arr.is_valid()` to verify the topological
  * correctness of the arrangement. Then it performs additional validity
- * tests. It checks that all \f$ x\f$-monotone curves associated with
+ * tests. It checks that all \f$x\f$-monotone curves associated with
  * arrangement edges are pairwise disjoint in their interior. Then it makes sure
  * that all holes and all isolated vertices are located within the proper
  * arrangement faces. Note that the test carried out by this function may take a
@@ -1253,8 +1259,8 @@ bool is_valid
  * its endpoints become isolated, they are removed as well. The call
  * `remove_edge(arr, e)` is equivalent to the call `arr.remove_edge (e, true,
  * true)`. However, this free function requires that `Traits` be a model of the
- * refined concept `ArrangementXMonotoneTraits_2`, which requires merge
+ * refined concept `AosXMonotoneTraits_2`, which requires merge
- * operations on \f$ x\f$-monotone curves. If one of the end-vertices of the
+ * operations on \f$x\f$-monotone curves. If one of the end-vertices of the
  * given edge becomes redundant after the edge is removed (see `remove_vertex()`
  * for the definition of a redundant vertex), it is removed, and its incident
  * edges are merged.  If the edge-removal operation causes two faces to merge,
@@ -1265,10 +1271,10 @@ bool is_valid
  *
  * <UL>
  * <LI>The instantiated traits class must model the concept
- * `ArrangementXMonotoneTraits_2`.
+ * `AosXMonotoneTraits_2`.
  * </UL>
  */
-template<typename GeometryTraits, typename TopologyTraits>
+template <typename GeometryTraits, typename TopologyTraits>
 typename Arrangement_on_surface_2<GeometryTraits, TopologyTraits>::Face_handle
 remove_edge
 (Arrangement_on_surface_2<GeometryTraits, TopologyTraits>& arr,
@@ -1287,9 +1293,9 @@ remove_edge
  *
  * <UL>
  * <LI>The instantiated `Traits` class must model the
- * `ArrangementXMonotoneTraits_2` concept. Not all expressions listed
+ * `AosXMonotoneTraits_2` concept. Not all expressions listed
  * by this concept are required. In fact the traits class must model the
- * `ArrangementBasicTraits_2` concept and support the merging
+ * `AosBasicTraits_2` concept and support the merging
  * functionality.
  * </UL>
  */
@@ -1323,9 +1329,9 @@ bool remove_vertex
  *
  * \pre If provided, `pl` must be attached to the given arrangement `arr`.
  * \pre The instantiated `GeometryTraits` class must model the
- *      `ArrangementXMonotoneTraits_2` concept.
+ *      `AosXMonotoneTraits_2` concept.
  * \pre The point-location object `pl`, must model the
- *      `ArrangementPointLocation_2` concept.
+ *      `AosPointLocation_2` concept.
  * \pre Dereferencing `oi` must yield a polymorphic object of type
  *      `std::variant<Arrangement_on_surface_2::Vertex_handle, Arrangement_on_surface_2::Halfedge_handle, Arrangement_on_surface_2::Face_handle>`.
  *

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_on_surface_with_history_2.h

@@ -5,18 +5,18 @@ namespace CGAL {
  * \anchor arr_refaos_with_hist
  *
  * An object `arr` of the class `Arrangement_on_surface_with_history_2`
- * represents the planar subdivision induced by a set of input curves \f$ \cal
+ * represents the planar subdivision induced by a set of input curves
- * C\f$.  The arrangement is represented as a doubly-connected edge-list (<span
+ * \f$\cal C\f$.  The arrangement is represented as a doubly-connected edge-list
- * class="textsc">Dcel</span>).  As is the case for the
+ * (<span class="textsc">Dcel</span>).  As is the case for the
  * `Arrangement_2<Traits,Dcel>`, each <span class="textsc">Dcel</span> vertex is
- * associated with a point and each edge is associated with an \f$ x\f$-monotone
+ * associated with a point and each edge is associated with an \f$x\f$-monotone
  * curve whose interior is disjoint from all other edges and vertices. Each such
- * \f$ x\f$-monotone curve is a subcurve of some \f$ C \in \cal C\f$ - or may
+ * \f$x\f$-monotone curve is a subcurve of some \f$C \in \cal C\f$ - or may
- * represent an overlap among several curves in \f$ \cal C\f$.
+ * represent an overlap among several curves in \f$\cal C\f$.
  *
  * The `Arrangement_on_surface_with_history_2` class-template extends the
  * `Arrangement_2` class-template by keeping an additional container of input
- * curves representing \f$ \cal C\f$, and by maintaining a cross-mapping between
+ * curves representing \f$\cal C\f$, and by maintaining a cross-mapping between
  * these curves and the arrangement edges they induce. This way it is possible
  * to determine the inducing curve(s) of each arrangement edge. This mapping
  * also allows the traversal of input curves, and the traversal of edges induced
@@ -26,33 +26,32 @@ namespace CGAL {
  *
  * <UL>
  * <LI>The `GeometryTraits` template-parameter should be substituted by a
- * model of the `ArrangementTraits_2` concept. The traits class defines the
+ * model of the `AosTraits_2` concept. The traits class defines the
  * `Curve_2` type, which represents an input curve.  It also defines the types
- * of \f$ x\f$-monotone curves and two-dimensional points, namely
+ * of \f$x\f$-monotone curves and two-dimensional points, namely
- * `ArrangementTraits_2::X_monotone_curve_2` and
+ * `AosTraits_2::X_monotone_curve_2` and
- * `ArrangementTraits_2::Point_2`, respectively, and supports basic
+ * `AosTraits_2::Point_2`, respectively, and supports basic
  * geometric predicates on them.
  * <LI>The `TopologyTraits` template-parameter should be substituted by a
- * class that is a model of the `ArrangementTopologyTraits` concept.
+ * class that is a model of the `AosTopologyTraits` concept.
  * </UL>
  *
  * \sa `Arrangement_with_history_2<GeometryTraits,Dcel>`
  * \sa `Arrangement_on_surface_2<GeometryTraits,TopologyTraits>`
- * \sa `ArrangementTraits_2`
+ * \sa `AosTraits_2`
- * \sa `ArrangementTopologyTraits`
+ * \sa `AosTopologyTraits`
  */
 template <typename GeometryTraits, typename TopologyTraits>
 class Arrangement_on_surface_with_history_2 :
-    public Arrangement_on_surface_2<GeometryTraits, TopologyTraits>
+    public Arrangement_on_surface_2<GeometryTraits, TopologyTraits> {
-{
 public:
   /// \name Types
   /// @{
 
-  //! the geometry traits class in use.
+  /// the geometry traits class in use.
   typedef GeometryTraits                                 Geometry_traits_2;
 
-  //! the topology traits class in use.
+  /// the topology traits class in use.
   typedef TopologyTraits                                 Topology_traits;
 
   /*! a private type used as an abbreviation of the
@@ -61,16 +60,16 @@ public:
   typedef Arrangement_on_surface_with_history_2<Geometry_traits_2,
                                                 TopologyTraits> Self;
 
-  //! the <span class="textsc">Dcel</span> representation of the arrangement.
+  /// the <span class="textsc">Dcel</span> representation of the arrangement.
   typedef typename Topology_traits::Dcel                 Dcel;
 
-  //! the point type, as defined by the traits class.
+  /// the point type, as defined by the traits class.
   typedef typename Geometry_traits_2::Point_2            Point_2;
 
-  //! the \f$ x\f$-monotone curve type, as defined by the traits class.
+  /// the \f$x\f$-monotone curve type, as defined by the traits class.
   typedef typename Geometry_traits_2::X_monotone_curve_2 X_monotone_curve_2;
 
-  //! the curve type, as defined by the traits class.
+  /// the curve type, as defined by the traits class.
   typedef typename Geometry_traits_2::Curve_2            Curve_2;
 
   /// @}
@@ -82,7 +81,7 @@ public:
    */
   /// @{
 
-  //! a handle for an input curve.
+  /// a handle for an input curve.
   typedef unspecified_type Curve_handle;
 
   /*! a bidirectional iterator over the curves that induce the arrangement.
@@ -123,13 +122,13 @@ public:
   /// \name Assignment Methods
   /// @{
 
-  //! assignment operator.
+  /// assignment operator.
   Self& operator=(other);
 
-  //! assigns the contents of another arrangement.
+  /// assigns the contents of another arrangement.
   void assign(const Self& other);
 
-  //! clears the arrangement.
+  /// clears the arrangement.
   void clear ();
 
   /// @}
@@ -140,31 +139,31 @@ public:
 
   /// @{
 
-  //! returns the number of input curves that induce the arrangement.
+  /// returns the number of input curves that induce the arrangement.
   Size number_of_curves() const;
 
-  //! returns the begin-iterator of the curves inducing the arrangement.
+  /// returns the begin-iterator of the curves inducing the arrangement.
   Curve_iterator curves_begin();
 
   //! returns the past-the-end iterator of the curves inducing the arrangement.
   Curve_iterator curves_end();
 
-  //! returns the number of arrangement edges induced by the curve `ch`.
+  /// returns the number of arrangement edges induced by the curve `ch`.
   Size number_of_induced_edges(Curve_handle ch) const;
 
-  //! returns the begin-iterator of the edges induced by the curve `ch`.
+  /// returns the begin-iterator of the edges induced by the curve `ch`.
   Induced_edge_iterator induced_edges_begin(Curve_handle ch) const;
 
-  //! returns the past-the-end iterator of the edges induced by the curve `ch`.
+  /// returns the past-the-end iterator of the edges induced by the curve `ch`.
   Induced_edge_iterator induced_edges_end(Curve_handle ch) const;
 
-  //! returns the number of input curves that originate the edge `e`.
+  /// returns the number of input curves that originate the edge `e`.
   Size number_of_originating_curves(Halfedge_handle e) const;
 
-  //! returns the begin-iterator of the curves originating the edge `e`.
+  /// returns the begin-iterator of the curves originating the edge `e`.
   Originating_curve_iterator originating_curves_begin(Halfedge_handle e) const;
 
-  //! returns the past-the-end iterator of the curves originating the edge `e`.
+  /// returns the past-the-end iterator of the curves originating the edge `e`.
   Originating_curve_iterator originating_curves_end(Halfedge_handle e) const;
 
   /// @}
@@ -192,9 +191,9 @@ public:
   /*! merges the edges represented by `e1` and `e2` into a single edge.  The
    * function returns a handle for one of the merged halfedges.
    *
-   * \pre `e1` and `e2` share a common end-vertex, of degree \f$ 2\f$, and the
+   * \pre `e1` and `e2` share a common end-vertex, of degree \f$2\f$, and the
-   *      \f$ x\f$-monotone curves associated with `e1` and `e2` are mergeable
+   *      \f$x\f$-monotone curves associated with `e1` and `e2` are mergeable
-   *      into a single \f$ x\f$-monotone curves.
+   *      into a single \f$x\f$-monotone curves.
    */
   Halfedge_handle merge_edge(Halfedge_handle e1, Halfedge_handle e2);
 
@@ -210,7 +209,6 @@ public:
                           bool remove_target = true);
 
   /// @}
-
 }; /* end Arrangement_on_surface_with_history_2 */
 
 /*! \ingroup PkgArrangementOnSurface2Insert
@@ -222,14 +220,14 @@ public:
  * computing its zone until reaching the right endpoint.
  *
  * The given point-location object `pl` is used to locate the left endpoints of
- * the \f$ x\f$-monotone curves. By default, the function uses the "walk along
+ * the \f$x\f$-monotone curves. By default, the function uses the "walk along
  * line" point-location strategy - namely an instance of the class
  * `Arr_walk_along_line_point_location<Arrangement_2<Traits,Dcel> >`.
  *
  * \pre If provided, `pl` is attached to the given arrangement `arr`.
  */
-template<typename GeometryTraits, typename TopologyTraits,
+template <typename GeometryTraits, typename TopologyTraits,
-         typename PointLocation>
+          typename PointLocation>
 typename Arrangement_on_surface_with_history_2<GeometryTraits, TopologyTraits>::Curve_handle
 insert
 (Arrangement_on_surface_with_history_2<GeometryTraits, TopologyTraits>& arr,
@@ -261,7 +259,6 @@ Size remove_curve
 (Arrangement_on_surface_with_history_2<GeometryTraits, TopologyTraits>& arr,
  typename Arrangement_on_surface_with_history_2<GeometryTraits, TopologyTraits>::Curve_handle ch);
 
-
 /*! \addtogroup PkgArrangementOnSurface2Overlay
  *
  * Computes the overlay of two arrangements with history `arr1` and `arr2`, and
@@ -281,17 +278,16 @@ void overlay
  Arrangement_on_surface_with_history_2<GeometryTraits, ResTopologyTraits>& res,
  OverlayTraits& ovl_tr);
 
-
 /*! \addtogroup PkgArrangementOnSurface2Overlay
  *
  * Computes the (simple) overlay of two arrangements with history `arr1` and
- *`arr2`, and sets the output arrangement with history `res` to represent the
+ * `arr2`, and sets the output arrangement with history `res` to represent the
- *overlaid arrangement. The function also constructs a consolidated set of
+ * overlaid arrangement. The function also constructs a consolidated set of
- *curves that induce `res`. It employs the default overlay-traits, which
+ * curves that induce `res`. It employs the default overlay-traits, which
- *practically does nothing.
+ * practically does nothing.
  *
  * \pre `res` does not refer to either `arr1` or `arr2` (that is, "self overlay"
- *is not supported).
+ * is not supported).
  */
 template <typename GeometryTraits, typename TopologyTraits1,
           typename TopologyTraits2, typename ResTopologyTraits>

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arrangement_with_history_2.h

@@ -5,17 +5,17 @@ namespace CGAL {
  * \anchor arr_refarr_with_hist
  *
  * An object `arr` of the class `Arrangement_with_history_2` represents the
- * planar subdivision induced by a set of input curves \f$ \cal C\f$.  The
+ * planar subdivision induced by a set of input curves \f$\cal C\f$.  The
  * arrangement is represented as a doubly-connected edge-list (\dcel).  As is
  * the case for the `Arrangement_2<Traits,Dcel>`, each \dcel vertex is
- * associated with a point and each edge is associated with an \f$ x\f$-monotone
+ * associated with a point and each edge is associated with an \f$x\f$-monotone
  * curve whose interior is disjoint from all other curves and points. Each such
- * \f$ x\f$-monotone curve is a subcurve of some \f$ C \in \cal C\f$, or may
+ * \f$x\f$-monotone curve is a subcurve of some \f$C \in \cal C\f$, or may
- * represent an overlap among several curves in \f$ \cal C\f$.
+ * represent an overlap among several curves in \f$\cal C\f$.
  *
  * The `Arrangement_with_history_2` class-template extends the `Arrangement_2`
  * class-template by keeping an additional container of input curves
- * representing \f$ \cal C\f$, and by maintaining a cross-mapping between these
+ * representing \f$\cal C\f$, and by maintaining a cross-mapping between these
  * curves and the arrangement edges they induce. This way it is possible to
  * determine the inducing curve(s) of each arrangement edge. This mapping also
  * allows the traversal of input curves, and the traversal of edges induced by
@@ -24,39 +24,39 @@ namespace CGAL {
  * The `Arrangement_with_history_2` template has two parameters:
  * <UL>
  * <LI>The `Traits` template-parameter should be substituted by a model of
- * the `ArrangementTraits_2` concept. The traits class defines the `Curve_2`
+ * the `AosTraits_2` concept. The traits class defines the `Curve_2`
  * type, which represents an input curve.  It also defines the types of \f$
  * x\f$-monotone curves and two-dimensional points, namely
- * `ArrangementTraits_2::X_monotone_curve_2` and `ArrangementTraits_2::Point_2`,
+ * `AosTraits_2::X_monotone_curve_2` and `AosTraits_2::Point_2`,
  * respectively, and supports basic geometric predicates on them.
  * <LI>The `Dcel` template-parameter should be substituted by a class that is
- * a model of the `ArrangementDcelWithRebind` concept. The value of this
+ * a model of the `AosDcelWithRebind` concept. The value of this
  * parameter is by default `Arr_default_dcel<Traits>`.
  * </UL>
  *
- * \sa `ArrangementDcel`
+ * \sa `AosDcel`
  * \sa `Arr_default_dcel<Traits>`
- * \sa `ArrangementTraits_2`
+ * \sa `AosTraits_2`
  * \sa `Arrangement_2<Traits,Dcel>`
  * \sa `insertion functions`
  * \sa `removal functions`
  * \sa `overlaying arrangements`
  */
 template <typename Traits, typename Dcel>
-class Arrangement_with_history_2 : public Arrangement_on_surface_with_history_2<Traits, typename Default_planar_topology<Traits, Dcel>::Traits> {
+class Arrangement_with_history_2 :
+    public Arrangement_on_surface_with_history_2<Traits, typename Default_planar_topology<Traits, Dcel>::Traits> {
 public:
-
   /// \name Types
   /// @{
 
-  //! the geometry traits class.
+  /// the geometry traits class.
   typedef Traits                                  Geometry_traits;
 
-  //! The topology traits.
+  /// The topology traits.
   typedef typename Default_planar_topology<Geometry_traits, Dcel>::Traits
     Topology_traits;
 
-  //! The base arrangement on surface type.
+  /// The base arrangement on surface type.
   typedef Arrangement_on_surface_with_history_2<Geometry_traits, Topology_traits>
     Base;
 
@@ -129,13 +129,13 @@ public:
  * computing its zone until reaching the right endpoint.
  *
  * The given point-location object `pl` is used to locate the left endpoints of
- * the \f$ x\f$-monotone curves. By default, the function uses the "walk along
+ * the \f$x\f$-monotone curves. By default, the function uses the "walk along
  * line" point-location strategy - namely an instance of the class
  * `Arr_walk_along_line_point_location<Arrangement_2<Traits,Dcel> >`.
  *
  * \pre If provided, `pl` is attached to the given arrangement `arr`.
  */
-template<typename Traits, typename Dcel, typename PointLocation>
+template <typename Traits, typename Dcel, typename PointLocation>
 typename Arrangement_with_history_2<Traits, Dcel>::Curve_handle
 insert(Arrangement_with_history_2<Traits, Dcel>& arr,
        const typename Traits::Curve_2& c,
@@ -161,7 +161,6 @@ template <typename Traits, typename Dcel>
 Size remove_curve(Arrangement_with_history_2<Traits,Dcel>& arr,
                   typename Arrangement_with_history_2<Traits,Dcel>::Curve_handle ch);
 
-
 /*! \addtogroup PkgArrangementOnSurface2Overlay
  * Computes the overlay of two arrangements with history `arr1` and `arr2`, and
  * sets the output arrangement with history `res` to represent the overlaid
@@ -170,14 +169,13 @@ Size remove_curve(Arrangement_with_history_2<Traits,Dcel>& arr,
  *
  * \pre `res` does not refer to either `arr1` or `arr2`.
  */
-template<typename Traits, typename Dcel1, typename Dcel2,
+template <typename Traits, typename Dcel1, typename Dcel2,
-         typename ResDcel, typename OverlayTraits>
+          typename ResDcel, typename OverlayTraits>
 void overlay(const Arrangement_with_history_2<Traits,Dcel1>& arr1,
              const Arrangement_with_history_2<Traits,Dcel2>& arr2,
              Arrangement_with_history_2<Traits,ResDcel>& res,
              OverlayTraits& ovl_tr);
 
-
 /*! \addtogroup PkgArrangementOnSurface2Overlay
  *
  * Computes the (simple) overlay of two arrangements with history `arr1` and
@@ -189,8 +187,7 @@ void overlay(const Arrangement_with_history_2<Traits,Dcel1>& arr1,
  * \pre `res` does not refer to either `arr1` or `arr2` (that is, "self overlay"
  * is not supported).
  */
-template<typename Traits, typename Dcel1, typename Dcel2,
+template <typename Traits, typename Dcel1, typename Dcel2, typename ResDcel>
-         typename ResDcel>
 void overlay(const Arrangement_with_history_2<Traits,Dcel1>& arr1,
              const Arrangement_with_history_2<Traits,Dcel2>& arr2,
              Arrangement_with_history_2<Traits,ResDcel>& res);

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/CORE_algebraic_number_traits.h

@@ -12,16 +12,16 @@ public:
   /// \name Types
   /// @{
 
-  //! The integer number type.
+  /// The integer number type.
   typedef CORE::BigInt                    Integer;
 
-  //! The rational number type.
+  /// The rational number type.
   typedef CORE::BigRat                    Rational;
 
-  //! The polynomial type.
+  /// The polynomial type.
   typedef CORE::Polynomial<Integer>       Polynomial;
 
-  //! The algebraic number type.
+  /// The algebraic number type.
   typedef CORE::Expr                      Algebraic;
 
   /// @}

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/IO/Arr_iostream.h

@@ -2,100 +2,89 @@ namespace CGAL {
 
 namespace IO {
 
-/*!
+/*! \defgroup PkgArrangementOnSurface2Read CGAL::IO::read()
-  \defgroup PkgArrangementOnSurface2Read CGAL::IO::read()
+ * \ingroup PkgArrangementOnSurface2IO
-  \ingroup PkgArrangementOnSurface2IO
+ *
+ * Reads a given arrangement from a given input stream
+ * using a specific input format.
+ *
+ * \cgalHeading{Requirements}
+ *
+ * <UL>
+ * <LI>The instantiated `Formatter` class must model the
+ *   `AosInputFormatter` concept.
+ * <LI>The instantiated `WithHistoryFormatter` class must model the
+ *   `AosWithHistoryInputFormatter` concept.
+ * </UL>
+ *
+ * \sa `PkgArrangementOnSurface2Write`
+ * \sa `PkgArrangementOnSurface2op_left_shift`
+ * \sa `PkgArrangementOnSurface2op_right_shift`
+ */
 
-Reads a given arrangement from a given input stream
-using a specific input format.
-
-\cgalHeading{Requirements}
-
-<UL>
-<LI>The instantiated `Formatter` class must model the
-  `ArrangementInputFormatter` concept.
-<LI>The instantiated `WithHistoryFormatter` class must model the
-  `ArrangementWithHistoryInputFormatter` concept.
-</UL>
-
-
-\sa `PkgArrangementOnSurface2Write`
-
-
-\sa `PkgArrangementOnSurface2op_left_shift`
-\sa `PkgArrangementOnSurface2op_right_shift`
-*/
 /// @{
 
-/*!
+/*! Reads the arrangement object `arr` from the given input stream `is`
-Reads the arrangement object `arr` from the given input stream `is`
+ * using a specific input format defined by \"formatter\".
-using a specific input format defined by \"formatter\".
+ */
-*/
+template <typename Traits, typename Dcel, typename Formatter>
-template<typename Traits, typename Dcel, typename Formatter>
+std::istream& read(Arrangement_2<Traits,Dcel>& arr,
-std::istream& read (Arrangement_2<Traits,Dcel>& arr,
+                   std::istream& is, Formatter& formatter);
-                    std::istream& is,
-                    Formatter& formatter);
-
 
 /// @}
 
-/*!
+/*! \defgroup PkgArrangementOnSurface2Write CGAL::IO::write()
-  \defgroup PkgArrangementOnSurface2Write CGAL::IO::write()
+ * \ingroup PkgArrangementOnSurface2IO
-  \ingroup PkgArrangementOnSurface2IO
+ *
+ * Writes a given arrangement into a given output stream
+ * using a specific output format.
+ *
+ * \cgalHeading{Requirements}
+ *
+ * <UL>
+ * <LI>The instantiated `Formatter` class must model the
+ *   `AosOutputFormatter` concept.
+ * <LI>The instantiated `WithHistoryFormatter` class must model the
+ *   `AosWithHistoryOutputFormatter` concept.
+ * </UL>
+ *
+ * \sa `PkgArrangementOnSurface2Read`
+ * \sa `PkgArrangementOnSurface2op_left_shift`
+ * \sa `PkgArrangementOnSurface2op_right_shift`
+ */
 
-Writes a given arrangement into a given output stream
-using a specific output format.
-
-\cgalHeading{Requirements}
-
-<UL>
-<LI>The instantiated `Formatter` class must model the
-  `ArrangementOutputFormatter` concept.
-<LI>The instantiated `WithHistoryFormatter` class must model the
-  `ArrangementWithHistoryOutputFormatter` concept.
-</UL>
-
-\sa `PkgArrangementOnSurface2Read`
-\sa `PkgArrangementOnSurface2op_left_shift`
-\sa `PkgArrangementOnSurface2op_right_shift`
-*/
 /// @{
 
-/*!
+/*! Writes the arrangement object `arr` into the given output stream
-Writes the arrangement object `arr` into the given output stream
+ * `os` using a specific output format defined by `formatter`.
-`os` using a specific output format defined by `formatter`.
+ */
-*/
+template <typename Traits, typename Dcel, typename Formatter>
-template<typename Traits, typename Dcel, typename Formatter>
+std::ostream& write(const Arrangement_2<Traits,Dcel>& arr,
-std::ostream& write (const Arrangement_2<Traits,Dcel>& arr,
+                    std::ostream& os, Formatter& formatter);
-                     std::ostream& os,
-                     Formatter& formatter);
 
 /// @}
 
 } // namespace IO
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2op_left_shift
-\ingroup PkgArrangementOnSurface2op_left_shift
+ * Inserts the arrangement object `arr` into the output stream
-Inserts the arrangement object `arr` into the output stream
+ * `os` using the output format defined by the
-`os` using the output format defined by the
+ * `Arr_text_formatter` class. Only the basic geometric and
-`Arr_text_formatter` class. Only the basic geometric and
+ * topological features of the arrangement are inserted. Auxiliary data
-topological features of the arrangement are inserted. Auxiliary data
+ * that may be attached to the \dcel features is ignored.
-that may be attached to the \dcel features is ignored.
+ */
-*/
+template <typename Traits, typename Dcel>
-template<typename Traits, typename Dcel>
+std::ostream& operator<<(std::ostream& os,
-std::ostream& operator<< (std::ostream& os,
+                         const Arrangement_2<Traits, Dcel>& arr);
-                          const Arrangement_2<Traits,Dcel>& arr);
 
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2op_right_shift
-\ingroup PkgArrangementOnSurface2op_right_shift
+ * Extracts an arrangement from a given input stream using the input
-Extracts an arrangement from a given input stream using the input
+ * format defined by the `Arr_text_formatter` class - that is, only the
-format defined by the `Arr_text_formatter` class - that is, only the
+ * basic geometric and topological features of the arrangement are read
-basic geometric and topological features of the arrangement are read
+ * and no auxiliary data is attached to the Dcel features.
-and no auxiliary data is attached to the Dcel features.
+ */
-*/
+template <typename Traits, typename Dcel>
-template<class Traits, class Dcel>
+std::istream& operator>>(std::istream& is, Arrangement_2<Traits, Dcel>& arr);
-std::istream& operator>>(std::istream& is, Arrangement_2<Traits,Dcel>& arr);
-
 
 } /* end namespace CGAL::IO*/

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/IO/Arr_text_formatter.h

@@ -1,93 +1,83 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2IO
-\ingroup PkgArrangementOnSurface2IO
+ *
+ * `Arr_extended_dcel_text_formatter` defines the format of an arrangement in an
+ * input or output stream (typically a file stream), thus enabling reading and
+ * writing an `Arrangement` instance using a simple text format. The
+ * `Arrangement` class should be instantiated with a \dcel class which in turn
+ * instantiates the `Arr_extended_dcel` template with the `VertexData`,
+ * `HalfedgeData` and `FaceData` types.  The formatter supports reading and
+ * writing the data objects attached to the arrangement vertices, halfedges and
+ * faces.
+ *
+ * The `Arr_extended_dcel_text_formatter` class assumes that the nested
+ * `Point_2` and the `Curve_2` types defined by the `Arrangement`
+ * template-parameter, as well as the `VertexData`, `HalfedgeData` and
+ * `FaceData` types, can all be written to an input stream using the `<<`
+ * operator and read from an input stream using the `>>` operator.
+ *
+ * \cgalModels{AosInputFormatter,AosOutputFormatter}
+ *
+ * \sa `PkgArrangementOnSurface2Read`
+ * \sa `PkgArrangementOnSurface2Write`
+ * \sa `Arr_extended_dcel<Traits,VData,HData,FData,V,H,F>`
+ */
+template <typename Arrangement>
+class Arr_extended_dcel_text_formatter {};
 
-`Arr_extended_dcel_text_formatter` defines the format of an arrangement in an input or output stream
-(typically a file stream), thus enabling reading and writing an `Arrangement`
-instance using a simple text format. The `Arrangement` class should be
-instantiated with a \dcel class which in turn instantiates the
-`Arr_extended_dcel` template with the `VertexData`, `HalfedgeData` and
-`FaceData` types.
-The formatter supports reading and writing the data objects attached to the
-arrangement vertices, halfedges and faces.
-
-The `Arr_extended_dcel_text_formatter` class assumes that the nested `Point_2` and the `Curve_2` types
-defined by the `Arrangement` template-parameter, as well as the `VertexData`,
-`HalfedgeData` and `FaceData` types, can all be written to an input stream using
-the `<<` operator and read from an input stream using the `>>` operator.
-
-\cgalModels{ArrangementInputFormatter,ArrangementOutputFormatter}
-
-\sa `PkgArrangementOnSurface2Read`
-\sa `PkgArrangementOnSurface2Write`
-\sa `Arr_extended_dcel<Traits,VData,HData,FData,V,H,F>`
-
-*/
-template< typename Arrangement >
-class Arr_extended_dcel_text_formatter {
-public:
-
-}; /* end Arr_extended_dcel_text_formatter */
 } /* end namespace CGAL */
 
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2IO
-\ingroup PkgArrangementOnSurface2IO
+ *
+ * `Arr_face_extended_text_formatter` defines the format of an arrangement in an
+ * input or output stream (typically a file stream), thus enabling reading and
+ * writing an `Arrangement` instance using a simple text format. The
+ * `Arrangement` class should be instantiated with a \dcel class which in turn
+ * instantiates the `Arr_face_extended_dcel` template with a `FaceData` type.
+ * The formatter supports reading and writing the data objects attached to the
+ * arrangement faces as well.
+ *
+ * The `Arr_face_extended_text_formatter` class assumes that the nested
+ * `Point_2` and the `Curve_2` types defined by the `Arrangement`
+ * template-parameter and that the `FaceData` type can all be written to an
+ * input stream using the `<<` operator and read from an input stream using the
+ * `>>` operator.
+ *
+ * \cgalModels{AosInputFormatter,AosOutputFormatter}
+ *
+ * \sa `PkgArrangementOnSurface2Read`
+ * \sa `PkgArrangementOnSurface2Write`
+ * \sa `Arr_face_extended_dcel<Traits,FData,V,H,F>`
+ */
+template <typename Arrangement>
+class Arr_face_extended_text_formatter {};
 
-`Arr_face_extended_text_formatter` defines the format of an arrangement in an input or output stream
-(typically a file stream), thus enabling reading and writing an `Arrangement`
-instance using a simple text format. The `Arrangement` class should be
-instantiated with a \dcel class which in turn instantiates the
-`Arr_face_extended_dcel` template with a `FaceData` type.
-The formatter supports reading and writing the data objects attached to the
-arrangement faces as well.
-
-The `Arr_face_extended_text_formatter` class assumes that the nested `Point_2` and the `Curve_2` types
-defined by the `Arrangement` template-parameter and that the `FaceData` type
-can all be written to an input stream using the `<<` operator and read from an input stream using the `>>` operator.
-
-\cgalModels{ArrangementInputFormatter,ArrangementOutputFormatter}
-
-\sa `PkgArrangementOnSurface2Read`
-\sa `PkgArrangementOnSurface2Write`
-\sa `Arr_face_extended_dcel<Traits,FData,V,H,F>`
-
-*/
-template< typename Arrangement >
-class Arr_face_extended_text_formatter {
-public:
-
-}; /* end Arr_face_extended_text_formatter */
 } /* end namespace CGAL */
 
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2IO
-\ingroup PkgArrangementOnSurface2IO
+ *
+ * `Arr_text_formatter` defines the format of an arrangement in an input or
+ * output stream (typically a file stream), thus enabling reading and writing an
+ * `Arrangement` instance using a simple text format. The arrangement is assumed
+ * to store no auxiliary data with its \dcel records (and if there are such
+ * records they will not be written or read by the formatter).
+ *
+ * The `Arr_text_formatter` class assumes that the nested `Point_2` and the
+ * `Curve_2` types defined by the `Arrangement` template-parameter can both be
+ * written to an input stream using the `<<` operator and read from an input
+ * stream using the `>>` operator.
+ *
+ * \cgalModels{AosInputFormatter,AosOutputFormatter}
+ *
+ * \sa `PkgArrangementOnSurface2Read`
+ * \sa `PkgArrangementOnSurface2Write`
+ */
+template <typename Arrangement>
+class Arr_text_formatter {};
 
-`Arr_text_formatter` defines the format of an arrangement in an input or output stream
-(typically a file stream), thus enabling reading and writing an `Arrangement`
-instance using a simple text format. The arrangement is assumed to store no auxiliary
-data with its \dcel records (and if there are such records they will not be written
-or read by the formatter).
-
-The `Arr_text_formatter` class assumes that the nested `Point_2` and the `Curve_2` types
-defined by the `Arrangement` template-parameter can both be written to an input
-stream using the `<<` operator and read from an input stream using the `>>`
-operator.
-
-\cgalModels{ArrangementInputFormatter,ArrangementOutputFormatter}
-
-\sa `PkgArrangementOnSurface2Read`
-\sa `PkgArrangementOnSurface2Write`
-
-*/
-template< typename Arrangement >
-class Arr_text_formatter {
-public:
-
-}; /* end Arr_text_formatter */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/IO/Arr_with_history_iostream.h

@@ -2,51 +2,46 @@ namespace CGAL {
 
 namespace IO {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2Read
-\ingroup PkgArrangementOnSurface2Read
+ *
-
+ * reads the arrangement-with-history object `arr` from the given
-Reads the arrangement-with-history object `arr` from the given
+ * input stream `is` using a specific input format defined by
-input stream `is` using a specific input format defined by
+ * \"formatter\".
-\"formatter\".
+ */
-
+template <typename Traits, typename Dcel,
-*/
-template<typename Traits, typename Dcel,
          typename WithHistoryFormatter>
-std::istream& read (Arrangement_with_history_2<Traits,Dcel>& arr,
+std::istream& read(Arrangement_with_history_2<Traits,Dcel>& arr,
-                    std::istream& is,
+                   std::istream& is, WithHistoryFormatter& formatter);
-                    WithHistoryFormatter& formatter);
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2Write
-\ingroup PkgArrangementOnSurface2Write
+ * writes the arrangement-with-history object `arr` into the given
-Writes the arrangement-with-history object `arr` into the given
+ * output stream `os` using a specific output format defined by
-output stream `os` using a specific output format defined by
+ * `formatter`.
-`formatter`.
+ */
-*/
+template <typename Traits, typename Dcel,
-template<typename Traits, typename Dcel,
          typename WithHistoryFormatter>
-std::ostream& write (const Arrangement_with_history_2<Traits,Dcel>& arr,
+std::ostream& write(const Arrangement_with_history_2<Traits,Dcel>& arr,
-                     std::ostream& os,
+                    std::ostream& os, WithHistoryFormatter& formatter);
-                     WithHistoryFormatter& formatter);
 
 } // namespace IO
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2op_left_shift
-\ingroup PkgArrangementOnSurface2op_left_shift
+ * inserts the arrangement-with-history object `arr` into the output
-Inserts the arrangement-with-history object `arr` into the output
+ * stream `os` using the output format defined by the
-stream `os` using the output format defined by the
+ * `Arr_with_history_text_formatter` class. Only the basic geometric
-`Arr_with_history_text_formatter` class. Only the basic geometric
+ * and topological features of the arrangement are inserted. Auxiliary
-and topological features of the arrangement are inserted. Auxiliary
+ * data that may be attached to the \dcel features is ignored.
-data that may be attached to the \dcel features is ignored.
+ */
-*/
+template <typename Traits, typename Dcel>
-template<typename Traits, typename Dcel>
+std::ostream& operator<<(std::ostream& os,
-std::ostream& operator<< (std::ostream& os,
+                         const Arrangement_with_history_2<Traits,Dcel>& arr);
-                          const Arrangement_with_history_2<Traits,Dcel>& arr);
+
+/*! \ingroup PkgArrangementOnSurface2op_right_shift
+ * extracts an arrangement-with-history from a given input stream using
+ * the default input format.
+ */
+template <typename Traits, typename Dcel>
+std::istream& operator>>(std::istream& is,
+                         Arrangement_with_history_2<Traits,Dcel>& arr);
 
-/*!
-\ingroup PkgArrangementOnSurface2op_right_shift
-Extracts an arrangement-with-history from a given input stream using
-the default input format.
-*/
-template<class Traits, class Dcel>
-std::istream& operator>>(std::istream& is, Arrangement_with_history_2<Traits,Dcel>& arr);
 }

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/IO/Arr_with_history_text_formatter.h

@@ -1,29 +1,24 @@
-
 namespace CGAL {
 
-/*!
+/*! \ingroup PkgArrangementOnSurface2IO
-\ingroup PkgArrangementOnSurface2IO
+ *
+ * `Arr_with_history_text_formatter` defines the format of an arrangement in an
+ * input or output stream (typically a file stream), thus enabling reading and
+ * writing an arrangement-with-history instance using a simple text format.
+ *
+ * The `ArrFormatter` parameter servers as a base class for
+ * `Arr_with_history_text_formatter` and must be a model of the
+ * `AosInputFormatter` and the `AosOutputFormatter` concepts. It is used to read
+ * or write the base arrangement, while the derived class is responsible for
+ * reading and writing the set of curves inducing the arrangement and
+ * maintaining the relations between these curves and the edges they induce.
+ *
+ * \cgalModels{AosWithHistoryInputFormatter,AosWithHistoryOutputFormatter}
+ *
+ * \sa `PkgArrangementOnSurface2Read`
+ * \sa `PkgArrangementOnSurface2Write`
+ */
+template <typename ArrFormatter>
+class Arr_with_history_text_formatter {};
 
-`Arr_with_history_text_formatter` defines the format of an arrangement in an input or output stream
-(typically a file stream), thus enabling reading and writing an
-arrangement-with-history instance using a simple text format.
-
-The `ArrFormatter` parameter servers as a base class for
-`Arr_with_history_text_formatter` and must be a model of the `ArrangementInputFormatter`
-and the `ArrangementOutputFormatter` concepts. It is used to read or write
-the base arrangement, while the derived class is responsible for reading and
-writing the set of curves inducing the arrangement and maintaining the
-relations between these curves and the edges they induce.
-
-\cgalModels{ArrangementWithHistoryInputFormatter,ArrangementWithHistoryOutputFormatter}
-
-\sa `PkgArrangementOnSurface2Read`
-\sa `PkgArrangementOnSurface2Write`
-
-*/
-template< typename ArrFormatter >
-class Arr_with_history_text_formatter {
-public:
-
-}; /* end Arr_with_history_text_formatter */
 } /* end namespace CGAL */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/draw_arrangement_2.h

@@ -25,51 +25,63 @@ namespace CGAL {
 
 /*! \ingroup PkgArrangementOnSurface2Draw
 
-  opens a new window and draws `arr`, an instance of the `CGAL::Arrangement_2` class template. Parameters of the drawing are taken from the optional graphics scene options parameter.
+ * The function opens a new window and draws `arr`, an instance of the
-
+ * `CGAL::Arrangement_2` class template. Parameters of the drawing are taken
-A call to this function blocks the execution of the program until the drawing window is closed. This function requires `CGAL_Qt6`, and is only available if the macro `CGAL_USE_BASIC_VIEWER` is defined.
+ * from the optional graphics scene options parameter.
-Linking with the cmake target `CGAL::CGAL_Basic_viewer` will link with `CGAL_Qt6` and add the definition `CGAL_USE_BASIC_VIEWER`.
+ *
-
+ * A call to this function blocks the execution of the program until the drawing
-
+ * window is closed. This function requires `CGAL_Qt6`, and is only available if
-\tparam GeometryTraits_2 a geometry traits type, a model of a 2D arrangement traits concept. At this point it must be an instance of either `CGAL::Arr_segment_traits_2` or `CGAL::Arr_conic_traits_2`.
+ * the macro `CGAL_USE_BASIC_VIEWER` is defined.  Linking with the cmake target
-\tparam Dcel the \dcel type, a model of the `ArrangementDcel` concept.
+ * `CGAL::CGAL_Basic_viewer` will link with `CGAL_Qt6` and add the definition
-\tparam GSOptions a model of `GraphicsSceneOptions` concept.
+ * `CGAL_USE_BASIC_VIEWER`.
-
+ *
-\param arr the 2D arrangement to draw.
+ * \tparam GeometryTraits_2 a geometry traits type, a model of a 2D arrangement
-\param gso the graphics scene options parameter.
+ * traits concept. At this point it must be an instance of either
-
+ * `CGAL::Arr_segment_traits_2` or `CGAL::Arr_conic_traits_2`.
-\sa `ArrangementDcel`
+ * \tparam Dcel the \dcel type, a model of the `AosDcel` concept.
-\sa `ArrangementTraits_2`
+ * \tparam GSOptions a model of `GraphicsSceneOptions` concept.
-*/
+ *
+ * \param arr the 2D arrangement to draw.
+ * \param gso the graphics scene options parameter.
+ *
+ * \sa `AosDcel`
+ * \sa `AosTraits_2`
+ */
 template <typename GeometryTraits_2, typename Dcel, typename GSOptions>
-void draw(const Arrangement_2<GeometryTraits_2, Dcel>& arr, const GSOptions& gso);
+void draw(const Arrangement_2<GeometryTraits_2, Dcel>& arr,
+          const GSOptions& gso);
 
 /*! \ingroup PkgArrangementOnSurface2Draw
-
+ *
-  A shortcut to `CGAL::draw(arr, Graphics_scene_options{})`.
+ *   A shortcut to `CGAL::draw(arr, Graphics_scene_options{})`.
-*/
+ */
 template <typename GeometryTraits_2, typename Dcel>
 void draw(const Arrangement_2<GeometryTraits_2, Dcel>& arr);
 
 /*! \ingroup PkgArrangementOnSurface2Draw
-
+ *
-adds the vertices, edges and faces of `arr` into the given graphic scene `gs`. Parameters of the cells are taken from the optional graphics scene options parameter `gso`. Note that `gs` is not cleared before being filled (to enable to draw several data structures in the same basic viewer).
+ * adds the vertices, edges and faces of `arr` into the given graphic scene
-
+ * `gs`. Parameters of the cells are taken from the optional graphics scene
-\tparam GeometryTraits_2 a geometry traits type, a model of a 2D arrangement traits concept. At this point it must be an instance of either `CGAL::Arr_segment_traits_2` or `CGAL::Arr_conic_traits_2`.
+ * options parameter `gso`. Note that `gs` is not cleared before being filled
-\tparam Dcel the \dcel type, a model of the `ArrangementDcel` concept.
+ * (to enable to draw several data structures in the same basic viewer).
-\tparam GSOptions a model of `GraphicsSceneOptions` concept.
+ *
-
+ * \tparam GeometryTraits_2 a geometry traits type, a model of a 2D arrangement
-\param arr the 2D arrangement to draw.
+ * traits concept. At this point it must be an instance of either
-\param gs the graphic scene to fill.
+ * `CGAL::Arr_segment_traits_2` or `CGAL::Arr_conic_traits_2`.
-\param gso the graphics scene options parameter.
+ * \tparam Dcel the \dcel type, a model of the `AosDcel` concept.
+ * \tparam GSOptions a model of `GraphicsSceneOptions` concept.
+ *
+ * \param arr the 2D arrangement to draw.
+ * \param gs the graphic scene to fill.
+ * \param gso the graphics scene options parameter.
  */
 template <typename GeometryTraits_2, typename Dcel, typename GSOptions>
 void add_to_graphics_scene(const Arrangement_2<GeometryTraits_2, Dcel>& arr,
                            CGAL::Graphics_scene& gs, const GSOptions& gso);
 
 /*! \ingroup PkgArrangementOnSurface2Draw
-
+ * A shortcut to `CGAL::add_to_graphics_scene(arr, gs,
-  A shortcut to `CGAL::add_to_graphics_scene(arr, gs, Graphics_scene_options{})`.
+ * Graphics_scene_options{})`.
  */
 template <typename GeometryTraits_2, typename Dcel>
 void add_to_graphics_scene(const Arrangement_2<GeometryTraits_2, Dcel>& arr,

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/AosApproximatePointTraits_2.h

@@ -0,0 +1,50 @@
+/*! \ingroup PkgArrangementOnSurface2ConceptsTraits
+ * \cgalConcept
+ *
+ * The concept `AosApproximatePointTraits_2` refines the basic traits concept
+ * `AosBasicTraits_2`. A model of this concept is able to approximate a point.
+ *
+ * \cgalRefines{AosBasicTraits_2}
+ *
+ * \cgalHasModelsBegin
+ * \cgalHasModels{CGAL::Arr_circle_segment_traits_2<Kernel>}
+ * \cgalHasModels{CGAL::Arr_conic_traits_2<RatKernel,AlgKernel,NtTraits>}
+ * \cgalHasModels{CGAL::Arr_geodesic_arc_on_sphere_traits_2}
+ * \cgalHasModels{CGAL::Arr_linear_traits_2<Kernel>}
+ * \cgalHasModels{CGAL::Arr_non_caching_segment_traits_2<Kernel>}
+ * \cgalHasModels{CGAL::Arr_segment_traits_2<Kernel>}
+ * \cgalHasModels{CGAL::Arr_polycurve_traits_2<GeometryTraits_2>}
+ * \cgalHasModels{CGAL::Arr_polyline_traits_2<SegmentTraits_2>}
+ * \cgalHasModels{CGAL::Arr_rational_function_traits_2<AlgebraicKernel_d_1>}
+ * \cgalHasModelsEnd
+ *
+ * \sa `AosConstructXMonotoneCurveTraits_2`
+ * \sa `AosXMonotoneTraits_2`
+ * \sa `AosTraits_2`
+ */
+class AosApproximatePointTraits_2 {
+public:
+  /// \name Types
+  /// @{
+
+  //! the number type used to approximate point coordinates, e.g., double.
+  typedef unspecified_type Approximate_number_type;
+
+  /// @}
+
+  /// \name Functor Types
+  /// @{
+
+  /// models the concept `AosTraits::Approximate_2`.
+  typedef unspecified_type Approximate_2;
+
+  /// @}
+
+  /// \name Accessing Functor Objects
+  /// @{
+
+  ///
+  Approximate_2 approximate_2_object() const;
+
+  /// @}
+}

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/AosApproximateTraits_2.h

@@ -0,0 +1,47 @@
+/*! \ingroup PkgArrangementOnSurface2ConceptsTraits
+ * \cgalConcept
+ *
+ * The concept `AosApproximateTraits_2` refines the concept
+ * `AosApproximatePointTraits_2`. A model of this concept is able to
+ * approximate a point and a curve (in addition to the ability to approximate the
+ * coordinates of a point).
+ *
+ * \cgalRefines{AosApproximatePointTraits_2}
+ *
+ * \cgalHasModelsBegin
+ * \cgalHasModels{CGAL::Arr_circle_segment_traits_2<Kernel>}
+ * \cgalHasModels{CGAL::Arr_conic_traits_2<RatKernel,AlgKernel,NtTraits>}
+ * \cgalHasModels{CGAL::Arr_geodesic_arc_on_sphere_traits_2}
+ * \cgalHasModels{CGAL::Arr_polyline_traits_2<SegmentTraits_2>}
+ * \cgalHasModels{CGAL::Arr_segment_traits_2<Kernel>}
+ * \cgalHasModelsEnd
+ *
+ * \sa `AosApproximatePointTraits_2`
+ * \sa `draw()`
+ */
+class AosApproximateTraits_2 {
+public:
+  /// \name Types
+  /// @{
+
+  //! the approximate point.
+  typedef unspecified_type Approximate_point_2;
+
+  /// @}
+
+  /// \name Functor Types
+  /// @{
+
+  /// models the concept `AosTraits::Approximate_2`.
+  typedef unspecified_type Approximate_2;
+
+  /// @}
+
+  /// \name Accessing Functor Objects
+  /// @{
+
+  ///
+  Approximate_2 approximate_2_object() const;
+
+  /// @}
+}

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/AosBasicTopologyTraits.h

@@ -1,7 +1,7 @@
 /*! \ingroup PkgArrangementOnSurface2ConceptsTopologyTraits
  * \cgalConcept
  *
- * The concept `ArrangementBasicTopologyTraits` defines the minimal
+ * The concept `AosBasicTopologyTraits` defines the minimal
  * functionality needed for a model of a topology traits, which can substitutes
  * the `TopolTraits` template parameters when the class template
  * `Arrangement_on_surface_2<GeomTraits, TopolTraits>` is instantiated.  In
@@ -13,19 +13,18 @@
  * \cgalHasModels{CGAL::Arr_spherical_topology_traits_2<GeometryTraits_2, Dcel>}
  * \cgalHasModelsEnd
  */
-
+class AosBasicTopologyTraits {
-class ArrangementBasicTopologyTraits {
 public:
   /// \name Types
   /// @{
 
-  //! models the concept `ArrTraits::Point_2`.
+  /// models the concept `AosTraits::Point_2`.
   typedef unspecified_type                              Point_2;
 
-  //! models the concept `ArrTraits::XMonotoneCurve_2`.
+  /// models the concept `AosTraits::XMonotoneCurve_2`.
   typedef unspecified_type                              X_monotone_curve_2;
 
-  //! models the concept `ArrangementDcel`.
+  /// models the concept `AosDcel`.
   typedef unspecified_type                              Dcel;
 
   /// @}
@@ -38,10 +37,10 @@ public:
   /// \name Access Functions
   /// @{
 
-  /*! obtains the DCEL (const version). */
+  /*! obtains the \dcel (const version). */
   const Dcel& dcel() const;
 
-  /*! obtains the DCEL (non-const version). */
+  /*! obtains the \dcel (non-const version). */
   Dcel& dcel();
 
   /// @}
@@ -49,5 +48,4 @@ public:
   /// \name Modifiers
   /// @{
   /// @}
-
 };

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/AosBasicTraits_2.h

@@ -1,23 +1,23 @@
 /*! \ingroup PkgArrangementOnSurface2ConceptsTraits
  * \cgalConcept
  *
- * The concept `ArrangementBasicTraits_2` defines the minimal set of geometric
+ * The concept `AosBasicTraits_2` defines the minimal set of geometric
  * predicates needed for the construction and maintenance of objects of the
  * class `Arrangement_2`, as well as performing simple queries (such as
  * point-location queries) on such arrangements.
  *
  * A model of this concept must define nested `Point_2` and `X_monotone_curve_2`
- * types, which represent planar points and continuous \f$ x\f$-monotone curves
+ * types, which represent planar points and continuous \f$x\f$-monotone curves
  * (a vertical segment is also considered to be <I>weakly</I> \f$
- * x\f$-monotone), respectively. The \f$ x\f$-monotone curves are assumed to be
+ * x\f$-monotone), respectively. The \f$x\f$-monotone curves are assumed to be
  * pairwise disjoint in their interiors, so they do not intersect except at
  * their endpoints.
  *
  * The `X_monotone_curve_2` curves of an arrangement are confined to an
  * iso-rectangular area called the parameter space. The iso-rectangule can be
  * unbounded, open, or closed. The set of predicates provided by a model the
- * concept `ArrangementBasicTraits_2` is sufficient for constructing
+ * concept `AosBasicTraits_2` is sufficient for constructing
- * arrangements of \f$ x\f$-monotone curves that do not reach or approach the
+ * arrangements of \f$x\f$-monotone curves that do not reach or approach the
  * boundary of the parameter space. The nature of the input curves, whether they
  * are expected to reach or approach the left, right, bottom, or top side of the
  * boundary of the parameter space, are conveyed through the definition of four
@@ -45,19 +45,15 @@
  * \cgalHasModels{CGAL::Arr_consolidated_curve_data_traits_2<Traits,Data>}
  * \cgalHasModelsEnd
  */
-
+class AosBasicTraits_2 {
-class ArrangementBasicTraits_2 {
 public:
-
   /// \name Types
   /// @{
 
-  /*! models the concept `ArrTraits::Point_2`.
+  /// models the concept `AosTraits::Point_2`.
-   */
   typedef unspecified_type Point_2;
 
-  /*! models the concept `ArrTraits::XMonotoneCurve_2`.
+  /// models the concept `AosTraits::XMonotoneCurve_2`.
-   */
   typedef unspecified_type X_monotone_curve_2;
 
   /// @}
@@ -65,24 +61,19 @@ public:
   /// \name Categories
   /// @{
 
-  /*! indicates whether the nested functor `Compare_at_x_left_2` is provided.
+  /// indicates whether the nested functor `Compare_at_x_left_2` is provided.
-   */
   typedef unspecified_type Has_left_category;
 
-  /*! Must be convertible to `CGAL::Arr_oblivious_side_tag`.
+  /// Must be convertible to `CGAL::Arr_oblivious_side_tag`.
-   */
   typedef unspecified_type Left_side_category;
 
-  /*! Must be convertible to `CGAL::Arr_oblivious_side_tag`.
+  /// Must be convertible to `CGAL::Arr_oblivious_side_tag`.
-   */
   typedef unspecified_type Bottom_side_category;
 
-  /*! Must be convertible to `CGAL::Arr_oblivious_side_tag`.
+  /// Must be convertible to `CGAL::Arr_oblivious_side_tag`.
-   */
   typedef unspecified_type Top_side_category;
 
-  /*!Must be convertible to `CGAL::Arr_oblivious_side_tag`.
+  /// Must be convertible to `CGAL::Arr_oblivious_side_tag`.
-   */
   typedef unspecified_type Right_side_category;
 
   /// @}
@@ -90,40 +81,35 @@ public:
   /// \name Functor Types
   /// @{
 
-  /*! models the concept `ArrTraits::CompareX_2`.
+  /// models the concept `AosTraits::CompareX_2`.
-   */
   typedef unspecified_type Compare_x_2;
 
-  /*! models the concept `ArrTraits::CompareXy_2`.
+  /// models the concept `AosTraits::CompareXy_2`.
-   */
   typedef unspecified_type Compare_xy_2;
 
-  /*! models the concept `ArrTraits::ConstructMinVertex_2`.
+  /// models the concept `AosTraits::ConstructMinVertex_2`.
-   */typedef unspecified_type Construct_min_vertex_2;
+  typedef unspecified_type Construct_min_vertex_2;
 
-  /*! models the concept `ArrTraits::ConstructMaxVertex_2`.
+  /// models the concept `AosTraits::ConstructMaxVertex_2`.
-   */
   typedef unspecified_type Construct_max_vertex_2;
 
-  /*! models the concept `ArrTraits::IsVertical_2`.
+  /*! models the concept `AosTraits::IsVertical_2`.
    */
   typedef unspecified_type Is_vertical_2;
 
-  /*! models the concept `ArrTraits::CompareYAtX_2`.
+  /*! models the concept `AosTraits::CompareYAtX_2`.
    */
   typedef unspecified_type Compare_y_at_x_2;
 
-  /*! models the concept `ArrTraits::CompareYAtXLeft_2`.  Required only if the
+  /*! models the concept `AosTraits::CompareYAtXLeft_2`.  Required only if the
    * `Has_left_category` category is convertible to `Tag_true`.
    */
   typedef unspecified_type Compare_y_at_x_left_2;
 
-  /*! models the concept `ArrTraits::CompareYAtXRight_2`.
+  /// models the concept `AosTraits::CompareYAtXRight_2`.
-   */
   typedef unspecified_type Compare_y_at_x_right_2;
 
-  /*! models the concept `ArrTraits::Equal_2`.
+  /// models the concept `AosTraits::Equal_2`.
-   */
   typedef unspecified_type Equal_2;
 
   /// @}
@@ -131,33 +117,32 @@ public:
   /// \name Accessing Functor Objects
   /// @{
 
-  //!
+  ///
   Compare_x_2 compare_x_2_object() const;
 
-  //!
+  ///
   Compare_xy_2 compare_xy_2_object() const;
 
-  //!
+  ///
   Construct_min_vertex_2 construct_min_vertex_2_object() const;
 
-  //!
+  ///
   Construct_max_vertex_2 construct_max_vertex_2_object() const;
 
-  //!
+  ///
   Is_vertical_2 is_vertical_2_object() const;
 
-  //!
+  ///
   Compare_y_at_x_2 compare_y_at_x_2_object() const;
 
-  //!
+  ///
   Compare_y_at_x_left_2 compare_y_at_x_left_2_object() const;
 
-  //!
+  ///
   Compare_y_at_x_right_2 compare_y_at_x_right_2_object() const;
 
-  //!
+  ///
   Equal_2 equal_2_object() const;
 
   /// @}
-
+}; /* end AosBasicTraits_2 */
-}; /* end ArrangementBasicTraits_2 */

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/AosBottomSideTraits_2.h

@@ -1,8 +1,7 @@
-/*!
+/*! \ingroup PkgArrangementOnSurface2ConceptsTraits
- * \ingroup PkgArrangementOnSurface2ConceptsTraits
  * \cgalConcept
  *
- * `ArrangementBottomSideTraits_2` is an abstract concept. It generalizes all
+ * `AosBottomSideTraits_2` is an abstract concept. It generalizes all
  * concepts that handle curves that either reach or approach the bottom boundary
  * side of the parameter space. (An "abstract" concept is a concept that is
  * useless on its own.) Only a combination of this concept and additional
@@ -10,14 +9,13 @@
  * boundary sides (that is, left, right, and top) are purposeful, and can have
  * models.
  *
- * \cgalRefines{ArrangementHorizontalSideTraits_2}
+ * \cgalRefines{AosHorizontalSideTraits_2}
  *
- * \sa `ArrangementLeftSideTraits_2`,
+ * \sa `AosLeftSideTraits_2`
- *     `ArrangementRightSideTraits_2`, and
+ * \sa `AosRightSideTraits_2`
- *     `ArrangementTopSideTraits_2`
+ * \sa `AosTopSideTraits_2`
  */
-
+class AosBottomSideTraits_2 {
-class ArrangementBottomSideTraits_2 {
 public:
   /// \name Categories
   /// @{
@@ -29,6 +27,7 @@ public:
 
   /// \name Functor Types
   /// @{
+  /// @}
 
   /// \name Accessing Functor Objects
   /// @{