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Merge branch 'master' into CGAL-Qt6-GF

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35
.github/workflows/reuse.yml vendored Normal file
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@ -0,0 +1,35 @@
# SPDX-FileCopyrightText: 2020 Free Software Foundation Europe e.V. <https://fsfe.org>
#
# SPDX-License-Identifier: GPL-3.0-or-later
name: REUSE Compliance Check
on: [push, pull_request]
jobs:
reuse:
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v3
- name: REUSE version
uses: fsfe/reuse-action@v1
with:
args: --version
- name: REUSE lint
uses: fsfe/reuse-action@v1
with:
args: --include-submodules lint
- name: REUSE SPDX SBOM
uses: fsfe/reuse-action@v1
with:
args: spdx
- name: install dependencies
run: sudo apt-get install -y cmake
- name: Create CGAL internal release
run: |
mkdir -p ./release
cmake -DDESTINATION=./release -DCGAL_VERSION=9.9 -P ./Scripts/developer_scripts/cgal_create_release_with_cmake.cmake
- name: REUSE lint release tarball
uses: fsfe/reuse-action@v1
with:
args: --root ./release/CGAL-9.9 --include-submodules lint

12
.reuse/dep5 Normal file
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@ -0,0 +1,12 @@
Format: https://www.debian.org/doc/packaging-manuals/copyright-format/1.0/
Upstream-Name: CGAL
Upstream-Contact: CGAL Editorial Board <info@cgal.org>
Source: https://github.com/CGAL/cgal
Files: .* *.cmake *.md .github/* Maintenance/* */TODO */doc/* */deb/* */applications/* */doc_html/* */scripts/* */developer_scripts/* */demo/* */examples/* */src/* */test/* */benchmarks/* */benchmark/* */package_info/* */data/* */cmake/*
Copyright: 1995-2023 The CGAL Project
License: CC0-1.0
Files: CMakeLists.txt GraphicsView/include/CGAL/Qt/ImageInterface.ui GraphicsView/include/CGAL/Qt/resources/qglviewer-icon.xpm Installation/AUTHORS Installation/CMakeLists.txt Installation/README Installation/auxiliary/cgal_create_cmake_script.1 Installation/auxiliary/gmp/README Installation/include/CGAL/license/gpl_package_list.txt MacOSX/auxiliary/cgal_app.icns copyright
Copyright: 1995-2023 The CGAL Project
License: CC0-1.0

2
AABB_tree/include/CGAL/AABB_halfedge_graph_segment_primitive.h
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@ -33,7 +33,7 @@ namespace CGAL {
/*!
* \ingroup PkgAABBTreeRef
* Primitive type for a edge of a polyhedral surface.
* Primitive type for an edge of a polyhedral surface.
* It wraps an `edge_descriptor` into a 3D segment.
* The class model of `HalfedgeGraph` from which the primitive is built should not be deleted
* while the AABB tree holding the primitive is in use.

2
AABB_tree/include/CGAL/AABB_tree.h
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@ -142,7 +142,7 @@ namespace CGAL {
/// An explicit call to `build()` must be made to ensure that the next call to
/// a query function will not trigger the construction of the data structure.
/// A call to `AABBTraits::set_shared_data(t...)` is made using the internally stored traits.
/// This procedure has a complexity of \f$O(n log(n))\f$, where \f$n\f$ is the number of
/// This procedure has a complexity of \cgalBigO{n log(n)}, where \f$n\f$ is the number of
/// primitives of the tree.
template<typename ... T>
void build(T&& ...);

2
Alpha_shapes_2/doc/Alpha_shapes_2/CGAL/Alpha_shape_2.h
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@ -80,7 +80,7 @@ use binary search.
`Alpha_shape_2::number_of_solid_components()` performs a graph traversal and takes time
linear in the number of faces of the underlying triangulation.
`Alpha_shape_2::find_optimal_alpha()` uses binary search and takes time
\f$ O(n \log n)\f$, where \f$ n\f$ is the number of points.
\cgalBigO{n \log n}, where \f$ n\f$ is the number of points.
*/
template< typename Dt, typename ExactAlphaComparisonTag >

2
Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Alpha_shape_3.h
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@ -77,7 +77,7 @@ use binary search.
`Alpha_shape_3::number_of_solid_components()` performs a graph traversal and takes time
linear in the number of cells of the underlying triangulation.
`Alpha_shape_3::find_optimal_alpha()` uses binary search and takes time
\f$ O(n \log n)\f$, where \f$ n\f$ is the number of points.
\cgalBigO{n \log n}, where \f$ n\f$ is the number of points.
*/
template< typename Dt, typename ExactAlphaComparisonTag >

1
Arithmetic_kernel/test/Arithmetic_kernel/CMakeLists.txt
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@ -39,6 +39,7 @@ if(GMP_FOUND)
create_single_source_cgal_program("Arithmetic_kernel.cpp")
create_single_source_cgal_program("LEDA_arithmetic_kernel.cpp")
create_single_source_cgal_program("CORE_arithmetic_kernel.cpp")
create_single_source_cgal_program("GMPXX_arithmetic_kernel.cpp")
create_single_source_cgal_program("Get_arithmetic_kernel.cpp")
else()

2
Arrangement_on_surface_2/demo/Arrangement_on_surface_2/AlgebraicCurveParser.cpp
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@ -12,7 +12,7 @@
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// SPDX-License-Identifier: GPL-3.0+
// SPDX-License-Identifier: GPL-3.0-or-later
//
// Author(s): Saurabh Singh <ssingh@cs.iitr.ac.in>
// Ahmed Essam <theartful.ae@gmail.com>

2
Arrangement_on_surface_2/demo/Arrangement_on_surface_2/AlgebraicCurveParser.h
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@ -12,7 +12,7 @@
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// SPDX-License-Identifier: GPL-3.0+
// SPDX-License-Identifier: GPL-3.0-or-later
//
// Author(s): Saurabh Singh <ssingh@cs.iitr.ac.in>
// Ahmed Essam <theartful.ae@gmail.com>

18
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt
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@ -1223,10 +1223,10 @@ halfedge \f$e_{\mathrm{pred}}\f$ directed toward \f$v\f$, such that
\f$c\f$ is located between the curves associated with
\f$e_{\mathrm{pred}}\f$ and the next halfedge in the clockwise order
in the circular list of halfedges around \f$v\f$; see
\cgalFigureRef{aos_fig-insert}. This search may take \f$O(d)\f$ time,
\cgalFigureRef{aos_fig-insert}. This search may take \cgalBigO{d} time,
where \f$d\f$ is the degree of the vertex \f$v\f$. \cgalFootnote{We
can store the handles to the halfedges incident to \f$v\f$ in an efficient
search structure to obtain \f$O(\log d)\f$ access time. However, as
search structure to obtain \cgalBigO{\log d} access time. However, as
\f$d\f$ is usually very small, this may lead to a waste of storage
space without a meaningful improvement in running time in practice.}
However, if the halfedge \f$e_{\mathrm{pred}}\f$ is known in advance,
@ -1488,9 +1488,9 @@ keep up-to-date as this arrangement changes.
As mentioned above, the triangulation strategy is provided only for
educational purposes, and thus we do not elaborate on this strategy.
The data structure needed by the landmark and the trapezoidal map RIC
strategies can be constructed in \f$O(N \log N)\f$ time, where \f$N\f$
strategies can be constructed in \cgalBigO{N \log N} time, where \f$N\f$
is the overall number of edges in the arrangement, but the constant
hidden in the \f$O()\f$ notation for the trapezoidal map RIC strategy
hidden in the \cgalBigO{&nbsp;} notation for the trapezoidal map RIC strategy
is much larger. Thus, construction needed by the landmark algorithm is
in practice significantly faster than the construction needed by the
trapezoidal map RIC strategy. In addition, although both resulting
@ -1647,7 +1647,7 @@ Section \ref arr_ssecpl. The output pairs are sorted in increasing
\f$xy\f$-lexicographical order of the query point.
The batched point-location operation is carried out by sweeping the
arrangement. Thus, it takes \f$O((m+N)\log{(m+N)})\f$ time, where
arrangement. Thus, it takes \cgalBigO{(m+N)\log{(m+N)}} time, where
\f$N\f$ is the number of edges in the arrangement. Issuing separate
queries exploiting a point-location strategy with logarithmic query
time per query, such as the trapezoidal map RIC strategy (see Section
@ -2037,11 +2037,11 @@ so it must be construct from scratch.
In the first case, we sweep over the input curves, compute their
intersection points, and construct the \dcel that represents their
arrangement. This process is performed in \f$O\left((n + k)\log
n\right)\f$ time, where \f$k\f$ is the total number of intersection
arrangement. This process is performed in \cgalBigO{left((n + k)\log
n\right} time, where \f$k\f$ is the total number of intersection
points. The running time is asymptotically better than the time needed
for incremental insertion if the arrangement is relatively sparse
(when \f$k\f$ is \f$O(\frac{n^2}{\log n}\f$)), but it is recommended
(when \f$k\f$ is \cgalBigO{\frac{n^2}{\log n}}), but it is recommended
that this aggregate construction process be used even for dense
arrangements, since the plane-sweep algorithm performs fewer geometric
operations compared to the incremental insertion algorithms, and hence
@ -4346,7 +4346,7 @@ a point with respect to an \f$x\f$-monotone polyline, we use binary
search to locate the relevant segment that contains the point in its
\f$x\f$-range. Then, we compute the position of the point with respect
to this segment. Thus, operations on \f$x\f$-monotone polylines of
size \f$m\f$ typically take \f$O(\log m)\f$ time.
size \f$m\f$ typically take \cgalBigO{\log m} time.
You are free to choose the underlying segment traits class. Your
decision could be based, for example, on the number of expected

4
Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_trapezoid_ric_point_location.h
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@ -12,9 +12,9 @@ Seidel \cgalCite{s-sfira-91} (see also [\cgalCite{bkos-cgaa-00} Chapter 6).
It subdivides each arrangement face to pseudo-trapezoidal cells, each
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 \f$ O(\log n)\f$ 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 \f$ O(n \log n)\f$ expected time
Constructing the search structures takes \cgalBigO{n \log n} expected time
and may require a small number of rebuilds \cgalCite{hkh-iiplgtds-12}. Therefore
attaching a trapezoidal point-location object to an existing arrangement
may incur some overhead in running times. In addition, the point-location

2
Arrangement_on_surface_2/include/CGAL/Arr_polycurve_basic_traits_2.h
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@ -2419,7 +2419,7 @@ protected:
/*! Obtain the index of the subcurve in the polycurve that contains the
* point q in its x-range. The function performs a binary search, so if the
* point q is in the x-range of the polycurve with n subcurves, the subcurve
* containing it can be located in O(log n) operations.
* containing it can be located in \cgalBigO{log n} operations.
* \param cv The polycurve curve.
* \param q The point.
* \return An index i such that q is in the x-range of cv[i].

2
BGL/examples/BGL_LCC/CMakeLists.txt
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@ -9,7 +9,7 @@ find_package(CGAL REQUIRED)
# create a target per cppfile
file(
GLOB_RECURSE cppfiles
GLOB cppfiles
RELATIVE ${CMAKE_CURRENT_SOURCE_DIR}
*.cpp)
foreach(cppfile ${cppfiles})

2
BGL/include/CGAL/boost/graph/Face_filtered_graph.h
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@ -42,7 +42,7 @@ namespace CGAL {
* <a href="https://www.boost.org/doc/libs/release/libs/graph/doc/filtered_graph.html"><code>boost::filtered_graph</code></a>,
* this class only requires a way to access the selected faces and will automatically select the
* edges/halfedges and vertices present in the adapted graph. A vertex is selected if it is incident to at least one
* selected face. A edge is selected if it is incident to at least a selected face. A halfedge is selected if its edge
* selected face. An edge is selected if it is incident to at least a selected face. A halfedge is selected if its edge
* is selected.
*
* Since this class is a model of the `FaceGraph` concept, there is a restriction on the set of selected faces:

125
BGL/test/BGL/test_Surface_mesh.cpp
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@ -1,125 +0,0 @@
#define BOOST_TEST_MODULE graph_traits test
#include <boost/test/unit_test.hpp>
#include <boost/test/floating_point_comparison.hpp>
BOOST_AUTO_TEST_CASE( edges_test )
{
edge_iterator eb, ee;
vertex_iterator vb, ve;
Surface_fixture f;
boost::tie(eb, ee) = edges(f.m);
boost::tie(vb, ve) = vertices(f.m);
BOOST_CHECK(std::distance(eb, ee) == 7);
BOOST_CHECK(std::distance(vb, ve) == 5);
Cube_fixture cf;
boost::tie(eb, ee) = edges(cf.m);
boost::tie(vb, ve) = vertices(cf.m);
BOOST_CHECK(std::distance(eb, ee) == 18);
BOOST_CHECK(std::distance(vb, ve) == 8);
}
BOOST_AUTO_TEST_CASE( out_edges_test )
{
Surface_fixture f;
BOOST_CHECK(out_degree(f.u, f.m) == 2);
BOOST_CHECK(out_degree(f.v, f.m) == 4);
std::pair<out_edge_iterator, out_edge_iterator> out = out_edges(f.v, f.m);
BOOST_CHECK(std::distance(out.first, out.second) == 4);
out_edge_iterator it = out.first;
while(it != out.second) {
// the source should always be u
BOOST_CHECK(source(*it, f.m) == f.v);
// the target never
BOOST_CHECK(target(*it, f.m) != f.v);
++it;
}
}
BOOST_AUTO_TEST_CASE( in_edges_test )
{
Surface_fixture f;
BOOST_CHECK(in_degree(f.u, f.m) == 2);
BOOST_CHECK(in_degree(f.x, f.m) == 3);
BOOST_CHECK(in_degree(f.v, f.m) == 4);
std::pair<in_edge_iterator, in_edge_iterator> in = in_edges(f.v, f.m);
BOOST_CHECK(std::distance(in.first, in.second) == 4);
in_edge_iterator it = in.first;
while(it != in.second) {
// the source should never be u
BOOST_CHECK(source(*it, f.m) != f.v);
// the target must always be u
BOOST_CHECK(target(*it, f.m) == f.v);
++it;
}
}
BOOST_AUTO_TEST_CASE( in_out_equality )
{
// in and out degrees must be equal for each vertex
Cube_fixture f;
for(Sm::Vertex_iterator it = f.m.vertices_begin();
it != f.m.vertices_end(); ++it) {
BOOST_CHECK(in_degree(*it, f.m) == out_degree(*it, f.m));
}
}
BOOST_AUTO_TEST_CASE( face_test )
{
Surface_fixture f;
std::pair<enclosure_iterator, enclosure_iterator>
enc = enclosure(f.f1, f.m);
BOOST_CHECK(enc.first != enc.second);
BOOST_CHECK(std::distance(enc.first, enc.second) == 3);
enclosure_iterator begin = enc.first;
while(begin != enc.second)
{
BOOST_CHECK(face(*begin, f.m) == f.f1);
++begin;
}
}
BOOST_AUTO_TEST_CASE( weight_map_test )
{
Surface_fixture f;
Cube_fixture c;
CGAL::SM_edge_weight_pmap<K> wm1 = boost::get(boost::edge_weight, c.m);
edge_iterator eb, ee;
boost::test_tools::check_is_close_t check_close;
for(boost::tie(eb, ee) = edges(c.m); eb != ee; ++eb) {
BOOST_CHECK(
check_close(wm1[*eb], 2.0, boost::test_tools::percent_tolerance_t<double>(0.00001))
|| check_close(wm1[*eb], 2.82843, boost::test_tools::percent_tolerance_t<double>(0.001)));
}
}
BOOST_AUTO_TEST_CASE( vertices_test )
{
Surface_fixture f;
// boost::property_map<Sm,boost::vertex_index_t>::type vi_map = get(f.m, boost::vertex_index);
// vertex_iterator b,e;
// for(boost::tie(b,e) = vertices(f.m);
// b!= e;
// ++b){
// std::cout << boost::get(vi_map, *(b)) << std::endl;
// }
// boost::property_map<Sm,boost::edge_weight_t>::type ew_map = get(f.m, boost::edge_weight);
// edge_iterator be, ee;
// for(boost::tie(be,ee) = edges(f.m);
// be!= ee;
// ++be){
// std::cout << boost::get(ew_map, *(be)) << std::endl;
// }
}

14
BGL/test/BGL/test_deprecated_io.cpp
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@ -21,18 +21,18 @@ int main()
SM sm_in, sm_out;
Point_3 p0(0,0,0), p1(1,0,0), p2(0,1,0);
CGAL::make_triangle(p0, p1, p2, sm_out);
bool ok = CGAL::write_off("tmp.off", sm_out);
bool ok = CGAL::write_off("tmp_deprecated.off", sm_out);
assert(ok);
ok = CGAL::read_off("tmp.off", sm_in);
ok = CGAL::read_off("tmp_deprecated.off", sm_in);
assert(ok);
assert(num_vertices(sm_in) == 3 && num_faces(sm_in) == 1);
sm_in.clear();
std::ofstream os("tmp.off");
std::ofstream os("tmp_deprecated.off");
ok = CGAL::write_off(os, sm_out);
assert(ok);
os.close();
std::ifstream is("tmp.off");
std::ifstream is("tmp_deprecated.off");
ok = CGAL::read_off(is, sm_in);
assert(ok);
assert(num_vertices(sm_in) == 3 && num_faces(sm_in) == 1);
@ -40,18 +40,18 @@ int main()
sm_in.clear();
#ifdef CGAL_USE_VTK
//vtk
os.open("tmp.vtp");
os.open("tmp_deprecated.vtp");
ok = CGAL::write_vtp(os, sm_out);
assert(ok);
os.close();
ok = CGAL::IO::read_VTP("tmp.vtp", sm_in);
ok = CGAL::IO::read_VTP("tmp_deprecated.vtp", sm_in);
assert(ok);
assert(num_vertices(sm_in) == 3 && num_faces(sm_in) == 1);
sm_in.clear();
#endif
//wrl
os.open("tmp.wrl");
os.open("tmp_deprecated.wrl");
ok = CGAL::write_wrl(os, sm_out);
assert(ok);
os.close();

22
Barycentric_coordinates_2/doc/Barycentric_coordinates_2/Barycentric_coordinates_2.txt
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@ -451,10 +451,10 @@ To fix the problem, we modify the weights \f$w_i\f$ as
</center>
After the above normalization, this gives us the precise algorithm to compute Wachspress coordinates
but with \f$O(n^2)\f$ performance only. The max speed \f$O(n)\f$ algorithm uses the standard
but with \cgalBigO{n^2} performance only. The max speed \cgalBigO{n} algorithm uses the standard
weights \f$w_i\f$. Note that mathematically this modification does not change the coordinates. One should
be cautious when using the unnormalized Wachspress weights. In that case, you must choose the
\f$O(n)\f$ type.
\cgalBigO{n} type.
It is known that for strictly convex polygons the denominator's zero set of the
Wachspress coordinates (\f$W^{wp} = 0~\f$) is a curve, which (in many cases) lies quite
@ -507,10 +507,10 @@ To fix the problem, similarly to the previous subsection, we modify the weights
</center>
After the above normalization, this yields the precise algorithm to compute discrete harmonic coordinates
but with \f$O(n^2)\f$ performance only. The max speed \f$O(n)\f$ algorithm uses the standard
but with \cgalBigO{n^2} performance only. The max speed \cgalBigO{n} algorithm uses the standard
weights \f$w_i\f$. Again, mathematically this modification does not change the coordinates,
one should be cautious when using the unnormalized discrete harmonic weights. In that case,
you must choose the \f$O(n)\f$ type.
you must choose the \cgalBigO{n} type.
\b Warning: as for Wachspress coordinates, we do not recommend using discrete harmonic coordinates
for exterior points, because the curve \f$W^{dh} = 0\f$ may have several components,
@ -563,7 +563,7 @@ After the normalization of these weights as before
\f$b_i = \frac{w_i}{W^{mv}}\qquad\f$ with \f$\qquad W^{mv} = \sum_{j=1}^n w_j\f$
</center>
we obtain the max precision \f$O(n^2)\f$ algorithm. The max speed \f$O(n)\f$ algorithm computes the
we obtain the max precision \cgalBigO{n^2} algorithm. The max speed \cgalBigO{n} algorithm computes the
weights \f$w_i\f$ using the pseudocode from <a href="https://www.inf.usi.ch/hormann/nsfworkshop/presentations/Hormann.pdf">here</a>.
These weights
@ -575,7 +575,7 @@ with \f$\qquad t_i = \frac{\text{det}(d_i, d_{i+1})}{r_ir_{i+1} + d_id_{i+1}}\f$
are also normalized. Note that they are unstable if a query point is closer than \f$\approx 1.0e-10\f$
to the polygon boundary, similarly to Wachspress and discrete harmonic coordinates and
one should be cautious when using the unnormalized mean value weights. In that case, you must choose the
\f$O(n)\f$ type.
\cgalBigO{n} type.
\anchor compute_hm_coord
@ -654,17 +654,17 @@ The resulting timings for all closed-form coordinates can be found in the figure
\cgalFigureBegin{analytic_timings, analytic_timings.png}
Time in seconds to compute \f$n\f$ coordinate values for a polygon with \f$n\f$ vertices
at 1 million query points with the max speed \f$O(n)\f$ algorithms (dashed) and
at 1 million query points with the max speed \cgalBigO{n} algorithms (dashed) and
the max precision \f$0(n^2)\f$ algorithms (solid) for Wachspress (blue), discrete
harmonic (red), and mean value (green) coordinates.
\cgalFigureEnd
From the figure above we observe that the \f$O(n^2)\f$ algorithm is as fast
as the \f$O(n)\f$ algorithm if we have a polygon with a small number of vertices.
From the figure above we observe that the \cgalBigO{n^2} algorithm is as fast
as the \cgalBigO{n} algorithm if we have a polygon with a small number of vertices.
But as the number of vertices is increased, the linear algorithm outperforms the squared one,
as expected. One of the reasons for this behavior is that for a small number of vertices
the multiplications of \f$n-2\f$ elements inside the \f$O(n^2)\f$ algorithm take almost the
same time as the corresponding divisions in the \f$O(n)\f$ algorithm. For a polygon with
the multiplications of \f$n-2\f$ elements inside the \cgalBigO{n^2} algorithm take almost the
same time as the corresponding divisions in the \cgalBigO{n} algorithm. For a polygon with
many vertices, these multiplications are substantially slower.
To benchmark harmonic coordinates, we used a MacBook Pro 2018 with 2.2 GHz Intel Core i7 processor (6 cores)

2
Bounding_volumes/doc/Bounding_volumes/CGAL/Approximate_min_ellipsoid_d.h
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@ -119,7 +119,7 @@ We implement Khachyian's algorithm for rounding
polytopes \cgalCite{cgal:k-rprnm-96}. Internally, we use
`double`-arithmetic and (initially a single)
Cholesky-decomposition. The algorithm's running time is
\f$ {\cal O}(nd^2(\epsilon^{-1}+\ln d + \ln\ln(n)))\f$, where \f$ n=|P|\f$ and
\cgalBigO{nd^2(\epsilon^{-1}+\ln d + \ln\ln(n))}, where \f$ n=|P|\f$ and
\f$ 1+\epsilon\f$ is the desired approximation ratio.
\cgalHeading{Example}

2
Bounding_volumes/doc/Bounding_volumes/CGAL/Min_sphere_of_spheres_d.h
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@ -76,7 +76,7 @@ We implement two algorithms, the LP-algorithm and a
heuristic \cgalCite{msw-sblp-92}. As described in the documentation of
concept `MinSphereOfSpheresTraits`, each has its advantages and
disadvantages: Our implementation of the LP-algorithm has maximal
expected running time \f$ O(2^d n)\f$, while the heuristic comes without
expected running time \cgalBigO{2^d n}, while the heuristic comes without
any complexity guarantee. In particular, the LP-algorithm runs in
linear time for fixed dimension \f$ d\f$. (These running times hold for the
arithmetic model, so they count the number of operations on

2
Bounding_volumes/doc/Bounding_volumes/CGAL/rectangular_p_center_2.h
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@ -245,7 +245,7 @@ must be a model for `RectangularPCenterTraits_2`.
\cgalHeading{Implementation}
The runtime is linear for \f$ p \in \{2,\,3\}\f$ and
\f$ \mathcal{O}(n \cdot \log n)\f$ for \f$ p = 4\f$ where \f$ n\f$ is the number of
\cgalBigO{n \cdot \log n} for \f$ p = 4\f$ where \f$ n\f$ is the number of
input points. These runtimes are worst case optimal. The \f$ 3\f$-center
algorithm uses a prune-and-search technique described in
\cgalCite{cgal:h-slacr-99}. The \f$ 4\f$-center implementation uses sorted matrix

2
Bounding_volumes/doc/Bounding_volumes/Concepts/MinSphereOfSpheresTraits.h
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@ -79,7 +79,7 @@ The recommended choice is the first, which is a synonym to the one
of the other two methods which we consider "the best in practice."
In case of `CGAL::LP_algorithm`, the minsphere will be computed
using the LP-algorithm \cgalCite{msw-sblp-92}, which in our
implementation has maximal expected running time \f$ O(2^d n)\f$ (in the
implementation has maximal expected running time \cgalBigO{2^d n} (in the
number of operations on the number type `FT`). In case of
`CGAL::Farthest_first_heuristic`, a simple heuristic will be
used instead which seems to work fine in practice, but comes without

8
Box_intersection_d/doc/Box_intersection_d/Box_intersection_d.txt
View File

@ -350,12 +350,12 @@ parameter the function switches from the streamed segment-tree
algorithm to the two-way-scan algorithm, see \cgalCite{cgal:ze-fsbi-02}
for the details.
The streamed segment-tree algorithm needs \f$ O(n \log^d (n) + k)\f$
worst-case running time and \f$ O(n)\f$ space, where \f$ n\f$ is the number of
The streamed segment-tree algorithm needs \cgalBigO{n \log^d (n) + k}
worst-case running time and \cgalBigO{n} space, where \f$ n\f$ is the number of
boxes in both input sequences, \f$ d\f$ the (constant) dimension of the
boxes, and \f$ k\f$ the output complexity, i.e., the number of pairwise
intersections of the boxes. The two-way-scan algorithm needs \f$ O(n \log
(n) + l)\f$ worst-case running time and \f$ O(n)\f$ space, where \f$ l\f$ is the
intersections of the boxes. The two-way-scan algorithm needs \cgalBigO{n \log
(n) + l} worst-case running time and \cgalBigO{n} space, where \f$ l\f$ is the
number of pairwise overlapping intervals in one dimensions (the
dimension where the algorithm is used instead of the segment tree).
Note that \f$ l\f$ is not necessarily related to \f$ k\f$ and using the

12
Box_intersection_d/doc/Box_intersection_d/CGAL/box_intersection_d.h
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@ -77,7 +77,7 @@ namespace CGAL {
\cgalHeading{Implementation}
The algorithm is trivially testing all pairs and runs therefore in time
\f$ O(nm)\f$ where \f$ n\f$ is the size of the first sequence and \f$ m\f$ is the
\cgalBigO{nm} where \f$ n\f$ is the size of the first sequence and \f$ m\f$ is the
size of the second sequence.
*/
@ -219,12 +219,12 @@ void box_intersection_all_pairs_d(
algorithm to the two-way-scan algorithm, see \cgalCite{cgal:ze-fsbi-02}
for the details.
The streamed segment-tree algorithm needs \f$ O(n \log^d (n) + k)\f$
worst-case running time and \f$ O(n)\f$ space, where \f$ n\f$ is the number of
The streamed segment-tree algorithm needs \cgalBigO{n \log^d (n) + k}
worst-case running time and \cgalBigO{n} space, where \f$ n\f$ is the number of
boxes in both input sequences, \f$ d\f$ the (constant) dimension of the
boxes, and \f$ k\f$ the output complexity, i.e., the number of pairwise
intersections of the boxes. The two-way-scan algorithm needs \f$ O(n \log
(n) + l)\f$ worst-case running time and \f$ O(n)\f$ space, where \f$ l\f$ is the
intersections of the boxes. The two-way-scan algorithm needs \cgalBigO{n \log
(n) + l} worst-case running time and \cgalBigO{n} space, where \f$ l\f$ is the
number of pairwise overlapping intervals in one dimensions (the
dimension where the algorithm is used instead of the segment tree).
Note that \f$ l\f$ is not necessarily related to \f$ k\f$ and using the
@ -397,7 +397,7 @@ namespace CGAL {
\cgalHeading{Implementation}
The algorithm is trivially testing all pairs and runs therefore in time
\f$ O(n^2)\f$ where \f$ n\f$ is the size of the input sequence. This algorithm
\cgalBigO{n^2} where \f$ n\f$ is the size of the input sequence. This algorithm
does not use the id-number of the boxes.
*/

12
Classification/include/CGAL/Classification/Image.h
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@ -16,6 +16,7 @@
#include <map>
#include <memory>
#include <CGAL/assertions.h>
#define CGAL_CLASSIFICATION_IMAGE_SIZE_LIMIT 100000000
@ -38,12 +39,15 @@ class Image
std::shared_ptr<Map> m_sparse;
Type m_default;
// Forbid using copy constructor
Image (const Image&)
{
}
public:
// Forbid using copy constructor
// Make it public for a strange VC++ std17 boost-1_82 error
// https://github.com/boostorg/core/issues/148
Image(const Image&)
{
CGAL_assertion(false);
}
Image () : m_width(0), m_height(0), m_depth(0)
{

2
Combinatorial_map/doc/Combinatorial_map/Combinatorial_map.txt
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@ -297,7 +297,7 @@ Several functions allow to create specific configurations of darts into a combin
\subsection ssecadvmarks Boolean Marks
It is often necessary to mark darts, for example to retrieve in <I>O(1)</I> if a given dart was already processed during a specific algorithm, for example, iteration over a given range. Users can also mark specific parts of a combinatorial map (for example mark all the darts belonging to objects having specific semantics). To answer these needs, a `GenericMap` has a certain number of Boolean marks (fixed by the constant \link GenericMap::NB_MARKS `NB_MARKS`\endlink). When one wants to use a Boolean mark, the following methods are available (with `cm` an instance of a combinatorial map):
It is often necessary to mark darts, for example to retrieve in \cgalBigO{1} if a given dart was already processed during a specific algorithm, for example, iteration over a given range. Users can also mark specific parts of a combinatorial map (for example mark all the darts belonging to objects having specific semantics). To answer these needs, a `GenericMap` has a certain number of Boolean marks (fixed by the constant \link GenericMap::NB_MARKS `NB_MARKS`\endlink). When one wants to use a Boolean mark, the following methods are available (with `cm` an instance of a combinatorial map):
<ul>
<li> get a new free mark: `size_type m = cm.`\link GenericMap::get_new_mark `get_new_mark()`\endlink (throws the exception Exception_no_more_available_mark if no mark is available);
<li> set mark `m` for a given dart `d0`: `cm.`\link GenericMap::mark `mark(d0,m)`\endlink;

2
Combinatorial_map/include/CGAL/Combinatorial_map.h
View File

@ -1154,7 +1154,7 @@ namespace CGAL {
}
/** Unmark all the darts of the map for a given mark.
* If all the darts are marked or unmarked, this operation takes O(1)
* If all the darts are marked or unmarked, this operation takes \cgalBigO{1}
* operations, otherwise it traverses all the darts of the map.
* @param amark the given mark.
*/

6
Cone_spanners_2/doc/Cone_spanners_2/Cone_spanners_2.txt
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@ -160,7 +160,7 @@ In constructing Theta graphs, this functor uses the algorithm from
Chapter 4 of the book by Narasimhan and Smid \cgalCite{cgal:ns-gsn-07}.
Basically, it is a sweep line algorithm and uses a
balanced search tree to store the vertices that have already been scanned.
It has the complexity of \f$O(n \log n)\f$, where \f$n\f$ is the number of vertices in the plane.
It has the complexity of \cgalBigO{n \log n}, where \f$n\f$ is the number of vertices in the plane.
This complexity has been proved to be optimal.
For more details on how to use this `Construct_theta_graph_2` functor to write an application to build Theta graphs,
@ -178,13 +178,13 @@ The functor `Construct_yao_graph_2` has a similar definition as `Construct_theta
The way of using these two template parameters is the same as that of `Construct_theta_graph_2`,
so please refer to the previous subsection for the details. We note here that construction algorithm for Yao graph
is a slight adaptation of the algorithm for constructing Theta graph, having a complexity of \f$O(n^2)\f$.
is a slight adaptation of the algorithm for constructing Theta graph, having a complexity of \cgalBigO{n^2}.
The increase of complexity in this adaptation is because in constructing Theta graph,
the searching of the 'closest' node by projection distance can be done by a balanced search tree,
but in constructing Yao graph, the searching of the 'closest' node by Euclidean distance cannot be
done by a balanced search tree.
Note that an optimal algorithm for constructing Yao graph with a complexity of \f$O(n \log n)\f$ is
Note that an optimal algorithm for constructing Yao graph with a complexity of \cgalBigO{n \log n} is
described in \cgalCite{cgal:cht-oacov-90}. However, this algorithm is much more complex to implement than
the current algorithm implemented, and it can hardly reuse the codes for constructing Theta graphs,
so it is not implemented in this package right now.

4
Convex_decomposition_3/doc/Convex_decomposition_3/Convex_decomposition_3.txt
View File

@ -18,11 +18,11 @@ Minkowski sums of the convex pieces, and unite the pair-wise sums.
While it is desirable to have a decomposition into a minimum number of
pieces, this problem is known to be NP-hard \cgalCite{c-cpplb-84}. Our
implementation decomposes a Nef polyhedron \f$ N\f$ into \f$ O(r^2)\f$ convex
implementation decomposes a Nef polyhedron \f$ N\f$ into \cgalBigO{r^2} convex
pieces, where \f$ r\f$ is the number of edges that have two adjacent
facets that span an angle of more than 180 degrees with respect to the
interior of the polyhedron. Those edges are also called reflex edges.
The bound of \f$ O(r^2)\f$ convex pieces is worst-case
The bound of \cgalBigO{r^2} convex pieces is worst-case
optimal \cgalCite{c-cpplb-84}.
\cgalFigureBegin{figverticalDecomposition,two_cubes_all_in_one.png}

2
Convex_decomposition_3/doc/Convex_decomposition_3/PackageDescription.txt
View File

@ -6,7 +6,7 @@
\cgalPkgPicture{Convex_decomposition_3/fig/Convex_decomposition_3-teaser.png}
\cgalPkgSummaryBegin
\cgalPkgAuthor{Peter Hachenberger}
\cgalPkgDesc{This packages provides a function for decomposing a bounded polyhedron into convex sub-polyhedra. The decomposition yields \f$ O(r^2)\f$ convex pieces, where \f$ r\f$ is the number of edges, whose adjacent facets form an angle of more than 180 degrees with respect to the polyhedron's interior. This bound is worst-case optimal. }
\cgalPkgDesc{This packages provides a function for decomposing a bounded polyhedron into convex sub-polyhedra. The decomposition yields \cgalBigO{r^2} convex pieces, where \f$ r\f$ is the number of edges, whose adjacent facets form an angle of more than 180 degrees with respect to the polyhedron's interior. This bound is worst-case optimal. }
\cgalPkgManuals{Chapter_Convex_Decomposition_of_Polyhedra,PkgConvexDecomposition3Ref}
\cgalPkgSummaryEnd
\cgalPkgShortInfoBegin

4
Convex_decomposition_3/include/CGAL/convex_decomposition_3.h
View File

@ -41,12 +41,12 @@ The function `convex_decomposition_3()` inserts additional facets
into the given `Nef_polyhedron_3` `N`, such that each bounded
marked volume (the outer volume is unbounded) is subdivided into convex
pieces. The modified polyhedron represents a decomposition into
\f$ O(r^2)\f$ convex pieces, where \f$ r\f$ is the number of edges that have two
\cgalBigO{r^2} convex pieces, where \f$ r\f$ is the number of edges that have two
adjacent facets that span an angle of more than 180 degrees with
respect to the interior of the polyhedron.
The worst-case running time of our implementation is
\f$ O(n^2r^4\sqrt[3]{nr^2}\log{(nr)})\f$, where \f$ n\f$ is the complexity of
\cgalBigO{n^2r^4\sqrt[3]{nr^2}\log{(nr)}}, where \f$ n\f$ is the complexity of
the polyhedron (the complexity of a `Nef_polyhedron_3` is the sum
of its `Vertices`, `Halfedges` and `SHalfedges`) and \f$ r\f$
is the number of reflex edges.

2
Convex_hull_2/doc/Convex_hull_2/CGAL/ch_akl_toussaint.h
View File

@ -44,7 +44,7 @@ functions that return instances of these types:
\cgalHeading{Implementation}
This function uses the algorithm of Akl and
Toussaint \cgalCite{at-fcha-78} that requires \f$ O(n \log n)\f$ time for \f$ n\f$ input
Toussaint \cgalCite{at-fcha-78} that requires \cgalBigO{n \log n} time for \f$ n\f$ input
points.

2
Convex_hull_2/doc/Convex_hull_2/CGAL/ch_bykat.h
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@ -45,7 +45,7 @@ functions that return instances of these types:
This function implements the non-recursive variation of
Eddy's algorithm \cgalCite{e-nchap-77} described in \cgalCite{b-chfsp-78}.
This algorithm requires \f$ O(n h)\f$ time
This algorithm requires \cgalBigO{n h} time
in the worst case for \f$ n\f$ input points with \f$ h\f$ extreme points.
*/
template <class InputIterator, class OutputIterator, class Traits>

2
Convex_hull_2/doc/Convex_hull_2/CGAL/ch_eddy.h
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@ -47,7 +47,7 @@ This function implements Eddy's algorithm
\cgalCite{e-nchap-77}, which is the two-dimensional version of the quickhull
algorithm \cgalCite{bdh-qach-96}.
This algorithm requires \f$ O(n h)\f$ time
This algorithm requires \cgalBigO{n h} time
in the worst case for \f$ n\f$ input points with \f$ h\f$ extreme points.
*/

4
Convex_hull_2/doc/Convex_hull_2/CGAL/ch_graham_andrew.h
View File

@ -44,7 +44,7 @@ functions that return instances of these types:
This function implements Andrew's variant of the Graham
scan algorithm \cgalCite{a-aeach-79} and follows the presentation of Mehlhorn
\cgalCite{m-mdscg-84}. This algorithm requires \f$ O(n \log n)\f$ time
\cgalCite{m-mdscg-84}. This algorithm requires \cgalBigO{n \log n} time
in the worst case for \f$ n\f$ input points.
@ -101,7 +101,7 @@ functions that return instances of these types:
\cgalHeading{Implementation}
This algorithm requires \f$ O(n)\f$ time in the worst case for
This algorithm requires \cgalBigO{n} time in the worst case for
\f$ n\f$ input points.
\cgalHeading{Example}

4
Convex_hull_2/doc/Convex_hull_2/CGAL/ch_jarvis.h
View File

@ -44,7 +44,7 @@ functions that return instances of these types:
\cgalHeading{Implementation}
This function uses the Jarvis march (gift-wrapping)
algorithm \cgalCite{j-ichfs-73}. This algorithm requires \f$ O(n h)\f$ time
algorithm \cgalCite{j-ichfs-73}. This algorithm requires \cgalBigO{n h} time
in the worst case for \f$ n\f$ input points with \f$ h\f$ extreme points.
*/
@ -97,7 +97,7 @@ functions that return instances of these types:
\cgalHeading{Implementation}
The function uses the Jarvis march (gift-wrapping) algorithm \cgalCite{j-ichfs-73}.
This algorithm requires \f$ O(n h)\f$ time in the worst
This algorithm requires \cgalBigO{n h} time in the worst
case for \f$ n\f$ input points with \f$ h\f$ extreme points
\pre `start_p` and `stop_p` are extreme points with respect to

8
Convex_hull_2/doc/Convex_hull_2/CGAL/convex_hull_2.h
View File

@ -47,9 +47,9 @@ functions that return instances of these types:
One of two algorithms is used,
depending on the type of iterator used to specify the input points. For
input iterators, the algorithm used is that of Bykat \cgalCite{b-chfsp-78}, which
has a worst-case running time of \f$ O(n h)\f$, where \f$ n\f$ is the number of input
has a worst-case running time of \cgalBigO{n h}, where \f$ n\f$ is the number of input
points and \f$ h\f$ is the number of extreme points. For all other types of
iterators, the \f$ O(n \log n)\f$ algorithm of of Akl and Toussaint
iterators, the \cgalBigO{n \log n} algorithm of of Akl and Toussaint
\cgalCite{at-fcha-78} is used.
@ -128,7 +128,7 @@ functions that return instances of these types:
This function uses Andrew's variant of Graham's scan algorithm
\cgalCite{a-aeach-79}, \cgalCite{m-mdscg-84}. The algorithm has worst-case running time
of \f$ O(n \log n)\f$ for \f$ n\f$ input points.
of \cgalBigO{n \log n} for \f$ n\f$ input points.
*/
@ -192,7 +192,7 @@ functions that return instances of these types:
This function uses Andrew's
variant of Graham's scan algorithm \cgalCite{a-aeach-79}, \cgalCite{m-mdscg-84}. The algorithm
has worst-case running time of \f$ O(n \log n)\f$ for \f$ n\f$ input points.
has worst-case running time of \cgalBigO{n \log n} for \f$ n\f$ input points.
*/
template <class InputIterator, class OutputIterator>

4
Convex_hull_2/doc/Convex_hull_2/CGAL/convexity_check_2.h
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@ -32,7 +32,7 @@ functions that return instances of these types:
\cgalHeading{Implementation}
The algorithm requires \f$ O(n)\f$ time for a set of \f$ n\f$ input points.
The algorithm requires \cgalBigO{n} time for a set of \f$ n\f$ input points.
@ -80,7 +80,7 @@ functions that return instances of these types:
\cgalHeading{Implementation}
The algorithm requires \f$ O(n)\f$ time for a set of \f$ n\f$ input points.
The algorithm requires \cgalBigO{n} time for a set of \f$ n\f$ input points.

12
Convex_hull_2/doc/Convex_hull_2/Convex_hull_2.txt
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@ -52,17 +52,17 @@ class need not be specified and defaults to types and operations defined
in the kernel in which the input point type is defined.
Given a sequence of \f$ n\f$ input points with \f$ h\f$ extreme points,
the function `convex_hull_2()` uses either the output-sensitive \f$ O(n h)\f$ algorithm of Bykat \cgalCite{b-chfsp-78}
(a non-recursive version of the quickhull \cgalCite{bdh-qach-96} algorithm) or the algorithm of Akl and Toussaint, which requires \f$ O(n \log n)\f$ time
the function `convex_hull_2()` uses either the output-sensitive \cgalBigO{n h} algorithm of Bykat \cgalCite{b-chfsp-78}
(a non-recursive version of the quickhull \cgalCite{bdh-qach-96} algorithm) or the algorithm of Akl and Toussaint, which requires \cgalBigO{n \log n} time
in the worst case. The algorithm chosen depends on the kind of
iterator used to specify the input points. These two algorithms are
also available via the functions `ch_bykat()` and `ch_akl_toussaint()`,
respectively. Also available are
the \f$ O(n \log n)\f$ Graham-Andrew scan algorithm \cgalCite{a-aeach-79}, \cgalCite{m-mdscg-84}
the \cgalBigO{n \log n} Graham-Andrew scan algorithm \cgalCite{a-aeach-79}, \cgalCite{m-mdscg-84}
(`ch_graham_andrew()`),
the \f$ O(n h)\f$ Jarvis march algorithm \cgalCite{j-ichfs-73}
the \cgalBigO{n h} Jarvis march algorithm \cgalCite{j-ichfs-73}
(`ch_jarvis()`),
and Eddy's \f$ O(n h)\f$ algorithm \cgalCite{e-nchap-77}
and Eddy's \cgalBigO{n h} algorithm \cgalCite{e-nchap-77}
(`ch_eddy()`), which corresponds to the
two-dimensional version of the quickhull algorithm.
The linear-time algorithm of Melkman for producing the convex hull of
@ -105,7 +105,7 @@ provide the computation of the counterclockwise
sequence of extreme points on the lower hull and upper hull,
respectively. The algorithm used in these functions is
Andrew's variant of Graham's scan algorithm \cgalCite{a-aeach-79}, \cgalCite{m-mdscg-84},
which has worst-case running time of \f$ O(n \log n)\f$.
which has worst-case running time of \cgalBigO{n \log n}.
There are also functions available for computing certain subsequences
of the sequence of extreme points on the convex hull. The function

2
Convex_hull_3/doc/Convex_hull_3/CGAL/convexity_check_3.h
View File

@ -16,7 +16,7 @@ vertices of the convex hull).
\cgalHeading{Implementation}
This function implements the tests described in \cgalCite{mnssssu-cgpvg-96} to
determine convexity and requires \f$ O(e + f)\f$ time for a polyhedron with
determine convexity and requires \cgalBigO{e + f} time for a polyhedron with
\f$ e\f$ edges and \f$ f\f$ faces.

2
Convex_hull_d/doc/Convex_hull_d/CGAL/Convex_hull_d.h
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@ -69,7 +69,7 @@ The time and space requirements are input dependent. Let \f$C_1\f$, \f$C_2\f$, \
let \f$ k_i\f$ be the number of facets of \f$ C_i\f$ that are visible from \f$ x\f$
and that are not already facets of \f$ C_{i-1}\f$.
Then the time for inserting \f$ x\f$ is \f$ O(dim \sum_i k_i)\f$ and
Then the time for inserting \f$ x\f$ is \cgalBigO{dim \sum_i k_i} and
the number of new simplices constructed during the insertion of \f$x\f$
is the number of facets of the hull which were not already facets
of the hull before the insertion.

12
Documentation/doc/CMakeLists.txt
View File

@ -241,6 +241,18 @@ else()
"#EXTRACT_ALL_NO_DETAILED_IF_EMPTY = NO")
endif()
option(CGAL_NO_ADDITIONAL_DETAILS
"Use CGAL special doxygen setting NO_ADDITIONAL_DETAILS." ON)
if(CGAL_NO_ADDITIONAL_DETAILS)
set(CGAL_OPT_NO_ADDITIONAL_DETAILS
"NO_ADDITIONAL_DETAILS = YES")
else()
# The default is NO, so we could leave it out, but it is better to have a commented out placeholder
# this will work for versions with and without the setting.
set(CGAL_OPT_NO_ADDITIONAL_DETAILS
"#NO_ADDITIONAL_DETAILS = NO")
endif()
#we use two directories for the generation/reading of tag files to prevent issues
#if the targets are built in parallel
set(CGAL_DOC_TAG_GEN_DIR "${CMAKE_BINARY_DIR}/doc_gen_tags")

2
Documentation/doc/Documentation/Developer_manual/Chapter_intro.txt
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@ -169,7 +169,7 @@ complexity are known. Also, the theoretic interest in efficiency for
realistic inputs, as opposed to worst-case situations, is
growing \cgalCite{v-ffrim-97}.
For practical purposes, insight into the constant factors hidden in the
\f$ O\f$-notation is necessary, especially if there are several competing
\cgalBigO{&nbsp;}-notation is necessary, especially if there are several competing
algorithms.
Therefore, different implementations should be supplied if there is

2
Documentation/doc/Documentation/Developer_manual/Chapter_kernels.txt
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@ -7,7 +7,7 @@
\authors Stefan Schirra
The layer of geometry kernels provides
basic geometric entities of constant size\cgalFootnote{In dimension \f$ d\f$, an entity of size \f$ O(d)\f$ is considered to be of constant size.} and
basic geometric entities of constant size\cgalFootnote{In dimension \f$ d\f$, an entity of size \cgalBigO{d} is considered to be of constant size.} and
primitive operations on them. Each entity is provided as both a
stand-alone class, which is parameterized by a kernel class, and as a
type in the kernel class. Each operation in the kernel is provided via

12
Documentation/doc/resources/1.8.13/BaseDoxyfile.in
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@ -159,9 +159,9 @@ ALIASES = "cgal=%CGAL" \
"cgalPkgSince{1}=<B>Introduced in:</B> \cgal \1<BR>" \
"cgalPkgDependsOn{1}=<B>Depends on:</B> \1 <BR>" \
"cgalPkgLicense{1}=<B>License:</B> \1 <BR>" \
"cgalPkgDemo{2}=<B>Windows Demo:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a><BR><B>Common Demo Dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDemo{4}=<B>Windows Demos:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\4\">\3</a><BR><B>Common Demo Dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDemo{6}=<B>Windows Demos:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\4\">\3</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\6\">\5</a><BR><B>Common Demo Dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDemo{2}=<B>Windows demo:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a><BR><B>Common demo dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDemo{4}=<B>Windows demos:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\4\">\3</a><BR><B>Common demo dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDemo{6}=<B>Windows demos:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\4\">\3</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\6\">\5</a><BR><B>Common demo dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDescriptionEnd=" \
"cgalModifBegin=\htmlonly <div class=\"CGALModification\"> \endhtmlonly \xrefitem Modification \"Modifications\" \"MODIFICATIONS\" " \
"cgalModifEnd=\htmlonly </div> \endhtmlonly \latexonly END MODIFICATIONS \endlatexonly" \
@ -188,7 +188,9 @@ ALIASES = "cgal=%CGAL" \
"cgalParamNEnd=</ul> \htmlonly[block] </div> \endhtmlonly </td><td></td></tr>" \
"cgalParamSectionBegin{1}=\cgalParamNBegin{\1}" \
"cgalParamSectionEnd=\cgalParamNEnd" \
"cgalParamPrecondition{1}=<li><b>Precondition: </b>\1</li>"
"cgalParamPrecondition{1}=<li><b>Precondition: </b>\1</li>" \
"cgalBigO{1}=\f$O(\1)\f$" \
"cgalBigOLarge{1}=\f$O\left(\1\right)\f$"
# Doxygen selects the parser to use depending on the extension of the files it
# parses. With this tag you can assign which parser to use for a given
@ -262,7 +264,7 @@ EXTRACT_ALL = YES
# the EXTRACT_ALL tag is set to NO.
# The default value is: NO.
EXTRACT_ALL_NO_DETAILED_IF_EMPTY = YES
${CGAL_OPT_EXTRACT_ALL_NO_DETAILED_IF_EMPTY}
# If the EXTRACT_STATIC tag is set to YES, all static members of a file will be
# included in the documentation.

12
Documentation/doc/resources/1.9.6/BaseDoxyfile.in
View File

@ -168,9 +168,9 @@ ALIASES = "cgal=%CGAL" \
"cgalPkgSince{1}=<B>Introduced in:</B> \cgal \1<BR>" \
"cgalPkgDependsOn{1}=<B>Depends on:</B> \1 <BR>" \
"cgalPkgLicense{1}=<B>License:</B> \1 <BR>" \
"cgalPkgDemo{2}=<B>Windows Demo:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a><BR><B>Common Demo Dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDemo{4}=<B>Windows Demos:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\4\">\3</a><BR><B>Common Demo Dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDemo{6}=<B>Windows Demos:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\4\">\3</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\6\">\5</a><BR><B>Common Demo Dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDemo{2}=<B>Windows demo:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a><BR><B>Common demo dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDemo{4}=<B>Windows demos:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\4\">\3</a><BR><B>Common demo dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDemo{6}=<B>Windows demos:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\2\">\1</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\4\">\3</a>, <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/\6\">\5</a><BR><B>Common demo dlls:</B> <a href=\"https://www.cgal.org/demo/${CGAL_CREATED_VERSION_NUM}/CGAL-demoDLLs.zip\">dlls</a><BR>" \
"cgalPkgDescriptionEnd=" \
"cgalModifBegin=\htmlonly <div class=\"CGALModification\"> \endhtmlonly \xrefitem Modification \"Modifications\" \"MODIFICATIONS\"" \
"cgalModifEnd=\htmlonly </div> \endhtmlonly \latexonly END MODIFICATIONS \endlatexonly" \
@ -197,7 +197,9 @@ ALIASES = "cgal=%CGAL" \
"cgalParamNEnd=</ul> \htmlonly[block] </div> \endhtmlonly </td><td></td></tr>" \
"cgalParamSectionBegin{1}=\cgalParamNBegin{\1}" \
"cgalParamSectionEnd=\cgalParamNEnd" \
"cgalParamPrecondition{1}=<li><b>Precondition: </b>\1</li>"
"cgalParamPrecondition{1}=<li><b>Precondition: </b>\1</li>" \
"cgalBigO{1}=\f$O(\1)\f$" \
"cgalBigOLarge{1}=\f$O\left(\1\right)\f$"
# Doxygen selects the parser to use depending on the extension of the files it
# parses. With this tag you can assign which parser to use for a given
@ -791,5 +793,5 @@ GENERATE_LEGEND = NO
# NO_ADDITIONAL_DETAILS tag is set to YES. This tag has no effect if
# the EXTRACT_ALL tag is set to NO.
# The default value is: NO.
NO_ADDITIONAL_DETAILS = YES
${CGAL_OPT_NO_ADDITIONAL_DETAILS}

2
Generalized_map/doc/Generalized_map/Generalized_map.txt
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@ -296,7 +296,7 @@ Several functions allow to create specific configurations of darts into a genera
\subsection ssecadvmarksgmap Boolean Marks
It is often necessary to mark darts, for example to retrieve in <I>O(1)</I> if a given dart was already processed during a specific algorithm, for example, iteration over a given range. Users can also mark specific parts of a generalized map (for example mark all the darts belonging to objects having specific semantics). To answer these needs, a `GeneralizedMap` has a certain number of Boolean marks (fixed by the constant \link GenericMap::NB_MARKS `NB_MARKS`\endlink). When one wants to use a Boolean mark, the following methods are available (with `gm` an instance of a generalized map):
It is often necessary to mark darts, for example to retrieve in \cgalBigO{1} if a given dart was already processed during a specific algorithm, for example, iteration over a given range. Users can also mark specific parts of a generalized map (for example mark all the darts belonging to objects having specific semantics). To answer these needs, a `GeneralizedMap` has a certain number of Boolean marks (fixed by the constant \link GenericMap::NB_MARKS `NB_MARKS`\endlink). When one wants to use a Boolean mark, the following methods are available (with `gm` an instance of a generalized map):
<ul>
<li> get a new free mark: `size_type m = gm.`\link GenericMap::get_new_mark `get_new_mark()`\endlink (throws the exception Exception_no_more_available_mark if no mark is available);
<li> set mark `m` for a given dart `d0`: `gm.`\link GenericMap::mark `mark(d0,m)`\endlink;

2
Generalized_map/include/CGAL/Generalized_map.h
View File

@ -1038,7 +1038,7 @@ namespace CGAL {
}
/** Unmark all the darts of the map for a given mark.
* If all the darts are marked or unmarked, this operation takes O(1)
* If all the darts are marked or unmarked, this operation takes \cgalBigO{1}
* operations, otherwise it traverses all the darts of the map.
* @param amark the given mark.
*/

4
Generator/doc/Generator/CGAL/random_convex_hull_in_disc_2.h
View File

@ -28,8 +28,8 @@ The generated polygon will have an average number of vertices \f$ n^\frac{1}{3}(
The implementation is based on an incremental construction of a convex hull. At each step, we choose a number of points to pick uniformly at random in the disc. Then, a subset of these points, that won't change the convex hull, is evaluated using a Binomial law.
As these points won't be generated, the time and size complexities are reduced \cgalCite{Devillers2014Generator}.
A tradeoff between time and memory is provided with the option `fast`, true by default. Using the `fast` option, both time and size expected complexities are \f$O\left(n^\frac{1}{3}\log^\frac{2}{3}n \right)\f$.
If this option is disabled, the expected size complexity becomes \f$O\left(n^\frac{1}{3}\right)\f$ but the expected time complexity becomes \f$O\left(n^\frac{1}{3}\log^2 n \right)\f$.
A tradeoff between time and memory is provided with the option `fast`, true by default. Using the `fast` option, both time and size expected complexities are \cgalBigOLarge{n^\frac{1}{3}\log^\frac{2}{3}n}.
If this option is disabled, the expected size complexity becomes \cgalBigOLarge{n^\frac{1}{3}} but the expected time complexity becomes \cgalBigOLarge{n^\frac{1}{3}\log^2 n}.
\cgalHeading{Example}

4
Generator/doc/Generator/CGAL/random_convex_set_2.h
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@ -31,8 +31,8 @@ R >` for some representation class `R`,
\cgalHeading{Implementation}
The implementation uses the centroid method
described in \cgalCite{cgal:s-zkm-96} and has a worst case running time of \f$ O(r
\cdot n + n \cdot \log n)\f$, where \f$ r\f$ is the time needed by `pg`
described in \cgalCite{cgal:s-zkm-96} and has a worst case running time of \cgalBigO{r
\cdot n + n \cdot \log n}, where \f$ r\f$ is the time needed by `pg`
to generate a random point.
\cgalHeading{Example}

4
Generator/doc/Generator/CGAL/random_polygon_2.h
View File

@ -37,11 +37,11 @@ The default traits class `Default_traits` is the kernel in which
The implementation is based on the method of eliminating self-intersections in
a polygon by using so-called "2-opt" moves. Such a move eliminates an
intersection between two edges by reversing the order of the vertices between
the edges. No more than \f$ O(n^3)\f$ such moves are required to simplify a polygon
the edges. No more than \cgalBigO{n^3} such moves are required to simplify a polygon
defined on \f$ n\f$ points \cgalCite{ls-utstp-82}.
Intersecting edges are detected using a simple sweep through the vertices
and then one intersection is chosen at random to eliminate after each sweep.
The worse-case running time is therefore \f$ O(n^4 \log n)\f$.
The worse-case running time is therefore \cgalBigO{n^4 \log n}.
\cgalHeading{Example}

2
HalfedgeDS/doc/HalfedgeDS/CGAL/HalfedgeDS_default.h
View File

@ -24,7 +24,7 @@ removal.
\cgalHeading{Implementation}
Currently, `HalfedgeDS_default` is derived from `CGAL::HalfedgeDS_list<Traits>`.
The copy constructor and the assignment operator need \f$ O(n)\f$ time with
The copy constructor and the assignment operator need \cgalBigO{n} time with
\f$ n\f$ the total number of vertices, halfedges, and faces.
*/

2
HalfedgeDS/doc/HalfedgeDS/CGAL/HalfedgeDS_list.h
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@ -20,7 +20,7 @@ iterators that supports removal.
\cgalHeading{Implementation}
`HalfedgeDS_list` uses internally the `CGAL::In_place_list` container class.
The copy constructor and the assignment operator need \f$ O(n)\f$ time with
The copy constructor and the assignment operator need \cgalBigO{n} time with
\f$ n\f$ the total number of vertices, halfedges, and faces.
`CGAL_ALLOCATOR(int)` is used as default argument for the

4
Heat_method_3/doc/Heat_method_3/Heat_method_3.txt
View File

@ -223,8 +223,8 @@ The algorithm is as follows:
The time complexity of the algorithm is determined primarily by the
choice of linear solver. In the current implementation, Cholesky
prefactorization is roughly \f$ O(N^{1.5})\f$ and computation of distances is
roughly \f$ O(N)\f$, where \f$ N\f$ is the number of vertices in the triangulation.
prefactorization is roughly \cgalBigO{N^{1.5}} and computation of distances is
roughly \cgalBigO{N}, where \f$ N\f$ is the number of vertices in the triangulation.
The algorithm uses two \f$ N \times N\f$ matrices, both with the same pattern of
non-zeros (in average 7 non-zeros
per row/column). The cost of computation is independent of the size

4
Inscribed_areas/doc/Inscribed_areas/CGAL/Largest_empty_iso_rectangle_2.h
View File

@ -14,8 +14,8 @@ that do not contain any point of the point set.
\cgalHeading{Implementation}
The algorithm is an implementation of \cgalCite{o-naler-90}. The runtime of an
insertion or a removal is \f$ O(\log n)\f$. A query takes \f$ O(n^2)\f$ worst
case time and \f$ O(n \log n)\f$ expected time. The working storage is \f$
insertion or a removal is \cgalBigO{\log n}. A query takes \cgalBigO{n^2} worst
case time and \cgalBigO{n \log n} expected time. The working storage is \f$
O(n)\f$.
*/

12
Inscribed_areas/doc/Inscribed_areas/CGAL/extremal_polygon_2.h
View File

@ -32,8 +32,8 @@ convex polygon (oriented clock- or counterclockwise).
\cgalHeading{Implementation}
The implementation uses monotone matrix search
\cgalCite{akmsw-gamsa-87} and has a worst case running time of \f$ O(k
\cdot n + n \cdot \log n)\f$, where \f$ n\f$ is the number of vertices in
\cgalCite{akmsw-gamsa-87} and has a worst case running time of \cgalBigO{k
\cdot n + n \cdot \log n}, where \f$ n\f$ is the number of vertices in
\f$ P\f$.
*/
@ -89,8 +89,8 @@ where `K` is a model of `Kernel`.
\cgalHeading{Implementation}
The implementation uses monotone matrix search
\cgalCite{akmsw-gamsa-87} and has a worst case running time of \f$ O(k
\cdot n + n \cdot \log n)\f$, where \f$ n\f$ is the number of vertices in
\cgalCite{akmsw-gamsa-87} and has a worst case running time of \cgalBigO{k
\cdot n + n \cdot \log n}, where \f$ n\f$ is the number of vertices in
\f$ P\f$.
\cgalHeading{Example}
@ -158,8 +158,8 @@ defined that computes the squareroot of a number.
\cgalHeading{Implementation}
The implementation uses monotone matrix search
\cgalCite{akmsw-gamsa-87} and has a worst case running time of \f$ O(k
\cdot n + n \cdot \log n)\f$, where \f$ n\f$ is the number of vertices in
\cgalCite{akmsw-gamsa-87} and has a worst case running time of \cgalBigO{k
\cdot n + n \cdot \log n}, where \f$ n\f$ is the number of vertices in
\f$ P\f$.
\cgalHeading{Example}

2
Inscribed_areas/include/CGAL/Largest_empty_iso_rectangle_2.h
View File

@ -46,7 +46,7 @@ namespace CGAL {
The algorithm checks all the empty rectangles that are bounded by either
points or edges of the bounding box (other empty rectangles can be enlarged
and remain empty). There are O(n^2) such rectangles. It is done in three
and remain empty). There are \cgalBigO{n^2} such rectangles. It is done in three
phases. In the first one empty rectangles that are bounded by two opposite
edges of the bounding box are checked. In the second one, other empty
rectangles that are bounded by one or two edges of the bounding box are

12
Installation/.reuse/dep5 Normal file
View File

@ -0,0 +1,12 @@
Format: https://www.debian.org/doc/packaging-manuals/copyright-format/1.0/
Upstream-Name: CGAL
Upstream-Contact: CGAL Editorial Board <info@cgal.org>
Source: https://github.com/CGAL/cgal
Files: *.cmake *.md doc/* doc_html/* scripts/* developer_scripts/* package_info/* demo/* examples/* src/* test/* benchmarks/* benchmark/* data/* cmake/*
Copyright: 1995-2023 The CGAL Project
License: CC0-1.0
Files: include/CGAL/Qt/ImageInterface.ui include/CGAL/Qt/resources/qglviewer-icon.xpm AUTHORS CMakeLists.txt README auxiliary/cgal_create_cmake_script.1 auxiliary/gmp/README include/CGAL/license/gpl_package_list.txt auxiliary/cgal_app.icns copyright VERSION
Copyright: 1995-2023 The CGAL Project
License: CC0-1.0

6
Interval_skip_list/doc/Interval_skip_list/CGAL/Interval_skip_list.h
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@ -9,10 +9,10 @@ allows to find all members of a set of intervals that overlap a point.
\cgalHeading{Implementation}
The insertion and deletion of a segment in the interval skip list
takes expected time \f$ O(\log^2 n)\f$, if the segment endpoints are
takes expected time \cgalBigO{\log^2 n}, if the segment endpoints are
chosen from a continuous distribution. A stabbing query takes expected
time \f$ O(\log n)\f$, and finding all intervals that contain a point
takes expected time \f$ O(\log n + k)\f$, where \f$ k\f$ is the number of
time \cgalBigO{\log n}, and finding all intervals that contain a point
takes expected time \cgalBigO{\log n + k}, where \f$ k\f$ is the number of
intervals.
The implementation is based on the code developed by Eric N. Hansen.

4
Kernel_d/doc/Kernel_d/CGAL/Kernel_d/Aff_transformation_d.h
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@ -17,10 +17,10 @@ by the constructors below.
Affine Transformations are implemented by matrices of number type
`RT` as a handle type. All operations like creation,
initialization, input and output on a transformation \f$ t\f$ take time
\f$ O(t.dimension()^2)\f$. `dimension()` takes constant time.
\cgalBigO{t.dimension()^2}. `dimension()` takes constant time.
The operations for inversion and composition have the cubic costs of
the used matrix operations. The space requirement is
\f$ O(t.dimension()^2)\f$.
\cgalBigO{t.dimension()^2}.
*/
template< typename Kernel >

4
Kernel_d/doc/Kernel_d/CGAL/Kernel_d/Direction_d.h
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@ -22,9 +22,9 @@ We provide the operations of the lower dimensional interface `dx()`,
Directions are implemented by arrays of integers as an item type. All
operations like creation, initialization, tests, inversion, input and
output on a direction \f$ d\f$ take time \f$ O(d.\mathit{dimension}())\f$.
output on a direction \f$ d\f$ take time \cgalBigO{d.\mathit{dimension}()}.
`dimension()`, coordinate access and conversion take constant
time. The space requirement is \f$ O(d.\mathit{dimension}())\f$.
time. The space requirement is \cgalBigO{d.\mathit{dimension}()}.
*/
template< typename Kernel >

4
Kernel_d/doc/Kernel_d/CGAL/Kernel_d/Hyperplane_d.h
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@ -27,8 +27,8 @@ other.
Hyperplanes are implemented by arrays of integers as an item type.
All operations like creation, initialization, tests, vector
arithmetic, input and output on a hyperplane \f$ h\f$ take time
\f$ O(h.dimension())\f$. coordinate access and `dimension()` take
constant time. The space requirement is \f$ O(h.dimension())\f$.
\cgalBigO{h.dimension()}. coordinate access and `dimension()` take
constant time. The space requirement is \cgalBigO{h.dimension()}.
*/
template< typename Kernel >

6
Kernel_d/doc/Kernel_d/CGAL/Kernel_d/Line_d.h
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@ -11,10 +11,10 @@ An instance of data type `Line_d` is an oriented line in
Lines are implemented by a pair of points as an item type. All
operations like creation, initialization, tests, direction
calculation, input and output on a line \f$ l\f$ take time
\f$ O(l.dimension())\f$. `dimension()`, coordinate and point
\cgalBigO{l.dimension()}. `dimension()`, coordinate and point
access, and identity test take constant time. The operations for
intersection calculation also take time \f$ O(l.dimension())\f$. The
space requirement is \f$ O(l.dimension())\f$.
intersection calculation also take time \cgalBigO{l.dimension()}. The
space requirement is \cgalBigO{l.dimension()}.
*/
template< typename Kernel >

4
Kernel_d/doc/Kernel_d/CGAL/Kernel_d/Point_d.h
View File

@ -24,9 +24,9 @@ dimensional interface `x()`, `y()`, `z()`, `hx()`,
Points are implemented by arrays of `RT` items. All operations
like creation, initialization, tests, point - vector arithmetic, input
and output on a point \f$ p\f$ take time \f$ O(p.dimension())\f$.
and output on a point \f$ p\f$ take time \cgalBigO{p.dimension()}.
`dimension()`, coordinate access and conversions take constant
time. The space requirement for points is \f$ O(p.dimension())\f$.
time. The space requirement for points is \cgalBigO{p.dimension()}.
*/
template< typename Kernel >

4
Kernel_d/doc/Kernel_d/CGAL/Kernel_d/Ray_d.h
View File

@ -12,9 +12,9 @@ it goes to infinity.
Rays are implemented by a pair of points as an item type. All
operations like creation, initialization, tests, direction
calculation, input and output on a ray \f$ r\f$ take time
\f$ O(r.dimension())\f$. `dimension()`, coordinate and point
\cgalBigO{r.dimension()}. `dimension()`, coordinate and point
access, and identity test take constant time. The space requirement is
\f$ O(r.dimension())\f$.
\cgalBigO{r.dimension()}.
*/
template< typename Kernel >

6
Kernel_d/doc/Kernel_d/CGAL/Kernel_d/Segment_d.h
View File

@ -14,11 +14,11 @@ called the target point of \f$ s\f$, both points are called endpoints of
Segments are implemented by a pair of points as an item type. All
operations like creation, initialization, tests, the calculation of
the direction and source - target vector, input and output on a
segment \f$ s\f$ take time \f$ O(s.dimension())\f$. `dimension()`,
segment \f$ s\f$ take time \cgalBigO{s.dimension()}. `dimension()`,
coordinate and end point access, and identity test take constant time.
The operations for intersection calculation also take time
\f$ O(s.dimension())\f$. The space requirement is
\f$ O(s.dimension())\f$.
\cgalBigO{s.dimension()}. The space requirement is
\cgalBigO{s.dimension()}.
*/
template< typename Kernel >

8
Kernel_d/doc/Kernel_d/CGAL/Kernel_d/Sphere_d.h
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@ -17,11 +17,11 @@ orientation of the defining points, i.e., `orientation(A)`.
Spheres are implemented by a vector of points as a handle type. All
operations like creation, initialization, tests, input and output of a
sphere \f$ s\f$ take time \f$ O(s.dimension()) \f$. `dimension()`,
sphere \f$ s\f$ take time \cgalBigO{s.dimension()}$. `dimension()`,
point access take constant time. The `center()`-operation takes
time \f$ O(d^3)\f$ on its first call and constant time thereafter. The
sidedness and orientation tests take time \f$ O(d^3)\f$. The space
requirement for spheres is \f$ O(s.dimension())\f$ neglecting the
time \cgalBigO{d^3} on its first call and constant time thereafter. The
sidedness and orientation tests take time \cgalBigO{d^3}. The space
requirement for spheres is \cgalBigO{s.dimension()} neglecting the
storage room of the points.
*/

4
Kernel_d/doc/Kernel_d/CGAL/Kernel_d/Vector_d.h
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@ -26,9 +26,9 @@ lower dimensional interface `x()`, `y()`, `z()`,
Vectors are implemented by arrays of variables of type `RT`. All
operations like creation, initialization, tests, vector arithmetic,
input and output on a vector \f$ v\f$ take time \f$ O(v.dimension())\f$.
input and output on a vector \f$ v\f$ take time \cgalBigO{v.dimension()}.
coordinate access, `dimension()` and conversions take constant
time. The space requirement of a vector is \f$ O(v.dimension())\f$.
time. The space requirement of a vector is \cgalBigO{v.dimension()}.
*/
template< typename Kernel >

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Boost Software License - Version 1.0 - August 17th, 2003
Permission is hereby granted, free of charge, to any person or organization
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SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
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ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
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GNU GENERAL PUBLIC LICENSE
Version 2, June 1991
Copyright (C) 1989, 1991 Free Software Foundation, Inc.
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
The licenses for most software are designed to take away your
freedom to share and change it. By contrast, the GNU General Public
License is intended to guarantee your freedom to share and change free
software--to make sure the software is free for all its users. This
General Public License applies to most of the Free Software
Foundation's software and to any other program whose authors commit to
using it. (Some other Free Software Foundation software is covered by
the GNU Library General Public License instead.) You can apply it to
your programs, too.
When we speak of free software, we are referring to freedom, not
price. Our General Public Licenses are designed to make sure that you
have the freedom to distribute copies of free software (and charge for
this service if you wish), that you receive source code or can get it
if you want it, that you can change the software or use pieces of it
in new free programs; and that you know you can do these things.
To protect your rights, we need to make restrictions that forbid
anyone to deny you these rights or to ask you to surrender the rights.
These restrictions translate to certain responsibilities for you if you
distribute copies of the software, or if you modify it.
For example, if you distribute copies of such a program, whether
gratis or for a fee, you must give the recipients all the rights that
you have. You must make sure that they, too, receive or can get the
source code. And you must show them these terms so they know their
rights.
We protect your rights with two steps: (1) copyright the software, and
(2) offer you this license which gives you legal permission to copy,
distribute and/or modify the software.
Also, for each author's protection and ours, we want to make certain
that everyone understands that there is no warranty for this free
software. If the software is modified by someone else and passed on, we
want its recipients to know that what they have is not the original, so
that any problems introduced by others will not reflect on the original
authors' reputations.
Finally, any free program is threatened constantly by software
patents. We wish to avoid the danger that redistributors of a free
program will individually obtain patent licenses, in effect making the
program proprietary. To prevent this, we have made it clear that any
patent must be licensed for everyone's free use or not licensed at all.
The precise terms and conditions for copying, distribution and
modification follow.
GNU GENERAL PUBLIC LICENSE
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
0. This License applies to any program or other work which contains
a notice placed by the copyright holder saying it may be distributed
under the terms of this General Public License. The "Program", below,
refers to any such program or work, and a "work based on the Program"
means either the Program or any derivative work under copyright law:
that is to say, a work containing the Program or a portion of it,
either verbatim or with modifications and/or translated into another
language. (Hereinafter, translation is included without limitation in
the term "modification".) Each licensee is addressed as "you".
Activities other than copying, distribution and modification are not
covered by this License; they are outside its scope. The act of
running the Program is not restricted, and the output from the Program
is covered only if its contents constitute a work based on the
Program (independent of having been made by running the Program).
Whether that is true depends on what the Program does.
1. You may copy and distribute verbatim copies of the Program's
source code as you receive it, in any medium, provided that you
conspicuously and appropriately publish on each copy an appropriate
copyright notice and disclaimer of warranty; keep intact all the
notices that refer to this License and to the absence of any warranty;
and give any other recipients of the Program a copy of this License
along with the Program.
You may charge a fee for the physical act of transferring a copy, and
you may at your option offer warranty protection in exchange for a fee.
2. You may modify your copy or copies of the Program or any portion
of it, thus forming a work based on the Program, and copy and
distribute such modifications or work under the terms of Section 1
above, provided that you also meet all of these conditions:
a) You must cause the modified files to carry prominent notices
stating that you changed the files and the date of any change.
b) You must cause any work that you distribute or publish, that in
whole or in part contains or is derived from the Program or any
part thereof, to be licensed as a whole at no charge to all third
parties under the terms of this License.
c) If the modified program normally reads commands interactively
when run, you must cause it, when started running for such
interactive use in the most ordinary way, to print or display an
announcement including an appropriate copyright notice and a
notice that there is no warranty (or else, saying that you provide
a warranty) and that users may redistribute the program under
these conditions, and telling the user how to view a copy of this
License. (Exception: if the Program itself is interactive but
does not normally print such an announcement, your work based on
the Program is not required to print an announcement.)
These requirements apply to the modified work as a whole. If
identifiable sections of that work are not derived from the Program,
and can be reasonably considered independent and separate works in
themselves, then this License, and its terms, do not apply to those
sections when you distribute them as separate works. But when you
distribute the same sections as part of a whole which is a work based
on the Program, the distribution of the whole must be on the terms of
this License, whose permissions for other licensees extend to the
entire whole, and thus to each and every part regardless of who wrote it.
Thus, it is not the intent of this section to claim rights or contest
your rights to work written entirely by you; rather, the intent is to
exercise the right to control the distribution of derivative or
collective works based on the Program.
In addition, mere aggregation of another work not based on the Program
with the Program (or with a work based on the Program) on a volume of
a storage or distribution medium does not bring the other work under
the scope of this License.
3. You may copy and distribute the Program (or a work based on it,
under Section 2) in object code or executable form under the terms of
Sections 1 and 2 above provided that you also do one of the following:
a) Accompany it with the complete corresponding machine-readable
source code, which must be distributed under the terms of Sections
1 and 2 above on a medium customarily used for software interchange; or,
b) Accompany it with a written offer, valid for at least three
years, to give any third party, for a charge no more than your
cost of physically performing source distribution, a complete
machine-readable copy of the corresponding source code, to be
distributed under the terms of Sections 1 and 2 above on a medium
customarily used for software interchange; or,
c) Accompany it with the information you received as to the offer
to distribute corresponding source code. (This alternative is
allowed only for noncommercial distribution and only if you
received the program in object code or executable form with such
an offer, in accord with Subsection b above.)
The source code for a work means the preferred form of the work for
making modifications to it. For an executable work, complete source
code means all the source code for all modules it contains, plus any
associated interface definition files, plus the scripts used to
control compilation and installation of the executable. However, as a
special exception, the source code distributed need not include
anything that is normally distributed (in either source or binary
form) with the major components (compiler, kernel, and so on) of the
operating system on which the executable runs, unless that component
itself accompanies the executable.
If distribution of executable or object code is made by offering
access to copy from a designated place, then offering equivalent
access to copy the source code from the same place counts as
distribution of the source code, even though third parties are not
compelled to copy the source along with the object code.
4. You may not copy, modify, sublicense, or distribute the Program
except as expressly provided under this License. Any attempt
otherwise to copy, modify, sublicense or distribute the Program is
void, and will automatically terminate your rights under this License.
However, parties who have received copies, or rights, from you under
this License will not have their licenses terminated so long as such
parties remain in full compliance.
5. You are not required to accept this License, since you have not
signed it. However, nothing else grants you permission to modify or
distribute the Program or its derivative works. These actions are
prohibited by law if you do not accept this License. Therefore, by
modifying or distributing the Program (or any work based on the
Program), you indicate your acceptance of this License to do so, and
all its terms and conditions for copying, distributing or modifying
the Program or works based on it.
6. Each time you redistribute the Program (or any work based on the
Program), the recipient automatically receives a license from the
original licensor to copy, distribute or modify the Program subject to
these terms and conditions. You may not impose any further
restrictions on the recipients' exercise of the rights granted herein.
You are not responsible for enforcing compliance by third parties to
this License.
7. If, as a consequence of a court judgment or allegation of patent
infringement or for any other reason (not limited to patent issues),
conditions are imposed on you (whether by court order, agreement or
otherwise) that contradict the conditions of this License, they do not
excuse you from the conditions of this License. If you cannot
distribute so as to satisfy simultaneously your obligations under this
License and any other pertinent obligations, then as a consequence you
may not distribute the Program at all. For example, if a patent
license would not permit royalty-free redistribution of the Program by
all those who receive copies directly or indirectly through you, then
the only way you could satisfy both it and this License would be to
refrain entirely from distribution of the Program.
If any portion of this section is held invalid or unenforceable under
any particular circumstance, the balance of the section is intended to
apply and the section as a whole is intended to apply in other
circumstances.
It is not the purpose of this section to induce you to infringe any
patents or other property right claims or to contest validity of any
such claims; this section has the sole purpose of protecting the
integrity of the free software distribution system, which is
implemented by public license practices. Many people have made
generous contributions to the wide range of software distributed
through that system in reliance on consistent application of that
system; it is up to the author/donor to decide if he or she is willing
to distribute software through any other system and a licensee cannot
impose that choice.
This section is intended to make thoroughly clear what is believed to
be a consequence of the rest of this License.
8. If the distribution and/or use of the Program is restricted in
certain countries either by patents or by copyrighted interfaces, the
original copyright holder who places the Program under this License
may add an explicit geographical distribution limitation excluding
those countries, so that distribution is permitted only in or among
countries not thus excluded. In such case, this License incorporates
the limitation as if written in the body of this License.
9. The Free Software Foundation may publish revised and/or new versions
of the General Public License from time to time. Such new versions will
be similar in spirit to the present version, but may differ in detail to
address new problems or concerns.
Each version is given a distinguishing version number. If the Program
specifies a version number of this License which applies to it and "any
later version", you have the option of following the terms and conditions
either of that version or of any later version published by the Free
Software Foundation. If the Program does not specify a version number of
this License, you may choose any version ever published by the Free Software
Foundation.
10. If you wish to incorporate parts of the Program into other free
programs whose distribution conditions are different, write to the author
to ask for permission. For software which is copyrighted by the Free
Software Foundation, write to the Free Software Foundation; we sometimes
make exceptions for this. Our decision will be guided by the two goals
of preserving the free status of all derivatives of our free software and
of promoting the sharing and reuse of software generally.
NO WARRANTY
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
REPAIR OR CORRECTION.
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
POSSIBILITY OF SUCH DAMAGES.
END OF TERMS AND CONDITIONS
How to Apply These Terms to Your New Programs
If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
convey the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
<one line to give the program's name and a brief idea of what it does.>
Copyright (C) <year> <name of author>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
Also add information on how to contact you by electronic and paper mail.
If the program is interactive, make it output a short notice like this
when it starts in an interactive mode:
Gnomovision version 69, Copyright (C) year name of author
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, the commands you use may
be called something other than `show w' and `show c'; they could even be
mouse-clicks or menu items--whatever suits your program.
You should also get your employer (if you work as a programmer) or your
school, if any, to sign a "copyright disclaimer" for the program, if
necessary. Here is a sample; alter the names:
Yoyodyne, Inc., hereby disclaims all copyright interest in the program
`Gnomovision' (which makes passes at compilers) written by James Hacker.
<signature of Ty Coon>, 1 April 1989
Ty Coon, President of Vice
This General Public License does not permit incorporating your program into
proprietary programs. If your program is a subroutine library, you may
consider it more useful to permit linking proprietary applications with the
library. If this is what you want to do, use the GNU Library General
Public License instead of this License.

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GNU GENERAL PUBLIC LICENSE
Version 2, June 1991
Copyright (C) 1989, 1991 Free Software Foundation, Inc.
51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
The licenses for most software are designed to take away your
freedom to share and change it. By contrast, the GNU General Public
License is intended to guarantee your freedom to share and change free
software--to make sure the software is free for all its users. This
General Public License applies to most of the Free Software
Foundation's software and to any other program whose authors commit to
using it. (Some other Free Software Foundation software is covered by
the GNU Library General Public License instead.) You can apply it to
your programs, too.
When we speak of free software, we are referring to freedom, not
price. Our General Public Licenses are designed to make sure that you
have the freedom to distribute copies of free software (and charge for
this service if you wish), that you receive source code or can get it
if you want it, that you can change the software or use pieces of it
in new free programs; and that you know you can do these things.
To protect your rights, we need to make restrictions that forbid
anyone to deny you these rights or to ask you to surrender the rights.
These restrictions translate to certain responsibilities for you if you
distribute copies of the software, or if you modify it.
For example, if you distribute copies of such a program, whether
gratis or for a fee, you must give the recipients all the rights that
you have. You must make sure that they, too, receive or can get the
source code. And you must show them these terms so they know their
rights.
We protect your rights with two steps: (1) copyright the software, and
(2) offer you this license which gives you legal permission to copy,
distribute and/or modify the software.
Also, for each author's protection and ours, we want to make certain
that everyone understands that there is no warranty for this free
software. If the software is modified by someone else and passed on, we
want its recipients to know that what they have is not the original, so
that any problems introduced by others will not reflect on the original
authors' reputations.
Finally, any free program is threatened constantly by software
patents. We wish to avoid the danger that redistributors of a free
program will individually obtain patent licenses, in effect making the
program proprietary. To prevent this, we have made it clear that any
patent must be licensed for everyone's free use or not licensed at all.
The precise terms and conditions for copying, distribution and
modification follow.
GNU GENERAL PUBLIC LICENSE
TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
0. This License applies to any program or other work which contains
a notice placed by the copyright holder saying it may be distributed
under the terms of this General Public License. The "Program", below,
refers to any such program or work, and a "work based on the Program"
means either the Program or any derivative work under copyright law:
that is to say, a work containing the Program or a portion of it,
either verbatim or with modifications and/or translated into another
language. (Hereinafter, translation is included without limitation in
the term "modification".) Each licensee is addressed as "you".
Activities other than copying, distribution and modification are not
covered by this License; they are outside its scope. The act of
running the Program is not restricted, and the output from the Program
is covered only if its contents constitute a work based on the
Program (independent of having been made by running the Program).
Whether that is true depends on what the Program does.
1. You may copy and distribute verbatim copies of the Program's
source code as you receive it, in any medium, provided that you
conspicuously and appropriately publish on each copy an appropriate
copyright notice and disclaimer of warranty; keep intact all the
notices that refer to this License and to the absence of any warranty;
and give any other recipients of the Program a copy of this License
along with the Program.
You may charge a fee for the physical act of transferring a copy, and
you may at your option offer warranty protection in exchange for a fee.
2. You may modify your copy or copies of the Program or any portion
of it, thus forming a work based on the Program, and copy and
distribute such modifications or work under the terms of Section 1
above, provided that you also meet all of these conditions:
a) You must cause the modified files to carry prominent notices
stating that you changed the files and the date of any change.
b) You must cause any work that you distribute or publish, that in
whole or in part contains or is derived from the Program or any
part thereof, to be licensed as a whole at no charge to all third
parties under the terms of this License.
c) If the modified program normally reads commands interactively
when run, you must cause it, when started running for such
interactive use in the most ordinary way, to print or display an
announcement including an appropriate copyright notice and a
notice that there is no warranty (or else, saying that you provide
a warranty) and that users may redistribute the program under
these conditions, and telling the user how to view a copy of this
License. (Exception: if the Program itself is interactive but
does not normally print such an announcement, your work based on
the Program is not required to print an announcement.)
These requirements apply to the modified work as a whole. If
identifiable sections of that work are not derived from the Program,
and can be reasonably considered independent and separate works in
themselves, then this License, and its terms, do not apply to those
sections when you distribute them as separate works. But when you
distribute the same sections as part of a whole which is a work based
on the Program, the distribution of the whole must be on the terms of
this License, whose permissions for other licensees extend to the
entire whole, and thus to each and every part regardless of who wrote it.
Thus, it is not the intent of this section to claim rights or contest
your rights to work written entirely by you; rather, the intent is to
exercise the right to control the distribution of derivative or
collective works based on the Program.
In addition, mere aggregation of another work not based on the Program
with the Program (or with a work based on the Program) on a volume of
a storage or distribution medium does not bring the other work under
the scope of this License.
3. You may copy and distribute the Program (or a work based on it,
under Section 2) in object code or executable form under the terms of
Sections 1 and 2 above provided that you also do one of the following:
a) Accompany it with the complete corresponding machine-readable
source code, which must be distributed under the terms of Sections
1 and 2 above on a medium customarily used for software interchange; or,
b) Accompany it with a written offer, valid for at least three
years, to give any third party, for a charge no more than your
cost of physically performing source distribution, a complete
machine-readable copy of the corresponding source code, to be
distributed under the terms of Sections 1 and 2 above on a medium
customarily used for software interchange; or,
c) Accompany it with the information you received as to the offer
to distribute corresponding source code. (This alternative is
allowed only for noncommercial distribution and only if you
received the program in object code or executable form with such
an offer, in accord with Subsection b above.)
The source code for a work means the preferred form of the work for
making modifications to it. For an executable work, complete source
code means all the source code for all modules it contains, plus any
associated interface definition files, plus the scripts used to
control compilation and installation of the executable. However, as a
special exception, the source code distributed need not include
anything that is normally distributed (in either source or binary
form) with the major components (compiler, kernel, and so on) of the
operating system on which the executable runs, unless that component
itself accompanies the executable.
If distribution of executable or object code is made by offering
access to copy from a designated place, then offering equivalent
access to copy the source code from the same place counts as
distribution of the source code, even though third parties are not
compelled to copy the source along with the object code.
4. You may not copy, modify, sublicense, or distribute the Program
except as expressly provided under this License. Any attempt
otherwise to copy, modify, sublicense or distribute the Program is
void, and will automatically terminate your rights under this License.
However, parties who have received copies, or rights, from you under
this License will not have their licenses terminated so long as such
parties remain in full compliance.
5. You are not required to accept this License, since you have not
signed it. However, nothing else grants you permission to modify or
distribute the Program or its derivative works. These actions are
prohibited by law if you do not accept this License. Therefore, by
modifying or distributing the Program (or any work based on the
Program), you indicate your acceptance of this License to do so, and
all its terms and conditions for copying, distributing or modifying
the Program or works based on it.
6. Each time you redistribute the Program (or any work based on the
Program), the recipient automatically receives a license from the
original licensor to copy, distribute or modify the Program subject to
these terms and conditions. You may not impose any further
restrictions on the recipients' exercise of the rights granted herein.
You are not responsible for enforcing compliance by third parties to
this License.
7. If, as a consequence of a court judgment or allegation of patent
infringement or for any other reason (not limited to patent issues),
conditions are imposed on you (whether by court order, agreement or
otherwise) that contradict the conditions of this License, they do not
excuse you from the conditions of this License. If you cannot
distribute so as to satisfy simultaneously your obligations under this
License and any other pertinent obligations, then as a consequence you
may not distribute the Program at all. For example, if a patent
license would not permit royalty-free redistribution of the Program by
all those who receive copies directly or indirectly through you, then
the only way you could satisfy both it and this License would be to
refrain entirely from distribution of the Program.
If any portion of this section is held invalid or unenforceable under
any particular circumstance, the balance of the section is intended to
apply and the section as a whole is intended to apply in other
circumstances.
It is not the purpose of this section to induce you to infringe any
patents or other property right claims or to contest validity of any
such claims; this section has the sole purpose of protecting the
integrity of the free software distribution system, which is
implemented by public license practices. Many people have made
generous contributions to the wide range of software distributed
through that system in reliance on consistent application of that
system; it is up to the author/donor to decide if he or she is willing
to distribute software through any other system and a licensee cannot
impose that choice.
This section is intended to make thoroughly clear what is believed to
be a consequence of the rest of this License.
8. If the distribution and/or use of the Program is restricted in
certain countries either by patents or by copyrighted interfaces, the
original copyright holder who places the Program under this License
may add an explicit geographical distribution limitation excluding
those countries, so that distribution is permitted only in or among
countries not thus excluded. In such case, this License incorporates
the limitation as if written in the body of this License.
9. The Free Software Foundation may publish revised and/or new versions
of the General Public License from time to time. Such new versions will
be similar in spirit to the present version, but may differ in detail to
address new problems or concerns.
Each version is given a distinguishing version number. If the Program
specifies a version number of this License which applies to it and "any
later version", you have the option of following the terms and conditions
either of that version or of any later version published by the Free
Software Foundation. If the Program does not specify a version number of
this License, you may choose any version ever published by the Free Software
Foundation.
10. If you wish to incorporate parts of the Program into other free
programs whose distribution conditions are different, write to the author
to ask for permission. For software which is copyrighted by the Free
Software Foundation, write to the Free Software Foundation; we sometimes
make exceptions for this. Our decision will be guided by the two goals
of preserving the free status of all derivatives of our free software and
of promoting the sharing and reuse of software generally.
NO WARRANTY
11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS
TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
REPAIR OR CORRECTION.
12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES,
INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING
OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
POSSIBILITY OF SUCH DAMAGES.
END OF TERMS AND CONDITIONS
How to Apply These Terms to Your New Programs
If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
convey the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
<one line to give the program's name and a brief idea of what it does.>
Copyright (C) <year> <name of author>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
Also add information on how to contact you by electronic and paper mail.
If the program is interactive, make it output a short notice like this
when it starts in an interactive mode:
Gnomovision version 69, Copyright (C) year name of author
Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, the commands you use may
be called something other than `show w' and `show c'; they could even be
mouse-clicks or menu items--whatever suits your program.
You should also get your employer (if you work as a programmer) or your
school, if any, to sign a "copyright disclaimer" for the program, if
necessary. Here is a sample; alter the names:
Yoyodyne, Inc., hereby disclaims all copyright interest in the program
`Gnomovision' (which makes passes at compilers) written by James Hacker.
<signature of Ty Coon>, 1 April 1989
Ty Coon, President of Vice
This General Public License does not permit incorporating your program into
proprietary programs. If your program is a subroutine library, you may
consider it more useful to permit linking proprietary applications with the
library. If this is what you want to do, use the GNU Library General
Public License instead of this License.

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@ -0,0 +1,674 @@
GNU GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
The GNU General Public License is a free, copyleft license for
software and other kinds of works.
The licenses for most software and other practical works are designed
to take away your freedom to share and change the works. By contrast,
the GNU General Public License is intended to guarantee your freedom to
share and change all versions of a program--to make sure it remains free
software for all its users. We, the Free Software Foundation, use the
GNU General Public License for most of our software; it applies also to
any other work released this way by its authors. You can apply it to
your programs, too.
When we speak of free software, we are referring to freedom, not
price. Our General Public Licenses are designed to make sure that you
have the freedom to distribute copies of free software (and charge for
them if you wish), that you receive source code or can get it if you
want it, that you can change the software or use pieces of it in new
free programs, and that you know you can do these things.
To protect your rights, we need to prevent others from denying you
these rights or asking you to surrender the rights. Therefore, you have
certain responsibilities if you distribute copies of the software, or if
you modify it: responsibilities to respect the freedom of others.
For example, if you distribute copies of such a program, whether
gratis or for a fee, you must pass on to the recipients the same
freedoms that you received. You must make sure that they, too, receive
or can get the source code. And you must show them these terms so they
know their rights.
Developers that use the GNU GPL protect your rights with two steps:
(1) assert copyright on the software, and (2) offer you this License
giving you legal permission to copy, distribute and/or modify it.
For the developers' and authors' protection, the GPL clearly explains
that there is no warranty for this free software. For both users' and
authors' sake, the GPL requires that modified versions be marked as
changed, so that their problems will not be attributed erroneously to
authors of previous versions.
Some devices are designed to deny users access to install or run
modified versions of the software inside them, although the manufacturer
can do so. This is fundamentally incompatible with the aim of
protecting users' freedom to change the software. The systematic
pattern of such abuse occurs in the area of products for individuals to
use, which is precisely where it is most unacceptable. Therefore, we
have designed this version of the GPL to prohibit the practice for those
products. If such problems arise substantially in other domains, we
stand ready to extend this provision to those domains in future versions
of the GPL, as needed to protect the freedom of users.
Finally, every program is threatened constantly by software patents.
States should not allow patents to restrict development and use of
software on general-purpose computers, but in those that do, we wish to
avoid the special danger that patents applied to a free program could
make it effectively proprietary. To prevent this, the GPL assures that
patents cannot be used to render the program non-free.
The precise terms and conditions for copying, distribution and
modification follow.
TERMS AND CONDITIONS
0. Definitions.
"This License" refers to version 3 of the GNU General Public License.
"Copyright" also means copyright-like laws that apply to other kinds of
works, such as semiconductor masks.
"The Program" refers to any copyrightable work licensed under this
License. Each licensee is addressed as "you". "Licensees" and
"recipients" may be individuals or organizations.
To "modify" a work means to copy from or adapt all or part of the work
in a fashion requiring copyright permission, other than the making of an
exact copy. The resulting work is called a "modified version" of the
earlier work or a work "based on" the earlier work.
A "covered work" means either the unmodified Program or a work based
on the Program.
To "propagate" a work means to do anything with it that, without
permission, would make you directly or secondarily liable for
infringement under applicable copyright law, except executing it on a
computer or modifying a private copy. Propagation includes copying,
distribution (with or without modification), making available to the
public, and in some countries other activities as well.
To "convey" a work means any kind of propagation that enables other
parties to make or receive copies. Mere interaction with a user through
a computer network, with no transfer of a copy, is not conveying.
An interactive user interface displays "Appropriate Legal Notices"
to the extent that it includes a convenient and prominently visible
feature that (1) displays an appropriate copyright notice, and (2)
tells the user that there is no warranty for the work (except to the
extent that warranties are provided), that licensees may convey the
work under this License, and how to view a copy of this License. If
the interface presents a list of user commands or options, such as a
menu, a prominent item in the list meets this criterion.
1. Source Code.
The "source code" for a work means the preferred form of the work
for making modifications to it. "Object code" means any non-source
form of a work.
A "Standard Interface" means an interface that either is an official
standard defined by a recognized standards body, or, in the case of
interfaces specified for a particular programming language, one that
is widely used among developers working in that language.
The "System Libraries" of an executable work include anything, other
than the work as a whole, that (a) is included in the normal form of
packaging a Major Component, but which is not part of that Major
Component, and (b) serves only to enable use of the work with that
Major Component, or to implement a Standard Interface for which an
implementation is available to the public in source code form. A
"Major Component", in this context, means a major essential component
(kernel, window system, and so on) of the specific operating system
(if any) on which the executable work runs, or a compiler used to
produce the work, or an object code interpreter used to run it.
The "Corresponding Source" for a work in object code form means all
the source code needed to generate, install, and (for an executable
work) run the object code and to modify the work, including scripts to
control those activities. However, it does not include the work's
System Libraries, or general-purpose tools or generally available free
programs which are used unmodified in performing those activities but
which are not part of the work. For example, Corresponding Source
includes interface definition files associated with source files for
the work, and the source code for shared libraries and dynamically
linked subprograms that the work is specifically designed to require,
such as by intimate data communication or control flow between those
subprograms and other parts of the work.
The Corresponding Source need not include anything that users
can regenerate automatically from other parts of the Corresponding
Source.
The Corresponding Source for a work in source code form is that
same work.
2. Basic Permissions.
All rights granted under this License are granted for the term of
copyright on the Program, and are irrevocable provided the stated
conditions are met. This License explicitly affirms your unlimited
permission to run the unmodified Program. The output from running a
covered work is covered by this License only if the output, given its
content, constitutes a covered work. This License acknowledges your
rights of fair use or other equivalent, as provided by copyright law.
You may make, run and propagate covered works that you do not
convey, without conditions so long as your license otherwise remains
in force. You may convey covered works to others for the sole purpose
of having them make modifications exclusively for you, or provide you
with facilities for running those works, provided that you comply with
the terms of this License in conveying all material for which you do
not control copyright. Those thus making or running the covered works
for you must do so exclusively on your behalf, under your direction
and control, on terms that prohibit them from making any copies of
your copyrighted material outside their relationship with you.
Conveying under any other circumstances is permitted solely under
the conditions stated below. Sublicensing is not allowed; section 10
makes it unnecessary.
3. Protecting Users' Legal Rights From Anti-Circumvention Law.
No covered work shall be deemed part of an effective technological
measure under any applicable law fulfilling obligations under article
11 of the WIPO copyright treaty adopted on 20 December 1996, or
similar laws prohibiting or restricting circumvention of such
measures.
When you convey a covered work, you waive any legal power to forbid
circumvention of technological measures to the extent such circumvention
is effected by exercising rights under this License with respect to
the covered work, and you disclaim any intention to limit operation or
modification of the work as a means of enforcing, against the work's
users, your or third parties' legal rights to forbid circumvention of
technological measures.
4. Conveying Verbatim Copies.
You may convey verbatim copies of the Program's source code as you
receive it, in any medium, provided that you conspicuously and
appropriately publish on each copy an appropriate copyright notice;
keep intact all notices stating that this License and any
non-permissive terms added in accord with section 7 apply to the code;
keep intact all notices of the absence of any warranty; and give all
recipients a copy of this License along with the Program.
You may charge any price or no price for each copy that you convey,
and you may offer support or warranty protection for a fee.
5. Conveying Modified Source Versions.
You may convey a work based on the Program, or the modifications to
produce it from the Program, in the form of source code under the
terms of section 4, provided that you also meet all of these conditions:
a) The work must carry prominent notices stating that you modified
it, and giving a relevant date.
b) The work must carry prominent notices stating that it is
released under this License and any conditions added under section
7. This requirement modifies the requirement in section 4 to
"keep intact all notices".
c) You must license the entire work, as a whole, under this
License to anyone who comes into possession of a copy. This
License will therefore apply, along with any applicable section 7
additional terms, to the whole of the work, and all its parts,
regardless of how they are packaged. This License gives no
permission to license the work in any other way, but it does not
invalidate such permission if you have separately received it.
d) If the work has interactive user interfaces, each must display
Appropriate Legal Notices; however, if the Program has interactive
interfaces that do not display Appropriate Legal Notices, your
work need not make them do so.
A compilation of a covered work with other separate and independent
works, which are not by their nature extensions of the covered work,
and which are not combined with it such as to form a larger program,
in or on a volume of a storage or distribution medium, is called an
"aggregate" if the compilation and its resulting copyright are not
used to limit the access or legal rights of the compilation's users
beyond what the individual works permit. Inclusion of a covered work
in an aggregate does not cause this License to apply to the other
parts of the aggregate.
6. Conveying Non-Source Forms.
You may convey a covered work in object code form under the terms
of sections 4 and 5, provided that you also convey the
machine-readable Corresponding Source under the terms of this License,
in one of these ways:
a) Convey the object code in, or embodied in, a physical product
(including a physical distribution medium), accompanied by the
Corresponding Source fixed on a durable physical medium
customarily used for software interchange.
b) Convey the object code in, or embodied in, a physical product
(including a physical distribution medium), accompanied by a
written offer, valid for at least three years and valid for as
long as you offer spare parts or customer support for that product
model, to give anyone who possesses the object code either (1) a
copy of the Corresponding Source for all the software in the
product that is covered by this License, on a durable physical
medium customarily used for software interchange, for a price no
more than your reasonable cost of physically performing this
conveying of source, or (2) access to copy the
Corresponding Source from a network server at no charge.
c) Convey individual copies of the object code with a copy of the
written offer to provide the Corresponding Source. This
alternative is allowed only occasionally and noncommercially, and
only if you received the object code with such an offer, in accord
with subsection 6b.
d) Convey the object code by offering access from a designated
place (gratis or for a charge), and offer equivalent access to the
Corresponding Source in the same way through the same place at no
further charge. You need not require recipients to copy the
Corresponding Source along with the object code. If the place to
copy the object code is a network server, the Corresponding Source
may be on a different server (operated by you or a third party)
that supports equivalent copying facilities, provided you maintain
clear directions next to the object code saying where to find the
Corresponding Source. Regardless of what server hosts the
Corresponding Source, you remain obligated to ensure that it is
available for as long as needed to satisfy these requirements.
e) Convey the object code using peer-to-peer transmission, provided
you inform other peers where the object code and Corresponding
Source of the work are being offered to the general public at no
charge under subsection 6d.
A separable portion of the object code, whose source code is excluded
from the Corresponding Source as a System Library, need not be
included in conveying the object code work.
A "User Product" is either (1) a "consumer product", which means any
tangible personal property which is normally used for personal, family,
or household purposes, or (2) anything designed or sold for incorporation
into a dwelling. In determining whether a product is a consumer product,
doubtful cases shall be resolved in favor of coverage. For a particular
product received by a particular user, "normally used" refers to a
typical or common use of that class of product, regardless of the status
of the particular user or of the way in which the particular user
actually uses, or expects or is expected to use, the product. A product
is a consumer product regardless of whether the product has substantial
commercial, industrial or non-consumer uses, unless such uses represent
the only significant mode of use of the product.
"Installation Information" for a User Product means any methods,
procedures, authorization keys, or other information required to install
and execute modified versions of a covered work in that User Product from
a modified version of its Corresponding Source. The information must
suffice to ensure that the continued functioning of the modified object
code is in no case prevented or interfered with solely because
modification has been made.
If you convey an object code work under this section in, or with, or
specifically for use in, a User Product, and the conveying occurs as
part of a transaction in which the right of possession and use of the
User Product is transferred to the recipient in perpetuity or for a
fixed term (regardless of how the transaction is characterized), the
Corresponding Source conveyed under this section must be accompanied
by the Installation Information. But this requirement does not apply
if neither you nor any third party retains the ability to install
modified object code on the User Product (for example, the work has
been installed in ROM).
The requirement to provide Installation Information does not include a
requirement to continue to provide support service, warranty, or updates
for a work that has been modified or installed by the recipient, or for
the User Product in which it has been modified or installed. Access to a
network may be denied when the modification itself materially and
adversely affects the operation of the network or violates the rules and
protocols for communication across the network.
Corresponding Source conveyed, and Installation Information provided,
in accord with this section must be in a format that is publicly
documented (and with an implementation available to the public in
source code form), and must require no special password or key for
unpacking, reading or copying.
7. Additional Terms.
"Additional permissions" are terms that supplement the terms of this
License by making exceptions from one or more of its conditions.
Additional permissions that are applicable to the entire Program shall
be treated as though they were included in this License, to the extent
that they are valid under applicable law. If additional permissions
apply only to part of the Program, that part may be used separately
under those permissions, but the entire Program remains governed by
this License without regard to the additional permissions.
When you convey a copy of a covered work, you may at your option
remove any additional permissions from that copy, or from any part of
it. (Additional permissions may be written to require their own
removal in certain cases when you modify the work.) You may place
additional permissions on material, added by you to a covered work,
for which you have or can give appropriate copyright permission.
Notwithstanding any other provision of this License, for material you
add to a covered work, you may (if authorized by the copyright holders of
that material) supplement the terms of this License with terms:
a) Disclaiming warranty or limiting liability differently from the
terms of sections 15 and 16 of this License; or
b) Requiring preservation of specified reasonable legal notices or
author attributions in that material or in the Appropriate Legal
Notices displayed by works containing it; or
c) Prohibiting misrepresentation of the origin of that material, or
requiring that modified versions of such material be marked in
reasonable ways as different from the original version; or
d) Limiting the use for publicity purposes of names of licensors or
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trade names, trademarks, or service marks; or
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it) with contractual assumptions of liability to the recipient, for
any liability that these contractual assumptions directly impose on
those licensors and authors.
All other non-permissive additional terms are considered "further
restrictions" within the meaning of section 10. If the Program as you
received it, or any part of it, contains a notice stating that it is
governed by this License along with a term that is a further
restriction, you may remove that term. If a license document contains
a further restriction but permits relicensing or conveying under this
License, you may add to a covered work material governed by the terms
of that license document, provided that the further restriction does
not survive such relicensing or conveying.
If you add terms to a covered work in accord with this section, you
must place, in the relevant source files, a statement of the
additional terms that apply to those files, or a notice indicating
where to find the applicable terms.
Additional terms, permissive or non-permissive, may be stated in the
form of a separately written license, or stated as exceptions;
the above requirements apply either way.
8. Termination.
You may not propagate or modify a covered work except as expressly
provided under this License. Any attempt otherwise to propagate or
modify it is void, and will automatically terminate your rights under
this License (including any patent licenses granted under the third
paragraph of section 11).
However, if you cease all violation of this License, then your
license from a particular copyright holder is reinstated (a)
provisionally, unless and until the copyright holder explicitly and
finally terminates your license, and (b) permanently, if the copyright
holder fails to notify you of the violation by some reasonable means
prior to 60 days after the cessation.
Moreover, your license from a particular copyright holder is
reinstated permanently if the copyright holder notifies you of the
violation by some reasonable means, this is the first time you have
received notice of violation of this License (for any work) from that
copyright holder, and you cure the violation prior to 30 days after
your receipt of the notice.
Termination of your rights under this section does not terminate the
licenses of parties who have received copies or rights from you under
this License. If your rights have been terminated and not permanently
reinstated, you do not qualify to receive new licenses for the same
material under section 10.
9. Acceptance Not Required for Having Copies.
You are not required to accept this License in order to receive or
run a copy of the Program. Ancillary propagation of a covered work
occurring solely as a consequence of using peer-to-peer transmission
to receive a copy likewise does not require acceptance. However,
nothing other than this License grants you permission to propagate or
modify any covered work. These actions infringe copyright if you do
not accept this License. Therefore, by modifying or propagating a
covered work, you indicate your acceptance of this License to do so.
10. Automatic Licensing of Downstream Recipients.
Each time you convey a covered work, the recipient automatically
receives a license from the original licensors, to run, modify and
propagate that work, subject to this License. You are not responsible
for enforcing compliance by third parties with this License.
An "entity transaction" is a transaction transferring control of an
organization, or substantially all assets of one, or subdividing an
organization, or merging organizations. If propagation of a covered
work results from an entity transaction, each party to that
transaction who receives a copy of the work also receives whatever
licenses to the work the party's predecessor in interest had or could
give under the previous paragraph, plus a right to possession of the
Corresponding Source of the work from the predecessor in interest, if
the predecessor has it or can get it with reasonable efforts.
You may not impose any further restrictions on the exercise of the
rights granted or affirmed under this License. For example, you may
not impose a license fee, royalty, or other charge for exercise of
rights granted under this License, and you may not initiate litigation
(including a cross-claim or counterclaim in a lawsuit) alleging that
any patent claim is infringed by making, using, selling, offering for
sale, or importing the Program or any portion of it.
11. Patents.
A "contributor" is a copyright holder who authorizes use under this
License of the Program or a work on which the Program is based. The
work thus licensed is called the contributor's "contributor version".
A contributor's "essential patent claims" are all patent claims
owned or controlled by the contributor, whether already acquired or
hereafter acquired, that would be infringed by some manner, permitted
by this License, of making, using, or selling its contributor version,
but do not include claims that would be infringed only as a
consequence of further modification of the contributor version. For
purposes of this definition, "control" includes the right to grant
patent sublicenses in a manner consistent with the requirements of
this License.
Each contributor grants you a non-exclusive, worldwide, royalty-free
patent license under the contributor's essential patent claims, to
make, use, sell, offer for sale, import and otherwise run, modify and
propagate the contents of its contributor version.
In the following three paragraphs, a "patent license" is any express
agreement or commitment, however denominated, not to enforce a patent
(such as an express permission to practice a patent or covenant not to
sue for patent infringement). To "grant" such a patent license to a
party means to make such an agreement or commitment not to enforce a
patent against the party.
If you convey a covered work, knowingly relying on a patent license,
and the Corresponding Source of the work is not available for anyone
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available, or (2) arrange to deprive yourself of the benefit of the
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consistent with the requirements of this License, to extend the patent
license to downstream recipients. "Knowingly relying" means you have
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covered work in a country, or your recipient's use of the covered work
in a country, would infringe one or more identifiable patents in that
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If, pursuant to or in connection with a single transaction or
arrangement, you convey, or propagate by procuring conveyance of, a
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work and works based on it.
A patent license is "discriminatory" if it does not include within
the scope of its coverage, prohibits the exercise of, or is
conditioned on the non-exercise of one or more of the rights that are
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in the business of distributing software, under which you make payment
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conveyed by you (or copies made from those copies), or (b) primarily
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or that patent license was granted, prior to 28 March 2007.
Nothing in this License shall be construed as excluding or limiting
any implied license or other defenses to infringement that may
otherwise be available to you under applicable patent law.
12. No Surrender of Others' Freedom.
If conditions are imposed on you (whether by court order, agreement or
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to collect a royalty for further conveying from those to whom you convey
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License would be to refrain entirely from conveying the Program.
13. Use with the GNU Affero General Public License.
Notwithstanding any other provision of this License, you have
permission to link or combine any covered work with a work licensed
under version 3 of the GNU Affero General Public License into a single
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14. Revised Versions of this License.
The Free Software Foundation may publish revised and/or new versions of
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option of following the terms and conditions either of that numbered
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Foundation. If the Program does not specify a version number of the
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by the Free Software Foundation.
If the Program specifies that a proxy can decide which future
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to choose that version for the Program.
Later license versions may give you additional or different
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15. Disclaimer of Warranty.
THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
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IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
16. Limitation of Liability.
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
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DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
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EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
SUCH DAMAGES.
17. Interpretation of Sections 15 and 16.
If the disclaimer of warranty and limitation of liability provided
above cannot be given local legal effect according to their terms,
reviewing courts shall apply local law that most closely approximates
an absolute waiver of all civil liability in connection with the
Program, unless a warranty or assumption of liability accompanies a
copy of the Program in return for a fee.
END OF TERMS AND CONDITIONS
How to Apply These Terms to Your New Programs
If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
<one line to give the program's name and a brief idea of what it does.>
Copyright (C) <year> <name of author>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
Also add information on how to contact you by electronic and paper mail.
If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:
<program> Copyright (C) <year> <name of author>
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<http://www.gnu.org/licenses/>.
The GNU General Public License does not permit incorporating your program
into proprietary programs. If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
<http://www.gnu.org/philosophy/why-not-lgpl.html>.

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GNU GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
Preamble
The GNU General Public License is a free, copyleft license for
software and other kinds of works.
The licenses for most software and other practical works are designed
to take away your freedom to share and change the works. By contrast,
the GNU General Public License is intended to guarantee your freedom to
share and change all versions of a program--to make sure it remains free
software for all its users. We, the Free Software Foundation, use the
GNU General Public License for most of our software; it applies also to
any other work released this way by its authors. You can apply it to
your programs, too.
When we speak of free software, we are referring to freedom, not
price. Our General Public Licenses are designed to make sure that you
have the freedom to distribute copies of free software (and charge for
them if you wish), that you receive source code or can get it if you
want it, that you can change the software or use pieces of it in new
free programs, and that you know you can do these things.
To protect your rights, we need to prevent others from denying you
these rights or asking you to surrender the rights. Therefore, you have
certain responsibilities if you distribute copies of the software, or if
you modify it: responsibilities to respect the freedom of others.
For example, if you distribute copies of such a program, whether
gratis or for a fee, you must pass on to the recipients the same
freedoms that you received. You must make sure that they, too, receive
or can get the source code. And you must show them these terms so they
know their rights.
Developers that use the GNU GPL protect your rights with two steps:
(1) assert copyright on the software, and (2) offer you this License
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For the developers' and authors' protection, the GPL clearly explains
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authors' sake, the GPL requires that modified versions be marked as
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authors of previous versions.
Some devices are designed to deny users access to install or run
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can do so. This is fundamentally incompatible with the aim of
protecting users' freedom to change the software. The systematic
pattern of such abuse occurs in the area of products for individuals to
use, which is precisely where it is most unacceptable. Therefore, we
have designed this version of the GPL to prohibit the practice for those
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stand ready to extend this provision to those domains in future versions
of the GPL, as needed to protect the freedom of users.
Finally, every program is threatened constantly by software patents.
States should not allow patents to restrict development and use of
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avoid the special danger that patents applied to a free program could
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patents cannot be used to render the program non-free.
The precise terms and conditions for copying, distribution and
modification follow.
TERMS AND CONDITIONS
0. Definitions.
"This License" refers to version 3 of the GNU General Public License.
"Copyright" also means copyright-like laws that apply to other kinds of
works, such as semiconductor masks.
"The Program" refers to any copyrightable work licensed under this
License. Each licensee is addressed as "you". "Licensees" and
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To "modify" a work means to copy from or adapt all or part of the work
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A "covered work" means either the unmodified Program or a work based
on the Program.
To "propagate" a work means to do anything with it that, without
permission, would make you directly or secondarily liable for
infringement under applicable copyright law, except executing it on a
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distribution (with or without modification), making available to the
public, and in some countries other activities as well.
To "convey" a work means any kind of propagation that enables other
parties to make or receive copies. Mere interaction with a user through
a computer network, with no transfer of a copy, is not conveying.
An interactive user interface displays "Appropriate Legal Notices"
to the extent that it includes a convenient and prominently visible
feature that (1) displays an appropriate copyright notice, and (2)
tells the user that there is no warranty for the work (except to the
extent that warranties are provided), that licensees may convey the
work under this License, and how to view a copy of this License. If
the interface presents a list of user commands or options, such as a
menu, a prominent item in the list meets this criterion.
1. Source Code.
The "source code" for a work means the preferred form of the work
for making modifications to it. "Object code" means any non-source
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A "Standard Interface" means an interface that either is an official
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The "System Libraries" of an executable work include anything, other
than the work as a whole, that (a) is included in the normal form of
packaging a Major Component, but which is not part of that Major
Component, and (b) serves only to enable use of the work with that
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implementation is available to the public in source code form. A
"Major Component", in this context, means a major essential component
(kernel, window system, and so on) of the specific operating system
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produce the work, or an object code interpreter used to run it.
The "Corresponding Source" for a work in object code form means all
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work) run the object code and to modify the work, including scripts to
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programs which are used unmodified in performing those activities but
which are not part of the work. For example, Corresponding Source
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such as by intimate data communication or control flow between those
subprograms and other parts of the work.
The Corresponding Source need not include anything that users
can regenerate automatically from other parts of the Corresponding
Source.
The Corresponding Source for a work in source code form is that
same work.
2. Basic Permissions.
All rights granted under this License are granted for the term of
copyright on the Program, and are irrevocable provided the stated
conditions are met. This License explicitly affirms your unlimited
permission to run the unmodified Program. The output from running a
covered work is covered by this License only if the output, given its
content, constitutes a covered work. This License acknowledges your
rights of fair use or other equivalent, as provided by copyright law.
You may make, run and propagate covered works that you do not
convey, without conditions so long as your license otherwise remains
in force. You may convey covered works to others for the sole purpose
of having them make modifications exclusively for you, or provide you
with facilities for running those works, provided that you comply with
the terms of this License in conveying all material for which you do
not control copyright. Those thus making or running the covered works
for you must do so exclusively on your behalf, under your direction
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Conveying under any other circumstances is permitted solely under
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3. Protecting Users' Legal Rights From Anti-Circumvention Law.
No covered work shall be deemed part of an effective technological
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11 of the WIPO copyright treaty adopted on 20 December 1996, or
similar laws prohibiting or restricting circumvention of such
measures.
When you convey a covered work, you waive any legal power to forbid
circumvention of technological measures to the extent such circumvention
is effected by exercising rights under this License with respect to
the covered work, and you disclaim any intention to limit operation or
modification of the work as a means of enforcing, against the work's
users, your or third parties' legal rights to forbid circumvention of
technological measures.
4. Conveying Verbatim Copies.
You may convey verbatim copies of the Program's source code as you
receive it, in any medium, provided that you conspicuously and
appropriately publish on each copy an appropriate copyright notice;
keep intact all notices stating that this License and any
non-permissive terms added in accord with section 7 apply to the code;
keep intact all notices of the absence of any warranty; and give all
recipients a copy of this License along with the Program.
You may charge any price or no price for each copy that you convey,
and you may offer support or warranty protection for a fee.
5. Conveying Modified Source Versions.
You may convey a work based on the Program, or the modifications to
produce it from the Program, in the form of source code under the
terms of section 4, provided that you also meet all of these conditions:
a) The work must carry prominent notices stating that you modified
it, and giving a relevant date.
b) The work must carry prominent notices stating that it is
released under this License and any conditions added under section
7. This requirement modifies the requirement in section 4 to
"keep intact all notices".
c) You must license the entire work, as a whole, under this
License to anyone who comes into possession of a copy. This
License will therefore apply, along with any applicable section 7
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work need not make them do so.
A compilation of a covered work with other separate and independent
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in or on a volume of a storage or distribution medium, is called an
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used to limit the access or legal rights of the compilation's users
beyond what the individual works permit. Inclusion of a covered work
in an aggregate does not cause this License to apply to the other
parts of the aggregate.
6. Conveying Non-Source Forms.
You may convey a covered work in object code form under the terms
of sections 4 and 5, provided that you also convey the
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(including a physical distribution medium), accompanied by the
Corresponding Source fixed on a durable physical medium
customarily used for software interchange.
b) Convey the object code in, or embodied in, a physical product
(including a physical distribution medium), accompanied by a
written offer, valid for at least three years and valid for as
long as you offer spare parts or customer support for that product
model, to give anyone who possesses the object code either (1) a
copy of the Corresponding Source for all the software in the
product that is covered by this License, on a durable physical
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c) Convey individual copies of the object code with a copy of the
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d) Convey the object code by offering access from a designated
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A separable portion of the object code, whose source code is excluded
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A "User Product" is either (1) a "consumer product", which means any
tangible personal property which is normally used for personal, family,
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"Installation Information" for a User Product means any methods,
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If you convey an object code work under this section in, or with, or
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if neither you nor any third party retains the ability to install
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The requirement to provide Installation Information does not include a
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Corresponding Source conveyed, and Installation Information provided,
in accord with this section must be in a format that is publicly
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unpacking, reading or copying.
7. Additional Terms.
"Additional permissions" are terms that supplement the terms of this
License by making exceptions from one or more of its conditions.
Additional permissions that are applicable to the entire Program shall
be treated as though they were included in this License, to the extent
that they are valid under applicable law. If additional permissions
apply only to part of the Program, that part may be used separately
under those permissions, but the entire Program remains governed by
this License without regard to the additional permissions.
When you convey a copy of a covered work, you may at your option
remove any additional permissions from that copy, or from any part of
it. (Additional permissions may be written to require their own
removal in certain cases when you modify the work.) You may place
additional permissions on material, added by you to a covered work,
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Notwithstanding any other provision of this License, for material you
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a) Disclaiming warranty or limiting liability differently from the
terms of sections 15 and 16 of this License; or
b) Requiring preservation of specified reasonable legal notices or
author attributions in that material or in the Appropriate Legal
Notices displayed by works containing it; or
c) Prohibiting misrepresentation of the origin of that material, or
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All other non-permissive additional terms are considered "further
restrictions" within the meaning of section 10. If the Program as you
received it, or any part of it, contains a notice stating that it is
governed by this License along with a term that is a further
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a further restriction but permits relicensing or conveying under this
License, you may add to a covered work material governed by the terms
of that license document, provided that the further restriction does
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If you add terms to a covered work in accord with this section, you
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where to find the applicable terms.
Additional terms, permissive or non-permissive, may be stated in the
form of a separately written license, or stated as exceptions;
the above requirements apply either way.
8. Termination.
You may not propagate or modify a covered work except as expressly
provided under this License. Any attempt otherwise to propagate or
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this License (including any patent licenses granted under the third
paragraph of section 11).
However, if you cease all violation of this License, then your
license from a particular copyright holder is reinstated (a)
provisionally, unless and until the copyright holder explicitly and
finally terminates your license, and (b) permanently, if the copyright
holder fails to notify you of the violation by some reasonable means
prior to 60 days after the cessation.
Moreover, your license from a particular copyright holder is
reinstated permanently if the copyright holder notifies you of the
violation by some reasonable means, this is the first time you have
received notice of violation of this License (for any work) from that
copyright holder, and you cure the violation prior to 30 days after
your receipt of the notice.
Termination of your rights under this section does not terminate the
licenses of parties who have received copies or rights from you under
this License. If your rights have been terminated and not permanently
reinstated, you do not qualify to receive new licenses for the same
material under section 10.
9. Acceptance Not Required for Having Copies.
You are not required to accept this License in order to receive or
run a copy of the Program. Ancillary propagation of a covered work
occurring solely as a consequence of using peer-to-peer transmission
to receive a copy likewise does not require acceptance. However,
nothing other than this License grants you permission to propagate or
modify any covered work. These actions infringe copyright if you do
not accept this License. Therefore, by modifying or propagating a
covered work, you indicate your acceptance of this License to do so.
10. Automatic Licensing of Downstream Recipients.
Each time you convey a covered work, the recipient automatically
receives a license from the original licensors, to run, modify and
propagate that work, subject to this License. You are not responsible
for enforcing compliance by third parties with this License.
An "entity transaction" is a transaction transferring control of an
organization, or substantially all assets of one, or subdividing an
organization, or merging organizations. If propagation of a covered
work results from an entity transaction, each party to that
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the predecessor has it or can get it with reasonable efforts.
You may not impose any further restrictions on the exercise of the
rights granted or affirmed under this License. For example, you may
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rights granted under this License, and you may not initiate litigation
(including a cross-claim or counterclaim in a lawsuit) alleging that
any patent claim is infringed by making, using, selling, offering for
sale, or importing the Program or any portion of it.
11. Patents.
A "contributor" is a copyright holder who authorizes use under this
License of the Program or a work on which the Program is based. The
work thus licensed is called the contributor's "contributor version".
A contributor's "essential patent claims" are all patent claims
owned or controlled by the contributor, whether already acquired or
hereafter acquired, that would be infringed by some manner, permitted
by this License, of making, using, or selling its contributor version,
but do not include claims that would be infringed only as a
consequence of further modification of the contributor version. For
purposes of this definition, "control" includes the right to grant
patent sublicenses in a manner consistent with the requirements of
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Each contributor grants you a non-exclusive, worldwide, royalty-free
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make, use, sell, offer for sale, import and otherwise run, modify and
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In the following three paragraphs, a "patent license" is any express
agreement or commitment, however denominated, not to enforce a patent
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sue for patent infringement). To "grant" such a patent license to a
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If you convey a covered work, knowingly relying on a patent license,
and the Corresponding Source of the work is not available for anyone
to copy, free of charge and under the terms of this License, through a
publicly available network server or other readily accessible means,
then you must either (1) cause the Corresponding Source to be so
available, or (2) arrange to deprive yourself of the benefit of the
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GNU LESSER GENERAL PUBLIC LICENSE
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END OF TERMS AND CONDITIONS
How to Apply These Terms to Your New Libraries
If you develop a new library, and you want it to be of the greatest possible use to the public, we recommend making it free software that everyone can redistribute and change. You can do so by permitting redistribution under these terms (or, alternatively, under the terms of the ordinary General Public License).
To apply these terms, attach the following notices to the library. It is safest to attach them to the start of each source file to most effectively convey the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found.
one line to give the library's name and an idea of what it does.
Copyright (C) year name of author
This library is free software; you can redistribute it and/or
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This library is distributed in the hope that it will be useful,
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You should have received a copy of the GNU Lesser General Public
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Also add information on how to contact you by electronic and paper mail.
You should also get your employer (if you work as a programmer) or your school, if any, to sign a "copyright disclaimer" for the library, if necessary. Here is a sample; alter the names:
Yoyodyne, Inc., hereby disclaims all copyright interest in
the library `Frob' (a library for tweaking knobs) written
by James Random Hacker.
signature of Ty Coon, 1 April 1990
Ty Coon, President of Vice
That's all there is to it!

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GNU LESSER GENERAL PUBLIC LICENSE
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a) Give prominent notice with each copy of the object code that the
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on the Library, uncombined with any other library facilities,
conveyed under the terms of this License.
b) Give prominent notice with the combined library that part of it
is a work based on the Library, and explaining where to find the
accompanying uncombined form of the same work.
6. Revised Versions of the GNU Lesser General Public License.
The Free Software Foundation may publish revised and/or new versions
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versions will be similar in spirit to the present version, but may
differ in detail to address new problems or concerns.
Each version is given a distinguishing version number. If the
Library as you received it specifies that a certain numbered version
of the GNU Lesser General Public License "or any later version"
applies to it, you have the option of following the terms and
conditions either of that published version or of any later version
published by the Free Software Foundation. If the Library as you
received it does not specify a version number of the GNU Lesser
General Public License, you may choose any version of the GNU Lesser
General Public License ever published by the Free Software Foundation.
If the Library as you received it specifies that a proxy can decide
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165
LICENSES/LGPL-3.0-or-later.txt Normal file
View File

@ -0,0 +1,165 @@
GNU LESSER GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
This version of the GNU Lesser General Public License incorporates
the terms and conditions of version 3 of the GNU General Public
License, supplemented by the additional permissions listed below.
0. Additional Definitions.
As used herein, "this License" refers to version 3 of the GNU Lesser
General Public License, and the "GNU GPL" refers to version 3 of the GNU
General Public License.
"The Library" refers to a covered work governed by this License,
other than an Application or a Combined Work as defined below.
An "Application" is any work that makes use of an interface provided
by the Library, but which is not otherwise based on the Library.
Defining a subclass of a class defined by the Library is deemed a mode
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A "Combined Work" is a work produced by combining or linking an
Application with the Library. The particular version of the Library
with which the Combined Work was made is also called the "Linked
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The "Minimal Corresponding Source" for a Combined Work means the
Corresponding Source for the Combined Work, excluding any source code
for portions of the Combined Work that, considered in isolation, are
based on the Application, and not on the Linked Version.
The "Corresponding Application Code" for a Combined Work means the
object code and/or source code for the Application, including any data
and utility programs needed for reproducing the Combined Work from the
Application, but excluding the System Libraries of the Combined Work.
1. Exception to Section 3 of the GNU GPL.
You may convey a covered work under sections 3 and 4 of this License
without being bound by section 3 of the GNU GPL.
2. Conveying Modified Versions.
If you modify a copy of the Library, and, in your modifications, a
facility refers to a function or data to be supplied by an Application
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a) under this License, provided that you make a good faith effort to
ensure that, in the event an Application does not supply the
function or data, the facility still operates, and performs
whatever part of its purpose remains meaningful, or
b) under the GNU GPL, with none of the additional permissions of
this License applicable to that copy.
3. Object Code Incorporating Material from Library Header Files.
The object code form of an Application may incorporate material from
a header file that is part of the Library. You may convey such object
code under terms of your choice, provided that, if the incorporated
material is not limited to numerical parameters, data structure
layouts and accessors, or small macros, inline functions and templates
(ten or fewer lines in length), you do both of the following:
a) Give prominent notice with each copy of the object code that the
Library is used in it and that the Library and its use are
covered by this License.
b) Accompany the object code with a copy of the GNU GPL and this license
document.
4. Combined Works.
You may convey a Combined Work under terms of your choice that,
taken together, effectively do not restrict modification of the
portions of the Library contained in the Combined Work and reverse
engineering for debugging such modifications, if you also do each of
the following:
a) Give prominent notice with each copy of the Combined Work that
the Library is used in it and that the Library and its use are
covered by this License.
b) Accompany the Combined Work with a copy of the GNU GPL and this license
document.
c) For a Combined Work that displays copyright notices during
execution, include the copyright notice for the Library among
these notices, as well as a reference directing the user to the
copies of the GNU GPL and this license document.
d) Do one of the following:
0) Convey the Minimal Corresponding Source under the terms of this
License, and the Corresponding Application Code in a form
suitable for, and under terms that permit, the user to
recombine or relink the Application with a modified version of
the Linked Version to produce a modified Combined Work, in the
manner specified by section 6 of the GNU GPL for conveying
Corresponding Source.
1) Use a suitable shared library mechanism for linking with the
Library. A suitable mechanism is one that (a) uses at run time
a copy of the Library already present on the user's computer
system, and (b) will operate properly with a modified version
of the Library that is interface-compatible with the Linked
Version.
e) Provide Installation Information, but only if you would otherwise
be required to provide such information under section 6 of the
GNU GPL, and only to the extent that such information is
necessary to install and execute a modified version of the
Combined Work produced by recombining or relinking the
Application with a modified version of the Linked Version. (If
you use option 4d0, the Installation Information must accompany
the Minimal Corresponding Source and Corresponding Application
Code. If you use option 4d1, you must provide the Installation
Information in the manner specified by section 6 of the GNU GPL
for conveying Corresponding Source.)
5. Combined Libraries.
You may place library facilities that are a work based on the
Library side by side in a single library together with other library
facilities that are not Applications and are not covered by this
License, and convey such a combined library under terms of your
choice, if you do both of the following:
a) Accompany the combined library with a copy of the same work based
on the Library, uncombined with any other library facilities,
conveyed under the terms of this License.
b) Give prominent notice with the combined library that part of it
is a work based on the Library, and explaining where to find the
accompanying uncombined form of the same work.
6. Revised Versions of the GNU Lesser General Public License.
The Free Software Foundation may publish revised and/or new versions
of the GNU Lesser General Public License from time to time. Such new
versions will be similar in spirit to the present version, but may
differ in detail to address new problems or concerns.
Each version is given a distinguishing version number. If the
Library as you received it specifies that a certain numbered version
of the GNU Lesser General Public License "or any later version"
applies to it, you have the option of following the terms and
conditions either of that published version or of any later version
published by the Free Software Foundation. If the Library as you
received it does not specify a version number of the GNU Lesser
General Public License, you may choose any version of the GNU Lesser
General Public License ever published by the Free Software Foundation.
If the Library as you received it specifies that a proxy can decide
whether future versions of the GNU Lesser General Public License shall
apply, that proxy's public statement of acceptance of any version is
permanent authorization for you to choose that version for the
Library.

6
LICENSES/LicenseRef-Commercial.txt Normal file
View File

@ -0,0 +1,6 @@
The CGAL software consists of several components, each of which is licensed under
an open source license. If the open source license is not suitable to your
needs, it is possible to obtain commercial licenses
from GeometryFactory (www.geometryfactory.com) for each component of CGAL.
Get more information at "contact@geometryfactory.com".

19
LICENSES/LicenseRef-RFL.txt Normal file
View File

@ -0,0 +1,19 @@
Copyright (c) 2014 Stefan Walk
Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
of the Software, and to permit persons to whom the Software is furnished to do
so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

17
LICENSES/MIT.txt Normal file
View File

@ -0,0 +1,17 @@
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.

2
Linear_cell_complex/benchmark/Linear_cell_complex_2/surface_mesh/Surface_mesh.h
View File

@ -1103,7 +1103,7 @@ public: //--------------------------------------------------- property handling
{
return Halfedge_property<T>(hprops_.add<T>(name, t));
}
/** add a edge property of type \c T with name \c name and default value \c t.
/** add an edge property of type \c T with name \c name and default value \c t.
fails if a property named \c name exists already, since the name has to be unique.
in this case it returns an invalid property */
template <class T> Edge_property<T> add_edge_property(const std::string& name, const T t=T())

1
Linear_cell_complex/test/Linear_cell_complex/CMakeLists.txt
View File

@ -14,6 +14,7 @@ create_single_source_cgal_program(Linear_cell_complex_2_test.cpp ${hfiles})
create_single_source_cgal_program(Linear_cell_complex_3_test.cpp ${hfiles})
create_single_source_cgal_program(Linear_cell_complex_4_test.cpp ${hfiles})
create_single_source_cgal_program(Linear_cell_complex_copy_test.cpp ${hfiles})
create_single_source_cgal_program(LCC_3_incremental_builder_test.cpp ${hfiles})
# Same targets, defining USE_COMPACT_CONTAINER_WITH_INDEX to test index version
add_executable(Linear_cell_complex_2_test_index Linear_cell_complex_2_test.cpp ${hfiles})

4
Maintenance/public_release/scripts/prepare_release
View File

@ -42,12 +42,12 @@ printf "Copy documentation to doc_html/ and doc_html_online/...\n"
[ -d "/srv/CGAL/www/${PUBLIC_RELEASE_NAME#CGAL-}/Manual" ] || mkdir -p "/srv/CGAL/www/${PUBLIC_RELEASE_NAME#CGAL-}/Manual"
cp "$PUBLIC_RELEASE_DIR"/*(.) "${RELEASE_CANDIDATES_DIR}/$PUBLIC_RELEASE_NAME"
files=("$MANUAL_TESTS_DIR/$INTERNAL_RELEASE"/output2/*)
files=("$MANUAL_TESTS_DIR/$INTERNAL_RELEASE"/output1/*)
if ((${#files[@]} == 0)); then
printf "ERROR: documentation files are missing\n"
error_code=1
else
rsync -a --exclude xml "$MANUAL_TESTS_DIR/$INTERNAL_RELEASE"/output2/* "$DEST_DIR/doc_html/"
rsync -a --exclude xml "$MANUAL_TESTS_DIR/$INTERNAL_RELEASE"/output1/* "$DEST_DIR/doc_html/"
pushd "$DEST_DIR/doc_html/Manual/search"
for i in g n c s i; do sed -i "s/..\/BGL$i/..\/BGL\/$i/g" *; done
popd

2
Matrix_search/doc/Matrix_search/CGAL/sorted_matrix_search.h
View File

@ -52,7 +52,7 @@ true.
The implementation uses an algorithm by
Frederickson and Johnson\cgalCite{fj-fkppc-83}, \cgalCite{fj-gsrsm-84} and runs in
\f$ \mathcal{O}(n \cdot k + f \cdot \log (n \cdot k))\f$, where \f$ n\f$ is
\cgalBigO{n \cdot k + f \cdot \log (n \cdot k)}, where \f$ n\f$ is
the number of input matrices, \f$ k\f$ denotes the maximal dimension of
any input matrix and \f$ f\f$ the time needed for one feasibility test.

3
Mesh_3/examples/Mesh_3/CMakeLists.txt
View File

@ -49,6 +49,9 @@ target_link_libraries(mesh_hybrid_mesh_domain PUBLIC CGAL::Eigen3_support)
create_single_source_cgal_program("mesh_implicit_sphere.cpp")
target_link_libraries(mesh_implicit_sphere PUBLIC CGAL::Eigen3_support)
create_single_source_cgal_program("mesh_implicit_ellipsoid.cpp")
target_link_libraries(mesh_implicit_ellipsoid PUBLIC CGAL::Eigen3_support)
create_single_source_cgal_program("mesh_implicit_sphere_variable_size.cpp")
target_link_libraries(mesh_implicit_sphere_variable_size PUBLIC CGAL::Eigen3_support)

303
Mesh_3/test/Mesh_3/implicit_functions.cpp
View File

@ -1,303 +0,0 @@
///////////////// Code for functions of famous surfaces /////////////////
// Sphere (r=1)
double sphere_function (double x, double y, double z) {
double x2=x*x, y2=y*y, z2=z*z;
return x2+y2+z2-1;
}
// Ellipsoid (r=1)
double ellipsoid_function (double x, double y, double z) {
double x2=x*x, y2=y*y, z2=z*z;
return x2+2*y2+4*z2-1;
}
// Torus (r=2)
double torus_function (double x, double y, double z) {
double x2=x*x, y2=y*y, z2=z*z;
double x4=x2*x2, y4=y2*y2, z4=z2*z2;
return x4 + y4 + z4 + 2 *x2* y2 + 2*
x2*z2 + 2*y2* z2 - 5 *x2 + 4* y2 - 5*z2+4;
}
// "Chair" (r=6)
double chair_function (double x, double y, double z) {
double x2=x*x, y2=y*y, z2=z*z;
double x4=x2*x2, y4=y2*y2, z4=z2*z2;
return x4-1.2*x2*y2+3.6*x2*z2-7.50*x2+y4+3.6*y2*z2-7.50*y2+.2*z4-7.50*z2+64.0625-16.0*z*y2+16.0*x2*z;
}
// "Tanglecube" (r=4)
double tanglecube_function (double x, double y, double z) {
double x2=x*x, y2=y*y, z2=z*z;
double x4=x2*x2, y4=y2*y2, z4=z2*z2;
return x4 - 5*x2 + y4 - 5*y2 + z4 - 5*z2 + 11.8;
}
double cube_function (double x, double y, double z){
if( x < 1 && -x < 1 &&
y < 1 && -y < 1 &&
z < 1 && -z < 1 )
return -1.;
return 1.;
}
// Barth's octic surface (degree 8)
double octic_function (double x, double y, double z) { // r=2
double x2=x*x, y2=y*y, z2=z*z;
double x4=x2*x2, y4=y2*y2, z4=z2*z2;
double x6=x4*x2, y6=y4*y2, z6=z4*z2;
double x8=x4*x4, y8=y4*y4, z8=z4*z4;
return 43.30495169 *x2* y2 + 43.30495169 *x2* z2 + 43.30495169 *y2 * z2 + 44.36067980 *x6* y2 + 44.36067980* x6 * z2 + 66.54101970* x4* y4 + 66.54101970* x4 * z4 + 44.36067980 *x2 * y6 - 11.70820393* x2 - 11.70820393* y2 - 11.70820393* z2 + 37.65247585 *x4 + 37.65247585 *y4 + 37.65247585* z4 + 11.09016995* x8 + 11.09016995 *y8 + 11.09016995* z8 + 133.0820394 *x2* y4* z2 + 133.0820394 *x2 * y2 * z4 + 44.36067980* x2 * z6 + 44.36067980 *y6 * z2 + 66.54101970 *y4 * z4 + 44.36067980 *y2 * z6 + 133.0820394* x4* y2 * z2 - 91.95742756 *x4 * y2 - 91.95742756 *x4 *z2 - 91.95742756* x2 * y4 - 91.95742756 *x2 *z4 - 91.95742756* y4 * z2 - 183.9148551* x2 *y2 *z2 - 30.65247585 *x6 - 30.65247585* y6 - 91.95742756 *y2 * z4 - 30.65247585* z6 + 1.618033988;
}
// "Heart"
double heart_function (double x, double y, double z) { // radius = 2
return (2*x*x+y*y+z*z-1)*(2*x*x+y*y+z*z-1)*(2*x*x+y*y+z*z-1) - (0.1*x*x+y*y)*z*z*z;
}
// Klein's bottle
double klein_function (double x, double y, double z) { // radius = 4
return (x*x+y*y+z*z+2*y-1)*((x*x+y*y+z*z-2*y-1)*(x*x+y*y+z*z-2*y-1)-8*z*z)+16*x*z*(x*x+y*y+z*z-2*y-1);
}
// Ring
double ring_function (double x, double y, double z) { // radius = ?
double e=0.1;
double f1 = x*x+y*y+z*z-1;
double f2 = x;
f1 = f1*f1-e*e;
f2 = f2*f2-e*e;
if (f1 < 0 && f2 < 0)
return -1.;
else if (f1 > 0 || f2 > 0)
return 1.;
else
return 0.;
}
// False knot
double false_knot_function (double x, double y, double z) { // radius = 1
double d=1.2, e=0.1;
double f1 = x*(x*x-z*z)-2*x*z*z-y*y+d*d-x*x-z*z-y*y;
double m2 = z*(x*x-z*z)+2*x*x*z;
double f2 = 4*y*y*(d*d-x*x-z*z-y*y) - m2*m2;
f1 = f1*f1-e*e;
f2 = f2*f2-e*e;
if (f1 < 0 && f2 < 0)
return -1.;
else if (f1 > 0 || f2 > 0)
return 1.;
else
return 0.;
}
// Knot 1
void puiss(double& x, double& y, int n) {
double xx = 1, yy = 0;
while(n>0) {
if (n&1) {
double xxx = xx, yyy = yy;
xx = xxx*x - yyy*y;
yy = xxx*y + yyy*x;
}
double xxx = x, yyy = y;
x=xxx*xxx-yyy*yyy;
y=2*xxx*yyy;
n/=2;
}
x = xx;
y = yy;
}
double knot1_function (double a, double b, double c) { // radius = 4
double e=0.1;
double x, y, z, t, den;
den=1+a*a+b*b+c*c;
x=2*a/den;
y=2*b/den;
z=2*c/den;
t=(1-a*a-b*b-c*c)/den;
double x3=x, y3=y, z2=z, t2=t;
puiss(x3,y3,3);
puiss(z2,t2,2);
double f1 = z2-x3;
double f2 = t2-y3;
f1 = f1*f1;
f2 = f2*f2;
e=e*e/(den-1);
if (f1+f2-e < 0)
return -1.;
else if (f1+f2-e > 0)
return 1.;
else
return 0.;
}
/*
double knot1_function (double x, double y, double z) { // radius = 4
double e=0.1;
double c1, c2, c3, c4, den;
den=1+x*x+y*y+z*z;
c1=2*x/den;
c2=2*y/den;
c3=2*z/den;
c4=(1-x*x-y*y-z*z)/den;
double f1 = c1*(c1*c1-c2*c2)-2*c1*c2*c2-c3*c3+c4*c4;
double f2 = c2*(c1*c1-c2*c2)+2*c1*c1*c2-2*c3*c4;
f1 = f1*f1;
f2 = f2*f2;
e=e*e/(den-1);
if (f1+f2-e < 0)
return -1.;
else if (f1+f2-e > 0)
return 1.;
else
return 0.;
}
*/
double knot1_surf1_function (double x, double y, double z) { // radius = 4
double c1, c2, c3, c4, den;
den=1+x*x+y*y+z*z;
c1=2*x/den;
c2=2*y/den;
c3=2*z/den;
c4=(1-x*x-y*y-z*z)/den;
return c1*(c1*c1-c2*c2)-2*c1*c2*c2-c3*c3+c4*c4;
}
double knot1_surf2_function (double x, double y, double z) { // radius = 4
double c1, c2, c3, c4, den;
den=1+x*x+y*y+z*z;
c1=2*x/den;
c2=2*y/den;
c3=2*z/den;
c4=(1-x*x-y*y-z*z)/den;
return c2*(c1*c1-c2*c2)+2*c1*c1*c2-2*c3*c4;
}
// Knot 2
double knot2_function (double a, double b, double c) { // radius = 4
double e=0.025;
double x, y, z, t, den;
den=1+a*a+b*b+c*c;
x=2*a/den;
y=2*b/den;
z=2*c/den;
t=(1-a*a-b*b-c*c)/den;
double x7=x, y7=y, x13=x, y13=y;
puiss(x7,y7,7);
puiss(x13,y13,13);
double z3=z, t3=t;
puiss(z3,t3,3);
double f1t = (z3-x7)*(z3-x7+100*x13) - (t3-y7)*(t3-y7+100*y13);
double f2t = (z3-x7)*(t3-y7+100*y13) + (t3-y7)*(z3-x7+100*x13);
double f1 = f1t*(z3-x7-100*x13) - f2t*(t3-y7-100*y13);
double f2 = f1t*(t3-y7-100*y13) + f2t*(z3-x7-100*x13);
f1 = f1*f1;
f2 = f2*f2;
e=e*e/(den-1);
if (f1+f2-e < 0)
return -1.;
else if (f1+f2-e > 0)
return 1.;
else
return 0.;
}
// Knot 3
double knot3_function (double a, double b, double c) { // radius = 4
double e=0.025;
double x, y, z, t, den;
den=1+a*a+b*b+c*c;
x=2*a/den;
y=2*b/den;
z=2*c/den;
t=(1-a*a-b*b-c*c)/den;
double x19=x, y19=y, z17=z, t17=t;
puiss(x19,y19,19);
puiss(z17,t17,17);
double f1 = z17-x19;
double f2 = t17-y19;
f1 = f1*f1;
f2 = f2*f2;
e=e*e/(den-1);
if (f1+f2-e < 0)
return -1.;
else if (f1+f2-e > 0)
return 1.;
else
return 0.;
}

36
Mesh_3/test/Mesh_3/implicit_functions.h
View File

@ -1,36 +0,0 @@
///////////////// Definitions of several famous surfaces /////////////////
double sphere_function (double, double, double); // (c=(0,0,0), r=1)
double ellipsoid_function (double, double, double); // (c=(0,0,0), r=1)
double torus_function (double, double, double); // (c=(0,0,0), r=2)
double chair_function (double, double, double); // (c=(0,0,0), r=6)
double tanglecube_function (double, double, double); // (c=(0,0,0), r=4)
double octic_function (double, double, double); // (c=(0,0,0), r=2)
double heart_function (double, double, double); // (c=(0,0,0), r=2)
double klein_function (double, double, double); // (c=(0,0,0), r=4)
double ring_function (double, double, double); // (c=(0,0,0), r=?)
double false_knot_function (double, double, double); // (c=(0,0,0), r=1)
double knot1_function (double, double, double); // (c=(0,0,0), r=4)
double knot2_function (double, double, double); // (c=(0,0,0), r=4)
double knot3_function (double, double, double); // (c=(0,0,0), r=4)
double cube_function (double, double, double); // (c=(0,0,0), r=2)
template <int Sq_radius>
double sphere_function (double x, double y, double z) // (c=(0,0,0), r=Sq_radius)
{
double x2=x*x, y2=y*y, z2=z*z;
return (x2+y2+z2)/Sq_radius - 1;
}
template <typename FT, typename P>
class FT_to_point_function_wrapper : public CGAL::cpp98::unary_function<P, FT>
{
typedef FT (*Implicit_function)(FT, FT, FT);
Implicit_function function;
public:
typedef P Point;
FT_to_point_function_wrapper(Implicit_function f) : function(f) {}
FT operator()(Point p) const { return function(p.x(), p.y(), p.z()); }
};

8
Minkowski_sum_2/doc/Minkowski_sum_2/CGAL/Polygon_convex_decomposition_2.h
View File

@ -5,8 +5,8 @@ namespace CGAL {
The `Greene_convex_decomposition_2` class implements the approximation algorithm of
Greene for the decomposition of an input polygon into convex
sub-polygons \cgalCite{g-dpcp-83}. This algorithm takes \f$ O(n \log n)\f$
time and \f$ O(n)\f$ space, where \f$ n\f$ is the size of the input polygon,
sub-polygons \cgalCite{g-dpcp-83}. This algorithm takes \cgalBigO{n \log n}
time and \cgalBigO{n} space, where \f$ n\f$ is the size of the input polygon,
and outputs a decomposition whose size is guaranteed to be no more
than four times the size of the optimal decomposition.
@ -38,7 +38,7 @@ and Mehlhorn for decomposing a polygon into convex
sub-polygons \cgalCite{hm-ftsp-83}. This algorithm constructs a
triangulation of the input polygon and proceeds by removing
unnecessary triangulation edges. Given the triangulation, the
algorithm requires \f$ O(n)\f$ time and space to construct a convex
algorithm requires \cgalBigO{n} time and space to construct a convex
decomposition (where \f$ n\f$ is the size of the input polygon), whose
size is guaranteed to be no more than four times the size of the
optimal decomposition.
@ -69,7 +69,7 @@ namespace CGAL {
The `Optimal_convex_decomposition_2` class provides an implementation of Greene's
dynamic programming algorithm for optimal decomposition of a
polygon into convex sub-polygons \cgalCite{g-dpcp-83}. Note that
this algorithm requires \f$ O(n^4)\f$ time and \f$ O(n^3)\f$ space in
this algorithm requires \cgalBigO{n^4} time and \cgalBigO{n^3} space in
the worst case, where \f$ n\f$ is the size of the input polygon.

4
Minkowski_sum_2/doc/Minkowski_sum_2/CGAL/Polygon_vertical_decomposition_2.h
View File

@ -8,8 +8,8 @@ decomposition of a polygon or a polygon with holes into pseudo trapezoids
utilizing the CGAL::decompose() free function of the
\ref chapterArrangement_on_surface_2 "2D Arrangements" package.
The algorithm operates in \f$ O(n \log n)\f$ time and takes
\f$ O(n)\f$ space at the worst case, where \f$ n\f$ is the
The algorithm operates in \cgalBigO{n \log n} time and takes
\cgalBigO{n} space at the worst case, where \f$ n\f$ is the
size of the input polygon.
\cgalModels `PolygonWithHolesConvexDecomposition_2`

2
Minkowski_sum_2/doc/Minkowski_sum_2/CGAL/Small_side_angle_bisector_decomposition_2.h
View File

@ -12,7 +12,7 @@ connect two reflex vertices with an edge. When this is not possible any
more, it eliminates the reflex vertices one by one by connecting them
to other convex vertices, such that the new edge best approximates
the angle bisector of the reflex vertex. The algorithm operates in
\f$ O(n^2)\f$ time and takes \f$ O(n)\f$ space at the worst case, where
\cgalBigO{n^2} time and takes \cgalBigO{n} space at the worst case, where
\f$ n\f$ is the size of the input polygon.
\cgalModels `PolygonConvexDecomposition_2`

10
Minkowski_sum_2/doc/Minkowski_sum_2/Minkowski_sum_2.txt
View File

@ -53,7 +53,7 @@ they form with the \f$ x\f$-axis; see the figure above.
The Minkowski sum can therefore be computed using an operation similar to the
merge step of the merge-sort algorithm\cgalFootnote{See, for example,
<a href="https://en.wikipedia.org/wiki/Merge_sort">
https://en.wikipedia.org/wiki/Merge_sort</a>.} in \f$ O(m + n)\f$ time,
https://en.wikipedia.org/wiki/Merge_sort</a>.} in \cgalBigO{m + n} time,
starting from the two bottommost vertices in \f$ P\f$ and in \f$ Q\f$ and
merging the ordered list of edges.
@ -294,7 +294,7 @@ the dynamic-programming algorithm of Greene \cgalCite{g-dpcp-83} for
computing an optimal decomposition of a polygon into a minimal number
of convex sub-polygons. While this algorithm results in a small number
of convex polygons, it consumes rather many resources, as it runs in
\f$ O(n^4) \f$ time and \f$ O(n^3) \f$ space in the worst case, where
\cgalBigO{n^4} time and \cgalBigO{n^3} space in the worst case, where
\f$ n \f$ is the number of vertices in the input polygon.
<LI>The `Hertel_Mehlhorn_convex_decomposition_2<Kernel>` class
@ -302,7 +302,7 @@ template implements the approximation algorithm suggested by Hertel and
Mehlhorn \cgalCite{hm-ftsp-83}, which triangulates the input polygon
and then discards unnecessary triangulation edges. After triangulation
(carried out by the constrained-triangulation procedure of CGAL) the
algorithm runs in \f$ O(n) \f$ time and space, and guarantees that the
algorithm runs in \cgalBigO{n} time and space, and guarantees that the
number of sub-polygons it generates is not more than four times the
optimum.
@ -310,7 +310,7 @@ optimum.
implementation of Greene's approximation algorithm
\cgalCite{g-dpcp-83}, which computes a convex decomposition of the
polygon based on its partitioning into \f$ y\f$-monotone polygons.
This algorithm runs in \f$ O(n \log n)\f$ time and \f$ O(n)\f$ space,
This algorithm runs in \cgalBigO{n \log n} time and \cgalBigO{n} space,
and has the same guarantee on the quality of approximation as Hertel
and Mehlhorn's algorithm.
@ -318,7 +318,7 @@ and Mehlhorn's algorithm.
template is an implementation of a decomposition algorithm introduced
in \cgalCite{cgal:afh-pdecm-02}. It is based on the angle-bisector
decomposition method suggested by Chazelle and Dobkin
\cgalCite{cd-ocd-85}, which runs in \f$ O(n^2)\f$ time. In addition,
\cgalCite{cd-ocd-85}, which runs in \cgalBigO{n^2} time. In addition,
it applies a heuristic by Flato that reduces the number of output
polygons in many common cases. The convex decompositions that it
produces usually yield efficient running times for Minkowski sum

2
Minkowski_sum_2/include/CGAL/Minkowski_sum_2/AABB_tree_with_join.h
View File

@ -182,7 +182,7 @@ namespace CGAL {
/// After one or more calls to `AABB_tree_with_join::insert()` the internal data
/// structure of the tree must be reconstructed. This procedure
/// has a complexity of \f$O(n log(n))\f$, where \f$n\f$ is the number of
/// has a complexity of \cgalBigO{n log(n)}, where \f$n\f$ is the number of
/// primitives of the tree. This procedure is called implicitly
/// at the first call to a query member function. You can call
/// AABB_tree_with_join::build() explicitly to ensure that the next call to

6
Minkowski_sum_2/include/CGAL/Polygon_convex_decomposition_2.h
View File

@ -22,7 +22,7 @@ namespace CGAL {
/*!
* \class
* The O(n^4) optimal strategy for decomposing a polygon into convex
* The \cgalBigO{n^4} optimal strategy for decomposing a polygon into convex
* sub-polygons.
*/
template <typename Kernel_,
@ -39,7 +39,7 @@ public:
/*!
* \class
* Hertel and Mehlhorn's O(n) approximation strategy for decomposing a
* Hertel and Mehlhorn's \cgalBigO{n} approximation strategy for decomposing a
* polygon into convex sub-polygons.
*/
template <typename Kernel_,
@ -56,7 +56,7 @@ public:
/*!
* \class
* Greene's O(n log(n)) approximation strategy for decomposing a polygon into
* Greene's \cgalBigO{n log(n)} approximation strategy for decomposing a polygon into
* convex sub-polygons.
*/
template <typename Kernel_,

2
Minkowski_sum_3/doc/Minkowski_sum_3/Minkowski_sum_3.txt
View File

@ -72,7 +72,7 @@ quadratic number of pieces, which is worst-case optimal. Then up to
\f$ m\f$ are the complexities of the two input polyhedra (the complexity of
a `Nef_polyhedron_3` is the sum of its `Vertices`,
`Halfedges` and `SHalfedges`). In total the operation runs in
\f$ O(n^3m^3)\f$ time.
\cgalBigO{n^3m^3} time.
Since the computation of the Minkowski sum takes quite some time, we
give the running times of some Minkowski sum computations. They were

2
Minkowski_sum_3/include/CGAL/minkowski_sum_3.h
View File

@ -28,7 +28,7 @@ namespace CGAL {
The function `minkowski_sum_3()` computes the Minkowski sum of two
given 3D Nef polyhedra \f$ N0\f$ and \f$ N1\f$. Note that the function runs in
\f$ O(n^3m^3)\f$ time in the worst case, where \f$ n\f$ and
\cgalBigO{n^3m^3} time in the worst case, where \f$ n\f$ and
\f$ m\f$ are the complexities of the two input polyhedra (the complexity of
a `Nef_polyhedron_3` is the sum of its `Vertices`,
`Halfedges` and `SHalfedges`).

2
Miscellany/doc/Miscellany/CGAL/Union_find.h
View File

@ -13,7 +13,7 @@ in the C++ standard. It has a default argument `CGAL_ALLOCATOR(T)`.
`Union_find<T,A>` is implemented with union by rank and path
compression. The running time for \f$ m\f$ set operations on \f$ n\f$ elements
is \f$ O(n \alpha(m,n))\f$ where \f$ \alpha(m,n)\f$ is the extremely slow growing
is \cgalBigO{n \alpha(m,n)} where \f$ \alpha(m,n)\f$ is the extremely slow growing
inverse of Ackermann's function.
*/

2
Miscellany/doc/Miscellany/CGAL/Unique_hash_map.h
View File

@ -28,7 +28,7 @@ of type `Data` specified in the definition of `map`.
\cgalHeading{Implementation}
`Unique_hash_map` is implemented via a chained hashing scheme. Access
operations `map``[i]` take expected time \f$ O(1)\f$. The `table_size`
operations `map``[i]` take expected time \cgalBigO{1}. The `table_size`
parameter passed to chained hashing can be used to avoid unnecessary
rehashing when set to the number of expected elements in the map.
The design is derived from the \stl `hash_map` and the \leda type

4
Miscellany/doc/Miscellany/Miscellany.txt
View File

@ -47,7 +47,7 @@ global macro `CGAL_PROFILE`.
The class `Unique_hash_map` implements an injective mapping between
a set of unique keys and a set of data values. This is implemented using
a chained hashing scheme and access operations take \f$ O(1)\f$ expected time.
a chained hashing scheme and access operations take \cgalBigO{1} expected time.
Such a mapping is useful, for example, when keys are pointers,
handles, iterators or circulators that refer to unique memory locations.
In this case, the default hash function is `Handle_hash_function`.
@ -57,7 +57,7 @@ In this case, the default hash function is `Handle_hash_function`.
\cgal also provides a class `Union_find` that implements a partition
of values into disjoint sets. This is implemented with union by rank and
path compression. The running time for \f$ m\f$ set operations on \f$ n\f$ elements
is \f$ O(n\alpha(m,n))\f$ where \f$ \alpha(m,n)\f$ is the extremely slowly growing
is \cgalBigO{n\alpha(m,n)} where \f$ \alpha(m,n)\f$ is the extremely slowly growing
inverse of Ackermann's function.
\section MiscellanyProtected Protected Access to Internal Representations

6
Nef_2/doc/Nef_2/CGAL/Nef_polyhedron_2.h
View File

@ -33,14 +33,14 @@ Operations like `empty` take constant time. The operations
`clear`, `complement`, `interior`, `closure`,
`boundary`, `regularization`, input and output take linear
time. All binary set operations and comparison operations take time
\f$ O(n \log n)\f$ where \f$ n\f$ is the size of the output plus the size of the
\cgalBigO{n \log n} where \f$ n\f$ is the size of the output plus the size of the
input.
The point location and ray shooting operations are implemented in two
flavors. The `NAIVE` operations run in linear query time without
any preprocessing, the `DEFAULT` operations (equals `LMWT`)
run in sub-linear query time, but preprocessing is triggered with the
first operation. Preprocessing takes time \f$ O(N^2)\f$, the sub-linear
first operation. Preprocessing takes time \cgalBigO{N^2}, the sub-linear
point location time is either logarithmic when LEDA's persistent
dictionaries are present or if not then the point location time is
worst-case linear, but experiments show often sublinear runtimes. Ray
@ -49,7 +49,7 @@ triangulation overlaid on the plane map representation. The cost of
the walk is proportional to the number of triangles passed in
direction `d` until an obstacle is met. In a minimum weight
triangulation of the obstacles (the plane map representing the
polyhedron) the theory provides a \f$ O(\sqrt{n})\f$ bound for the number
polyhedron) the theory provides a \cgalBigO{\sqrt{n}} bound for the number
of steps. Our locally minimum weight triangulation approximates the
minimum weight triangulation only heuristically (the calculation of
the minimum weight triangulation is conjectured to be NP hard). Thus

2
Nef_2/include/CGAL/Nef_2/PM_point_locator.h
View File

@ -159,7 +159,7 @@ public:
const Direction& d, bool& collinear) const
/*{\Xop returns a halfedge |e| bounding a wedge in between two
neighbored edges in the adjacency list of |v| which contains |d|.
If |d| extends along a edge then |e| is this edge. If |d| extends
If |d| extends along an edge then |e| is this edge. If |d| extends
into the interior of such a wedge then |e| is the first edge hit
when |d| is rotated clockwise. \precond |v| is not isolated.}*/
{ CGAL_NEF_TRACEN("out_wedge "<<PV(v));

2
Nef_3/include/CGAL/Nef_3/SNC_simplify.h
View File

@ -169,7 +169,7 @@ class SNC_simplify_base : public SNC_decorator<SNC_structure> {
}
bool is_part_of_edge(Vertex_handle v) {
/* determines if a vertex v is part of a edge, checking at its local
/* determines if a vertex v is part of an edge, checking at its local
graph for exactly two antipodal vertices */
SM_decorator SD(&*v);

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