diff --git a/Alpha_shapes_3/doc/Alpha_shapes_3/Alpha_shapes_3.txt b/Alpha_shapes_3/doc/Alpha_shapes_3/Alpha_shapes_3.txt index fc3696023f9..d440d65382d 100644 --- a/Alpha_shapes_3/doc/Alpha_shapes_3/Alpha_shapes_3.txt +++ b/Alpha_shapes_3/doc/Alpha_shapes_3/Alpha_shapes_3.txt @@ -198,10 +198,13 @@ We currently do not specify concepts for the underlying triangulation type. Models that work for a family of alpha-shapes are the instantiations of the classes `Delaunay_triangulation_3` and `Periodic_3_Delaunay_triangulation_3` (see -example \ref AlphaShape_3DExampleForPeriodicAlphaShapes). A model that works for a fixed alpha-shape are the instantiations +example \ref AlphaShape_3DExampleForPeriodicAlphaShapes). +A model that works for a fixed alpha-shape are the instantiations of the class `Delaunay_triangulation_3`. -A model that works for a weighted alpha-shape is -the class `Regular_triangulation_3`. The triangulation needs a geometric traits class +Models that work for a weighted alpha-shape are the instantiations +of the classes `Regular_triangulation_3` and +`Periodic_3_regular_triangulation_3`. +The triangulation needs a geometric traits class and a triangulation data structure as template parameters. \subsection AlphaShape3D_ConceptAndModelsAlphaShapes Alpha Shapes @@ -234,19 +237,20 @@ and `Fixed_alpha_shape_cell_base_3`, respectively. \subsection AlphaShape3D_ConceptAndModelsTDS Triangulation data structure -Additionally requirements are put when using `Regular_triangulation_3` or -`Periodic_3_Delaunay_triangulation_3` as underlying triangulations: +Additionally requirements are put when using weighted or +periodic triangulations as underlying triangulation: \section Alpha_shapes_3AlphaShape3OrFixedAlphaShape3 Alpha_shape_3 vs. Fixed_alpha_shape_3 @@ -320,14 +324,15 @@ them with a traits with inexact constructions, the tag \subsection AlphaShape_3DExampleForPeriodicAlphaShapes Example for Periodic Alpha Shapes -The following example shows how to use the periodic Delaunay +The following example shows how to use a periodic Delaunay triangulation (Chapter \ref Chapter_3D_Periodic_Triangulations "3D Periodic Triangulations") as underlying -triangulation for the alpha shape computation. +triangulation for the alpha shape computation. Usage of a weighted Delaunay periodic +triangulation is presented in the example: \ref Alpha_shapes_3/ex_weighted_periodic_alpha_shapes_3.cpp "ex_weighted_periodic_alpha_shapes_3.cpp". In order to define the original domain and to benefit from the -built-in heuristic optimizations of the periodic Delaunay -triangulation computation, it is recommended to first construct the -triangulation and then construct the alpha shape from it. The alpha +built-in heuristic optimizations of the periodic triangulation computation, +it is recommended to first construct the triangulation and +then construct the alpha shape from it. The alpha shape constructor that takes a point range can be used as well but in this case the original domain cannot be specified and the default unit cube will be chosen and no optimizations will be used. diff --git a/Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Alpha_shape_3.h b/Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Alpha_shape_3.h index 1ad2fcf5ff3..50734a63de7 100644 --- a/Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Alpha_shape_3.h +++ b/Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Alpha_shape_3.h @@ -17,8 +17,9 @@ The modifying functions `insert` and `remove` will overwrite the one inherited from the underlying triangulation class `Dt`. At the moment, only the static version is implemented. -\tparam Dt must be either `Delaunay_triangulation_3`, `Regular_triangulation_3` -or `Periodic_3_triangulation_3`. Note that `Dt::Geom_traits`, `Dt::Vertex`, and `Dt::Face` +\tparam Dt must be either `Delaunay_triangulation_3`, `Regular_triangulation_3`, +`Periodic_3_Delaunay_triangulation_3` or `Periodic_3_regular_triangulation_3`. +Note that `Dt::Geom_traits`, `Dt::Vertex`, and `Dt::Face` must be model the concepts `AlphaShapeTraits_3`, `AlphaShapeVertex_3` and `AlphaShapeCell_3`, respectively. diff --git a/Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Fixed_alpha_shape_3.h b/Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Fixed_alpha_shape_3.h index 8d60d020c27..71b7394b4ef 100644 --- a/Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Fixed_alpha_shape_3.h +++ b/Alpha_shapes_3/doc/Alpha_shapes_3/CGAL/Fixed_alpha_shape_3.h @@ -12,8 +12,9 @@ represents connectivity and order among its faces. Each \f$ k\f$-dimensional face of the `Dt` is associated with a classification that specifies its status in the alpha complex, alpha being fixed. -\tparam Dt must be either `Delaunay_triangulation_3`, `Regular_triangulation_3` -or `Periodic_3_triangulation_3`. Note that `Dt::Geom_traits`, `Dt::Vertex`, and `Dt::Face` +\tparam Dt must be either `Delaunay_triangulation_3`, `Regular_triangulation_3`, +`Periodic_3_Delaunay_triangulation_3` or `Periodic_3_regular_triangulation_3`. +Note that `Dt::Geom_traits`, `Dt::Vertex`, and `Dt::Face` must be model the concepts `AlphaShapeTraits_3`, `AlphaShapeVertex_3` and `AlphaShapeFace_3`, respectively. diff --git a/Alpha_shapes_3/doc/Alpha_shapes_3/examples.txt b/Alpha_shapes_3/doc/Alpha_shapes_3/examples.txt index ab726f84c6d..1ab05e5c8a9 100644 --- a/Alpha_shapes_3/doc/Alpha_shapes_3/examples.txt +++ b/Alpha_shapes_3/doc/Alpha_shapes_3/examples.txt @@ -5,5 +5,6 @@ \example Alpha_shapes_3/ex_fixed_weighted_alpha_shapes_3.cpp \example Alpha_shapes_3/ex_periodic_alpha_shapes_3.cpp \example Alpha_shapes_3/ex_weighted_alpha_shapes_3.cpp +\example Alpha_shapes_3/ex_weighted_periodic_alpha_shapes_3.cpp \example Alpha_shapes_2/ex_alpha_projection_traits.cpp */ diff --git a/Periodic_3_triangulation_3/doc/Periodic_3_triangulation_3/Periodic_3_triangulation_3.txt b/Periodic_3_triangulation_3/doc/Periodic_3_triangulation_3/Periodic_3_triangulation_3.txt index 65efd89d0e9..a1998b9165b 100644 --- a/Periodic_3_triangulation_3/doc/Periodic_3_triangulation_3/Periodic_3_triangulation_3.txt +++ b/Periodic_3_triangulation_3/doc/Periodic_3_triangulation_3/Periodic_3_triangulation_3.txt @@ -455,8 +455,9 @@ of a 3D regular triangulation. \subsection Periodic_3_triangulation_3PeriodicAlphaShapes Periodic Alpha Shapes -It is possible to use the class `Periodic_3_Delaunay_triangulation_3` -as underlying triangulation for computing alpha shapes. For an example see +It is possible to use the classes `Periodic_3_Delaunay_triangulation_3` +and `Periodic_3_regular_triangulation_3` as underlying triangulations +to compute alpha shapes. Examples of usage can be found in Section \ref AlphaShape_3DExampleForPeriodicAlphaShapes of the chapter on 3D alpha shapes.