mirror of https://github.com/CGAL/cgal
Improved Periodic_3 documentation
This commit is contained in:
Mael Rouxel-Labbé
parent
e338cce067
commit
596fb64ffe
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@ -7,18 +7,16 @@ namespace CGAL {
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The class `Periodic_3_Delaunay_triangulation_3` represents a
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Delaunay triangulation in three-dimensional periodic space.
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\tparam Periodic_3DelaunayTriangulationTraits_3 is the geometric traits class.
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\tparam PT must be a model of the concept `Periodic_3DelaunayTriangulationTraits_3`.
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\tparam TriangulationDataStructure_3 is the triangulation data structure.
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Its default value is
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`Triangulation_data_structure_3<Triangulation_vertex_base_3<PT,Periodic_3_triangulation_ds_vertex_base_3<>>,Triangulation_cell_base_3<PT,Periodic_3_triangulation_ds_cell_base_3<>>>`.
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\tparam TDS must be a model of the concept `TriangulationDataStructure_3`. Its default value
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is `Triangulation_data_structure_3<Triangulation_vertex_base_3<PT,Periodic_3_triangulation_ds_vertex_base_3<>>,Triangulation_cell_base_3<PT,Periodic_3_triangulation_ds_cell_base_3<>>>`.
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*/
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template< typename Periodic_3DelaunayTriangulationTraits_3, typename TriangulationDataStructure_3 >
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template< typename PT, typename TDS >
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class Periodic_3_Delaunay_triangulation_3 :
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public Periodic_3_triangulation_3<Periodic_3DelaunayTriangulationTraits_3,
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TriangulationDataStructure_3>
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{
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public Periodic_3_triangulation_3<PT, TDS>
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{
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public:
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/// \name Creation
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@ -8,7 +8,7 @@ The class `Periodic_3_Delaunay_triangulation_traits_3` is designed as a default
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class `Periodic_3_Delaunay_triangulation_3<Periodic_3DelaunayTriangulationTraits_3,TriangulationDataStructure_3>`.
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\tparam Traits must be a model of the `DelaunayTriangulationTraits_3` concept.
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\tparam Periodic_3Offset_3 must be a model of the concept `Periodic_3Offset_3` and defaults to `Periodic_3_offset_3`.
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\tparam Offset must be a model of the concept `Periodic_3Offset_3` and defaults to `Periodic_3_offset_3`.
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If `Traits` is a `CGAL::Filtered_kernel` (detected when `Traits::Has_filtered_predicates` exists
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and is `true`), this class automatically provides filtered predicates. Similarly, statically filtered predicates
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@ -18,9 +18,9 @@ By default, this holds for `CGAL::Exact_predicates_inexact_constructions_kernel`
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\cgalModels Periodic_3DelaunayTriangulationTraits_3
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*/
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template< typename Traits, typename Periodic_3Offset_3 >
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template< typename Traits, typename Offset >
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class Periodic_3_Delaunay_triangulation_traits_3
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: public Periodic_3_triangulation_traits_base_3 < Traits, Periodic_3Offset_3> {
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: public Periodic_3_triangulation_traits_base_3 < Traits, Offset> {
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public:
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}; /* end Periodic_3_Delaunay_triangulation_traits_3 */
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} /* end namespace CGAL */
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@ -7,19 +7,18 @@ namespace CGAL {
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The class `Periodic_3_regular_triangulation_3` represents a
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weighted Delaunay triangulation in three-dimensional periodic space.
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\tparam Periodic_3RegularTriangulationTraits_3 is the geometric traits class.
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\tparam PT must be a model of the concept `Periodic_3RegularTriangulationTraits_3`.
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\tparam TriangulationDataStructure_3 is the triangulation data structure.
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\tparam TDS must be a model of the concept `TriangulationDataStructure_3`.
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Its default value is
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`Triangulation_data_structure_3<Regular_triangulation_vertex_base_3<PT,Periodic_3_triangulation_ds_vertex_base_3<> >,
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Regular_triangulation_cell_base_3<PT,Periodic_3_triangulation_ds_cell_base_3<>>>`.
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*/
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template< typename Periodic_3TriangulationTraits_3, typename TriangulationDataStructure_3 >
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template< typename PT, typename TDS >
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class Periodic_3_regular_triangulation_3 :
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public Periodic_3_triangulation_3<Periodic_3TriangulationTraits_3,
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TriangulationDataStructure_3>
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{
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public Periodic_3_triangulation_3<PT, TDS>
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{
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public:
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/// \name Types
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@ -230,7 +229,7 @@ specifying where to start the search.
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\pre `c` is a cell of `rt` and `p` lies in the original domain `domain`.
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*/
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Vertex_handle nearest_power_vertex(const Weighted_point & p,
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Vertex_handle nearest_power_vertex(const Bare_point & p,
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Cell_handle c = Cell_handle()) const;
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/// @}
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@ -343,13 +342,13 @@ Bare_point dual(Cell_handle c) const;
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/*!
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Returns the dual of facet `f`, which is a periodic segment.
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*/
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Periodic_segment dual(Facet f) const;
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Periodic_segment_3 dual(Facet f) const;
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/*!
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same as the previous method for facet `(c,i)`.
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\pre \f$ i\in\{0,1,2,3\}\f$
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*/
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Periodic_segment dual(Cell_handle c, int i) const;
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Periodic_segment_3 dual(Cell_handle c, int i) const;
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/*!
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Returns in the output iterator the points of the dual polygon of
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@ -8,19 +8,18 @@ The class `Periodic_3_regular_triangulation_traits_3` is designed as a default t
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class `Periodic_3_regular_triangulation_3<Periodic_3RegularTriangulationTraits_3,TriangulationDataStructure_3>`.
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\tparam Traits must be a model of the `RegularTriangulationTraits_3` concept.
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\tparam Periodic_3Offset_3 must be a model of the concept `Periodic_3Offset_3` and defaults to `Periodic_3_offset_3`.
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\cgalModels Periodic_3RegularTriangulationTraits_3
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\tparam Offset must be a model of the concept `Periodic_3Offset_3` and defaults to `Periodic_3_offset_3`.
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If `Traits` is a `CGAL::Filtered_kernel` (detected when `Traits::Has_filtered_predicates` exists
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and is `true`), this class automatically provides filtered predicates.
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By default, this holds for `CGAL::Exact_predicates_inexact_constructions_kernel` and
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`CGAL::Exact_predicates_exact_constructions_kernel`.
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\cgalModels Periodic_3RegularTriangulationTraits_3
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*/
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template< typename Traits, typename Periodic_3Offset_3 >
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template< typename Traits, typename Offset >
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class Periodic_3_regular_triangulation_traits_3 :
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public Periodic_3_triangulation_traits_base_3< Traits, Periodic_3Offset_3 > {
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public Periodic_3_triangulation_traits_base_3< Traits, Offset > {
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public:
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}; /* end Periodic_3_regular_triangulation_traits_3 */
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} /* end namespace CGAL */
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@ -4,18 +4,18 @@ namespace CGAL {
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/*!
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\ingroup PkgPeriodic3Triangulation3MainClasses
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The class `Periodic_triangulation_3` represents a 3-dimensional
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The class `Periodic_3_triangulation_3` represents a 3-dimensional
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triangulation of a point set in \f$ \mathbb T_c^3\f$.
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\tparam PT must be a model of the `Periodic_3TriangulationTraits_3` concept.
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\tparam PT must be a model of the concept `Periodic_3TriangulationTraits_3`.
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\tparam TDS must be a model of `TriangulationDataStructure_3` concept
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with some additional functionality in cells and vertices.
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\tparam TDS must be a model of the concept `TriangulationDataStructure_3`
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with some additional functionality in cells and vertices.
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Its default value is
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`Triangulation_data_structure_3<Triangulation_vertex_base_3<PT,Periodic_3_triangulation_ds_vertex_base_3<>>,Triangulation_cell_base_3<PT,Periodic_3_triangulation_ds_cell_base_3<>>>`.
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\sa `Periodic_3_Delaunay_triangulation_3`
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\sa `Periodic_3_regular_triangulation_3`
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*/
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template< typename PT, typename TDS >
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class Periodic_3_triangulation_3 {
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@ -53,9 +53,18 @@ store the number of sheets in each direction of space.
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typedef array<int,3> Covering_sheets;
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/*!
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The point type of the triangulation.
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\note This type is equal to `Geometric_traits::Point_3` when considering periodic
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Delaunay triangulations and to `Geometric_traits::Weighted_point_3` when
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considering periodic weighted Delaunay triangulations.
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*/
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typedef Geometric_traits::Point_3 Point;
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typedef TDS::Vertex::Point Point;
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/*!
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The geometric basic 3D point type.
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*/
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typedef Geometric_traits::Point_3 Point_3;
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/*!
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@ -73,35 +82,53 @@ typedef Geometric_traits::Triangle_3 Triangle;
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typedef Geometric_traits::Tetrahedron_3 Tetrahedron;
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/*!
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Represents a point-offset pair. The point in the
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pair lies in the original domain.
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Represents a point-offset pair. The point in the pair lies in the original domain.
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Note that the inner type is `Point`.
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*/
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typedef std::pair< Point, Offset >
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Periodic_point;
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typedef std::pair< Point, Offset > Periodic_point;
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/*!
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Represents a point-offset pair. The point in the pair lies in the original domain.
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Note that the inner type is `Point_3`.
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*/
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typedef array< Periodic_point, 2>
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Periodic_segment;
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typedef std::pair< Point_3, Offset > Periodic_point_3;
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/*!
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A periodic segment. Note that the inner type is `Periodic_point`.
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*/
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typedef array< Periodic_point, 3>
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Periodic_triangle;
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typedef array< Periodic_point, 2> Periodic_segment;
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/*!
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A periodic segment. Note that the inner type is `Periodic_point_3`.
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*/
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typedef array< Periodic_point, 4>
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Periodic_tetrahedron;
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typedef array< Periodic_point_3, 2> Periodic_segment_3;
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/*!
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A periodic triangle. Note that the inner type is `Periodic_point`.
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*/
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typedef array< Periodic_point, 3> Periodic_triangle;
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/*!
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A periodic triangle. Note that the inner type is `Periodic_point_3`.
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*/
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typedef array< Periodic_point_3, 3> Periodic_triangle_3;
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/*!
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A periodic tetrahedron. Note that the inner type is `Periodic_point`.
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*/
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typedef array< Periodic_point, 4> Periodic_tetrahedron;
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/*!
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A periodic tetrahedron. Note that the inner type is `Periodic_point_3`.
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*/
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typedef array< Periodic_point_3, 4> Periodic_tetrahedron_3;
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/// @}
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/*! \name
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Only vertices (\f$ 0\f$-faces) and cells (\f$ 3\f$-faces) are stored. Edges (\f$ 1\f$-faces) and facets (\f$ 2\f$-faces) are not explicitly represented and thus there are no corresponding classes (see Section \ref P3Triangulation3secintro).
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Only vertices (\f$ 0\f$-faces) and cells (\f$ 3\f$-faces) are stored.
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Edges (\f$ 1\f$-faces) and facets (\f$ 2\f$-faces) are not explicitly represented
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and thus there are no corresponding classes (see Section \ref P3Triangulation3secintro).
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*/
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/// @{
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@ -208,6 +235,8 @@ typedef Triangulation_data_structure::Facet_circulator Facet_circulator;
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/// @}
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/// \name Geometric Iterators:
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/// The following iterators have value type `Periodic_segment`, `Periodic_triangle`,
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/// and `Periodic_tetrahedron`, which have inner type `Point`.
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/// @{
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/*!
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@ -511,6 +540,8 @@ size_type number_of_stored_facets() const;
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/// @}
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/// \name Geometric Access Functions
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/// The following functions return object of types `Periodic_segment`,
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/// `Periodic_triangle`, and `Periodic_tetrahedron`, which have inner type `Point`.
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/// @{
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/*!
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@ -599,33 +630,92 @@ A translation in accordance with `offset` is applied on the point-offet pairs.
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Periodic_tetrahedron periodic_tetrahedron(const Cell_handle c, Offset offset) const;
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/// \name
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/// \warning The following functions were renamed with %CGAL 4.11 to clarify
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/// that they return geometric objects with inner type `Point_3`.
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///
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/// Note that a traits class providing exact constructions should be
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/// used in order to guarantee the following operations to be exact
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/// (as opposed to computing the triangulation only, which requires
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/// only exact predicates).
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///
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/// @{
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/*!
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Converts the `Periodic_point` `s` (point-offset pair) to the
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corresponding `Point` in \f$ \mathbb R^3\f$.
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Converts the periodic point of type `PP` to a `Point_3`. The type `PP` can be either
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`Periodic_point` or `Periodic_point_3`.
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*/
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Point point(const Periodic_point & p ) const;
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template<typename PP>
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Point_3 construct_point(const PP & pp) const;
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/*!
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Converts the `Periodic_segment` `s` to a `Segment`.
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Converts the `Point` `p` to a `Point_3`.
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*/
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Segment segment(const Periodic_segment & s) const;
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Point_3 construct_point(const Point & p) const;
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/*!
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Converts the `Periodic_triangle` `t` to a `Triangle`.
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Same as above, with offsets.
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*/
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Triangle triangle(const Periodic_triangle & t) const;
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template<typename P>
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Point_3 construct_point(const P& p1, const Offset& o1) const;
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/*!
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Converts the `Periodic_tetrahedron` `t` to a `Tetrahedron`.
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Converts the periodic segment of type `PS` to a `Segment`. The type `PS` can be
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either `Periodic_segment` or `Periodic_segment_3`.
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*/
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Tetrahedron tetrahedron(const Periodic_tetrahedron & t)
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const;
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template<typename PS>
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Segment construct_segment(const PS & s) const;
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/*!
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Creates a segment from two points. The type `P` can be either `Point` or `Point_3`.
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*/
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template<typename P>
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Segment construct_segment(const P& p1, const P& p2) const;
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/*!
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Same as above, with offsets.
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*/
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template<typename P>
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Segment construct_segment(const P& p1, const P& p2, const Offset& o1, const Offset& o2) const;
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/*!
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Converts the periodic triangle of type `PT` to a `Triangle`. The type `PT` can
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be either `Periodic_triangle` or `Periodic_triangle_3`.
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*/
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template<typename PT>
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Triangle construct_triangle(const PT & t) const;
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/*!
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Creates a triangle from three points. The type `P` can be either `Point` or `Point_3`.
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*/
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template<typename P>
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Triangle construct_triangle(const P& p1, const P& p2, const P& p3) const;
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/*!
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Same as above, with offsets.
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*/
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template<typename P>
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Triangle construct_triangle(const P& p1, const P& p2, const P& p3,
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const Offset& o1, const Offset& o2, const Offset& o3) const;
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/*!
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Converts the periodic tetrahedron of type `PT` to a `Tetrahedron`. The type `PT`
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can be either `Periodic_tetrahedron` or `Periodic_tetrahedron_3`.
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*/
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template<typename PT>
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Tetrahedron construct_tetrahedron(const PT & t) const;
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/*!
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Creates a tetrahedron from four points. The type `P` can be either `Point` or `Point_3`.
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*/
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template<typename P>
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Tetrahedron construct_tetrahedron(const P& p1, const P& p2, const P& p3, const P& p4) const;
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/*!
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Same as above, with offsets.
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*/
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template<typename P>
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Tetrahedron construct_tetrahedron(const P& p1, const P& p2, const P& p3, const P& p4,
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const Offset& o1, const Offset& o2, const Offset& o3, const Offset& o4) const;
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/// @}
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@ -10,9 +10,8 @@ location queries.
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\cgalHeading{Template Parameters}
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It is templated by a parameter which must be instantiated by one of the \cgal periodic triangulation classes. <I>In the current
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implementation, only `Periodic_3_Delaunay_triangulation_3` is
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supported for `PTr`.</I>
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\tparam PTr must be one of the \cgal periodic triangulation classes. <I>In the current
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implementation, only `Periodic_3_Delaunay_triangulation_3` is supported for.</I>
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`PTr::Vertex` has to be a model of the concept
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`Periodic_3TriangulationHierarchyVertexBase_3`.
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@ -21,14 +20,14 @@ supported for `PTr`.</I>
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`Periodic_3DelaunayTriangulationTraits_3`.
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`Periodic_3_triangulation_hierarchy_3` offers exactly the same functionalities as `PTr`.
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Most of them (point location, insertion, removal \f$ \ldots\f$ ) are overloaded to
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improve their efficiency by using the hierarchic structure.
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Most of these functionalities (point location, insertion, removal \f$ \ldots\f$ )
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are overloaded to improve their efficiency by using the hierarchic structure.
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Note that, since the algorithms that are provided are randomized, the
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running time of constructing a triangulation with a hierarchy may be
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improved when shuffling the data points.
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However, the I/O operations are not overloaded. So, writing a
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However, the I/O operations are not overloaded. Thus, writing a
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hierarchy into a file will lose the hierarchic structure and reading
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it from the file will result in an ordinary triangulation whose
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efficiency will be the same as `PTr`.
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@ -5,10 +5,10 @@ namespace CGAL {
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\ingroup PkgPeriodic3Triangulation3TraitsClasses
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The class `Periodic_3_triangulation_traits_3` is designed as a default traits class for the
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class `Periodic_3_triangulation_3<Periodic_3TriangulationTraits_3,TriangulationDataStructure_3>`.
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class `Periodic_3_triangulation_3<Periodic_3TriangulationTraits_3,TriangulationDataStructure_3>`.
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\tparam Traits must be a model of the `TriangulationTraits_3` concept.
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\tparam Periodic_3Offset_3 must be a model of the concept `Periodic_3Offset_3` and defaults to `Periodic_3_offset_3`.
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\tparam Offset must be a model of the concept `Periodic_3Offset_3` and defaults to `Periodic_3_offset_3`.
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If `Traits` is a `CGAL::Filtered_kernel` (detected when `Traits::Has_filtered_predicates` exists
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and is `true`), this class automatically provides filtered predicates. Similarly, statically filtered predicates
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|
@ -18,7 +18,7 @@ By default, this holds for `CGAL::Exact_predicates_inexact_constructions_kernel`
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\cgalModels Periodic_3TriangulationTraits_3
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*/
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||||
template< typename Traits, typename Periodic_3Offset_3 >
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template< typename Traits, typename Offset >
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class Periodic_3_triangulation_traits_3 : public Traits {
|
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public:
|
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}; /* end Periodic_3_triangulation_traits_3 */
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|
|
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|||
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@ -273,7 +273,7 @@ The second parameter `Periodic_3Offset_3` defaults to
|
|||
|
||||
The kernels `Cartesian`, `Homogeneous`,
|
||||
`Simple_cartesian`, `Simple_homogeneous` and
|
||||
`Filtered_kernel` can all be used as \cgalModels of the concepts
|
||||
`Filtered_kernel` can all be used as models of the concepts
|
||||
`TriangulationTraits_3`, `DelaunayTriangulationTraits_3`, and
|
||||
`RegularTriangulationTraits_3`.
|
||||
The periodic triangulation classes provide exact
|
||||
|
|
@ -423,7 +423,7 @@ data structure.
|
|||
|
||||
\cgalExample{Periodic_3_triangulation_3/simple_regular_example.cpp}
|
||||
|
||||
\subsubsection Periodic_3_triangulation_3P3TR3FirstExample Point Insertion and Vertex Removal
|
||||
\subsubsection Periodic_3_triangulation_3P3TR3PointInsertionAndVertexRemoval Point Insertion and Vertex Removal
|
||||
|
||||
This example shows the incremental construction of a 3D regular triangulation,
|
||||
and the removal of a vertex. It uses the default parameter of the
|
||||
|
|
|
|||
|
|
@ -1,5 +1,6 @@
|
|||
/*!
|
||||
\example Periodic_3_triangulation_3/simple_example.cpp
|
||||
\example Periodic_3_triangulation_3/simple_regular_example.cpp
|
||||
\example Periodic_3_triangulation_3/colored_vertices.cpp
|
||||
\example Periodic_3_triangulation_3/periodic_adding_handles.cpp
|
||||
\example Periodic_3_triangulation_3/covering.cpp
|
||||
|
|
|
|||
|
|
@ -6,8 +6,8 @@ namespace CGAL
|
|||
*
|
||||
* @class Robust_weighted_circumcenter_filtered_traits_3
|
||||
*
|
||||
* Overrides Construct_weighted_circumcenter_3(), Compute_squared_radius_3(),
|
||||
* and Compute_squared_radius_smallest_orthogonal_sphere_3() with robust versions.
|
||||
* Overrides the kernel functors Construct_weighted_circumcenter_3, Compute_squared_radius_3,
|
||||
* and Compute_squared_radius_smallest_orthogonal_sphere_3 with robust versions.
|
||||
*
|
||||
* Robustness is achieved by using exact computations if the geometric configuration
|
||||
* is close to degenerate.
|
||||
|
|
|
|||
Loading…
Reference in New Issue