mirror of https://github.com/CGAL/cgal
147 lines
4.9 KiB
TeX
147 lines
4.9 KiB
TeX
% +------------------------------------------------------------------------+
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% | Reference manual page: DelaunayTriangulationTraits_2.tex
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% +------------------------------------------------------------------------+
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% | 12.04.2000 Author
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% | Package: Package
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% |
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\RCSdef{\RCSDelaunaytriangulationtraitsRev}{$Id$}
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\RCSdefDate{\RCSDelaunaytriangulationtraitsDate}{$Date$}
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% |
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%%RefPage: end of header, begin of main body
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% +------------------------------------------------------------------------+
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\begin{ccRefConcept}{DelaunayTriangulationTraits_2}
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%% \ccHtmlCrossLink{} %% add further rules for cross referencing links
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%% \ccHtmlIndexC[concept]{} %% add further index entries
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\ccDefinition
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In addition to the requirements
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of the concept \ccc{TriangulationTraits_2}
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described \ccRefPage{TriangulationTraits_2},
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the concept \ccRefName\
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provide a predicate to check the empty circle
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property. The correponding predicate type
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is called type \ccc{Side_of_oriented_circle_2}.
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The additional types \ccc{Line_2},
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\ccc{Ray_2} and the constructor objects
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\ccc{Construct_ray_2}
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\ccc{Construct_circumcenter_2}, \ccc{Construct_bisector_2},
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\ccc{Construct_midpoint}
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are used to build the dual Voronoi diagram
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and are required only if the dual functions are called.
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The additional predicate type \ccc{Compare_distance_2} is
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required if calls to
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\ccc{nearest_vertex(..)} are issued.
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\ccRefines
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\ccc{TriangulationTraits_2}
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\ccTypes
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\ccThree{DelaunayTriangulationTraits_2}{traits(dt)xxx}{}
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\ccThreeToTwo
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\ccNestedType{Line_2}{The line type. This type is required only if
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some dual
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functions are called.}
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\ccGlue
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\ccNestedType{Ray_2}{The type for ray. This type is required only if
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some dual
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functions are called.}
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\ccNestedType{Side_of_oriented_circle_2}{Predicate type.
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Provides the operator : \\
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\ccc{Oriented_side operator()(Point p, Point q, Point r, Point s)}
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which takes four points $p, q, r, s$ as arguments and returns
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\ccc{ON_POSITIVE_SIDE}, \ccc{ON_NEGATIVE_SIDE} or,
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\ccc{ON_ORIENTED_BOUNDARY} according to the position of points \ccc{s}
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with respect to the oriented circle through $p,q$
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and $r$.}
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\ccGlue
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\ccNestedType{Compare_distance_2} {Predicate type. Provides
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the operator : \\
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\ccc{Comparison_result operator()(Point_2 p, Point_2 q, Point_2 r)}
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which returns \ccc{SMALLER}, \ccc{EQUAL} or \ccc{LARGER}
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according to the distance between p and q being smaller, equal or larger
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than the distance between p and r. This type is only require if
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\ccc{nearest_vertex} queries are issued.}
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\ccNestedType{Construct_circumcenter_2}{Constructor object. Provides
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the operator : \\
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\ccc{ Point_2 operator()(Point_2 p, Point_2 q, Point_2 r)} which returns
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the circumcenter of the three points \ccc{p, q} anf \ccc{r}.
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This type is required only if functions
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relative to the dual Voronoi diagram are called.}
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\ccGlue
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\ccNestedType{Construct_bisector_2}{Constructor object. Provides
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the operator : \\
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\ccc{ Line_2 operator()(Point_2 p, Point_2 q)} which constructs the
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bisector line of points \ccc{p} and \ccc{q}.
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This type is required only if functions
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relative to the dual Voronoi diagram are called.}
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\ccGlue
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\ccNestedType{Construct_ray_2}{A constructor object to build
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a ray from a point and a line. Provides : \\
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\ccc{Ray_2 operator() ( Point_2 p, Line_2 l);}}
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\ccCreation
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\ccCreationVariable{traits} %% choose variable name
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\ccConstructor{DelaunayTriangulationTraits_2();}{default constructor.}
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\ccGlue
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\ccConstructor{DelaunayTriangulationTraits_2(DelaunayTriangulationTraits_2
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dtt);}{copy constructor}
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\ccGlue
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\ccMethod{DelaunayTriangulationTraits_2
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operator=(traits2);}{Assignment operator.}
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\ccHeading{Access to predicate and constructor objects}
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\ccThree{Construct_circumcenter_2}{traits.construct_circumcenter_2_object();}{}
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\ccMethod{Side_of_oriented_circle_2
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side_of_oriented_circle_2_object();}{}
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The following functions are required only if
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member functions of the Delaunay triangulation
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relative to the dual Voronoi diagram are called.
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\ccMethod{Compare_distance_2
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compare_distance_2_object();} {}
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\ccGlue
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\ccMethod{Construct_circumcenter_2 construct_circumcenter_2_object();}{}
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\ccGlue
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\ccMethod{Construct_bisector_2 construct_bisector_2_object();}{}
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\ccGlue
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\ccMethod{Construct_direction_2 construct_direction_2_object();} {}
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\ccGlue
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\ccMethod{Construct_ray_2 construct_ray_2_object();} {}
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\ccHasModels
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\cgal kernels\\
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\ccc{CGAL::Triangulation_euclidean_traits_2<Rep>}.
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The following traits class provide everything except types and member
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functions required for the dual Voronoi diagram~;\\
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\ccc{CGAL::Triangulation_euclidean_traits_xy_3<Rep>}, \\
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\ccc{CGAL::Triangulation_euclidean_traits_yz_3<Rep>}, \\
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\ccc{CGAL::Triangulation_euclidean_traits_zx_3<Rep>}.
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\ccSeeAlso
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\ccc{TriangulationTraits_2}
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\end{ccRefConcept}
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% +------------------------------------------------------------------------+
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%%RefPage: end of main body, begin of footer
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% EOF
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% +------------------------------------------------------------------------+
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