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@ -57,7 +57,7 @@ defined for upper envelopes. In the rest of this chapter, we refer to
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both these diagrams as <I>envelope diagrams</I>.
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It is easy to see that an envelope diagram is no more than a planar
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arrangement (see Chapter \ref chapterArrangement_on_surface_2 ), represented
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arrangement (see Chapter \ref chapterArrangement_on_surface_2 "2D Arrangements"), represented
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using an extended \sc{Dcel} structure, such that every \sc{Dcel}
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record (namely each face, halfedge and vertex) stores an additional
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container of it originators: the \f$ xy\f$-monotone surfaces that induce
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@ -933,7 +933,7 @@ Comparison_result compare_x(const CGAL::Line_2<Kernel> &l1,
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/*!
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\defgroup compare_x_circular compare_x (2D Circular Kernel)
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\ingroup compare_x
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel.
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel "2D Circular Geometry Kernel".
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\code
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#include <CGAL/global_functions_circular_kernel_2.h>
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@ -961,7 +961,7 @@ Comparison_result
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/*!
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\defgroup compare_x_spherical compare_x (3D Spherical Kernel)
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\ingroup compare_x
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel.
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel".
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\code
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#include <CGAL/global_functions_spherical_kernel_3.h>
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@ -1036,7 +1036,7 @@ compare_xy(const CGAL::Point_3<Kernel>& p, const CGAL::Point_3<Kernel>& q);
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/*!
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\defgroup compare_xy_circular compare_xy (2D Circular Kernel)
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\ingroup compare_xy
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel.
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel "2D Circular Geometry Kernel".
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\code
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#include <CGAL/global_functions_circular_kernel_2.h>
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@ -1067,7 +1067,7 @@ compare_xy(const CGAL::Circular_arc_point_2<CircularKernel> &p,
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/*!
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\defgroup compare_xy_spherical compare_xy (3D Spherical Kernel)
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\ingroup compare_xy
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel.
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel".
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\code
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#include <CGAL/global_functions_spherical_kernel_3.h>
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@ -1254,7 +1254,7 @@ Comparison_result compare_y_at_x(const CGAL::Point_2<Kernel> &p,
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/*!
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\name With the 2D Circular Kernel
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See \ref Chapter_2D_Circular_Geometry_Kernel.
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See \ref Chapter_2D_Circular_Geometry_Kernel "2D Circular Geometry Kernel".
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\code
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#include <CGAL/global_functions_circular_kernel_2.h>
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@ -1299,7 +1299,7 @@ global function are available.
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/*!
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\defgroup compary_y_linear compare_y (2D/3D Linear Kernel)
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\ingroup compare_y
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\details See Chapter \ref chapterkernel23
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\details See Chapter \ref chapterkernel23 "2D and 3D Geometry Kernel"
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\anchor figcompare13
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\image html compare1.gif
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@ -1354,7 +1354,7 @@ Comparison_result compare_y(const CGAL::Line_2<Kernel> &l1,
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/*!
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\defgroup compare_y_circular compare_y (2D Circular Kernel)
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\ingroup compare_y
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel.
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel "2D Circular Geometry Kernel".
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\code
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#include <CGAL/global_functions_circular_kernel_2.h>
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@ -1381,7 +1381,7 @@ compare_y(const CGAL::Circular_arc_point_2<CircularKernel> &p,
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/*!
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\defgroup compare_y_spherical compare_y (3D Spherical Kernel)
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\ingroup compare_y
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel.
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel".
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\code
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#include <CGAL/global_functions_circular_kernel_3.h>
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@ -1444,7 +1444,7 @@ compare_xyz(const CGAL::Point_3<Kernel>& p, const CGAL::Point_3<Kernel>& q);
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/*!
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\defgroup compare_xyz_spherical compare_xyz (3D Spherical Kernel)
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\ingroup compare_xyz
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel"
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\code
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#include <CGAL/global_functions_circular_kernel_3.h>
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@ -1505,7 +1505,7 @@ Comparison_result compare_z(const CGAL::Point_3<Kernel> &p, const CGAL::Point_3<
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\defgroup compare_z_spherical compare_z (3D Spherical Kernel)
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\ingroup compare_z
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel"
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\code
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#include <CGAL/global_functions_circular_kernel_3.h>
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@ -20,7 +20,7 @@ function are available.
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\sa \ref do_intersect_spherical
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\sa `intersection`
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\details See Chapter \ref chapterkernel23 for details on a linear kernel instantiation.
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\details See Chapter \ref chapterkernel23 "2D and 3D Geometry Kernel" for details on a linear kernel instantiation.
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*/
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/// @{
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/*!
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@ -79,7 +79,7 @@ bool do_intersect(Type1<Kernel> obj1, Type2<Kernel> obj2);
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\sa \ref do_intersect_spherical
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\sa `intersection`
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel for details on a circular kernel instantiation.
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel "2D Circular Geometry Kernel" for details on a circular kernel instantiation.
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When using a circular kernel, in addition to the function overloads documented \ref do_intersect_linear "here",
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@ -105,7 +105,7 @@ the following:
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- `Circular_arc_2<CircularKernel>`
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An example illustrating this is presented in
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Chapter \ref Chapter_2D_Circular_Geometry_Kernel.
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Chapter \ref Chapter_2D_Circular_Geometry_Kernel "2D Circular Geometry Kernel".
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*/
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bool do_intersect(Type1<CircularKernel> obj1, Type2<CircularKernel> obj2);
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/// @}
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@ -123,7 +123,7 @@ bool do_intersect(Type1<CircularKernel> obj1, Type2<CircularKernel> obj2);
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\sa \ref do_intersect_circular
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\sa `intersection`
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel for details on a spherical kernel instantiation.
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel" for details on a spherical kernel instantiation.
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When using a circular kernel, in addition to the function overloads documented \ref do_intersect_linear "here",
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@ -151,7 +151,7 @@ the following:
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- `Circular_arc_3<SphericalKernel>`
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An example illustrating this is presented in
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Chapter \ref Chapter_3D_Spherical_Geometry_Kernel.
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Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel".
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*/
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bool do_intersect(Type1<SphericalKernel> obj1, Type2<SphericalKernel> obj2);
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@ -190,7 +190,7 @@ function are available.
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\sa `CGAL::do_intersect`
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\sa `CGAL::Object`
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\details See Chapter \ref chapterkernel23 for details on a linear kernel instantiation.
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\details See Chapter \ref chapterkernel23 "2D and 3D Geometry Kernel" for details on a linear kernel instantiation.
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*/
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/// @{
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@ -433,7 +433,7 @@ Object intersection(const Plane_3<Kernel>& pl1,
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\sa `CGAL::do_intersect`
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\sa `CGAL::Object`
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel for details on a circular kernel instantiation.
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\details See Chapter \ref Chapter_2D_Circular_Geometry_Kernel "2D Circular Geometry Kernel" for details on a circular kernel instantiation.
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When using a circular kernel, in addition to the function overloads documented \ref intersection_linear "here",
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the following function overloads are also available.
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@ -492,7 +492,7 @@ intersection(const Type1 &obj1, const Type2 &obj2,
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\sa `CGAL::do_intersect`
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\sa `CGAL::Object`
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel for details on a spherical kernel instantiation.
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\details See Chapter \ref Chapter_3D_Spherical_Geometry_Kernel "3D Spherical Geometry Kernel" for details on a spherical kernel instantiation.
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When using a spherical kernel, in addition to the function overloads documented \ref intersection_linear "here",
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the following function overloads are also available.
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@ -21,7 +21,7 @@ though the basic building blocks are changing continuously.
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This chapter describes a number of such kinetic data structures
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implemented using the Kinetic framework described in
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Chapter \ref chapterkinetic. We first, in
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Chapter \ref chapterkinetic "Kinetic Framework". We first, in
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Section \ref seckds_intro introduce kinetic data structures and
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sweepline algorithms. This section can be skipped if the reader is
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already familiar with the area. The next sections,
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@ -165,7 +165,7 @@ combinatorial structure needs to be updated.
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\section seckds_overview An Overview of the Kinetic Framework
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The provided kinetic data structures are implemented on top of the
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Kinetic framework presented in Chapter \ref chapterkinetic. It is
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Kinetic framework presented in Chapter \ref chapterkinetic "Kinetic Framework". It is
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not necessary to know the details of the framework, but some
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familiarity is useful. Here we presented a quick overview of the
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framework.
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@ -10,7 +10,7 @@ namespace CGAL {
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This chapter describes a framework for implementing kinetic data
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structures and sweepline algorithms. If you just would like to use
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existing kinetic data structures, please read
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Chapter \ref chapterkds instead. Readers wishing to brush up on
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Chapter \ref chapterkds "Kinetic Data Structures" instead. Readers wishing to brush up on
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their familiarity with kinetic data structures or better understand
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the terminology we use should read Section \ref seckds_intro of that
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chapter. A brief overview of the framework can be found in
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@ -81,7 +81,7 @@ Orientation of a cell.
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\cgalFigureEnd
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As in the underlying combinatorial triangulation (see
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Chapter \ref chapterTDS3), the neighbors of a cell are indexed with
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Chapter \ref chapterTDS3 "3D Triangulation Data Structure"), the neighbors of a cell are indexed with
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0, 1, 2, 3 in such a way that the neighbor indexed by \f$ i\f$ is opposite
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to the vertex with the same index. Also edges (\f$ 1\f$-faces) and facets
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(\f$ 2\f$-faces) are not explicitly represented: a facet is given by a cell
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@ -131,7 +131,7 @@ A periodic triangulation is said to be `locally valid` iff
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<B>(a)-(b)</B> Its underlying combinatorial graph, the triangulation
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data structure, is `locally valid`
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(see Section \ref TDS3secintro of Chapter \ref chapterTDS3)
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(see Section \ref TDS3secintro of Chapter \ref chapterTDS3 "3D Triangulation Data Structure")
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<B>(c)</B> Any cell has its vertices ordered according to positive
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orientation. See \cgalFigureRef{P3Triangulation3figorient}.
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@ -155,7 +155,7 @@ points and vertex removal.
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The class `Periodic_3_triangulation_hierarchy_3` is the adaptation
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of the hierarchical structure described in
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chapter \ref chapterTriangulation3 to the periodic case.
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chapter \ref chapterTriangulation3 "3D Triangulations" to the periodic case.
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\section P3Triangulation3secdesign Software Design
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@ -193,7 +193,7 @@ manual.
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<LI> the <B>triangulation data structure</B> class, which stores the
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combinatorial structure, described in
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Section \ref P3Triangulation3sectds and in more detail in
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Chapter \ref chapterTDS3. The triangulation data structure needs
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Chapter \ref chapterTDS3 "3D Triangulation Data Structure". The triangulation data structure needs
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models of the concepts `Periodic_3TriangulationDSCellBase_3` and
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`Periodic_3TriangulationDSVertexBase_3` as template parameters.
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</UL>
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@ -205,7 +205,7 @@ The first template parameter of the Delaunay triangulation class
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is the geometric traits class, described by the concept
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`Periodic_3DelaunayTriangulationTraits_3`. It is different to the
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DelaunayTriangulationTraits_3 (see
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chapter \ref Triangulation3secTraits) in that it
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chapter \ref Triangulation3secTraits "3D Triangulations") in that it
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implements all objects, predicates and constructions with
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using offsets.
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@ -239,7 +239,7 @@ The second template parameter of the main classes
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`Periodic_3_Delaunay_triangulation_3` is a
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triangulation data structure class. This class can be seen as a container for
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the cells and vertices maintaining incidence and adjacency relations (see
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Chapter \ref chapterTDS3). A model of this triangulation data structure is
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Chapter \ref chapterTDS3 "3D Triangulation Data Structure"). A model of this triangulation data structure is
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`Triangulation_data_structure_3`, and it is described by the
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`TriangulationDataStructure_3` concept. This model is itself
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parameterized by a vertex base class and a cell base class, which gives the
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@ -321,7 +321,7 @@ covering space anymore, so the triangulation is not <I>extensible</I>.
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For large point sets there are two optimizations available. Firstly,
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there is spatial sorting that sorts the input points according to a
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Hilbert curve, see chapter \ref secspatial_sorting.
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Hilbert curve, see chapter \ref secspatial_sorting "Spatial Sorting".
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The second one inserts 36 appropriately chosen dummy points to avoid
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the use of a 27-sheeted covering space in the beginning. The 36 dummy
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points are deleted in the end. If the point set turns out to not have
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@ -374,7 +374,7 @@ algorithms \cite cgal:ct-c3pt-09 and on the package with Monique
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Teillaud.
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The package follows the design of the 3D Triangulations package
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(see Chapter \ref Chapter_3D_Triangulations).
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(see Chapter \ref Chapter_3D_Triangulations "3D Triangulations").
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*/
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} /* namespace CGAL */
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@ -33,7 +33,7 @@ halfedges and facets are documented separately. A default traits
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class, a default items class and an incremental builder conclude the
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references. The polyhedral surface is based on the highly flexible
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design of the halfedge data structure, see the reference for
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`HalfedgeDS` in Chapter \ref PkgHDS
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`HalfedgeDS` in Chapter \ref Chapter_Halfedge_Data_Structures "Halfedge Data Structures"
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or \cite k-ugpdd-99, but the default instantiation of the polyhedral
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surface can be used without knowing the halfedge data structure.
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@ -23,7 +23,7 @@ The polyhedral surface is realized as a container class that manages
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vertices, halfedges, facets with their incidences, and that maintains
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the combinatorial integrity of them. It is based on the highly
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flexible design of the halfedge data structure, see the introduction
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in Chapter \ref chapterHalfedgeDS "Halfedge Data Structure" and \cite k-ugpdd-99. However, the
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in Chapter \ref chapterHalfedgeDS "Halfedge Data Structures" and \cite k-ugpdd-99. However, the
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polyhedral surface can be used and understood without knowing the
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underlying design. Some of the examples in this chapter introduce also
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gradually into first applications of this flexibility.
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@ -453,7 +453,7 @@ attribute is available in the type `Polyhedron_3::Facet`. However,
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typedef for `My_face`, but it is derived therefrom. Thus,
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everything that we put in the local face type except constructors is
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then available in the `Polyhedron_::Facet` type. For more
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details, see the Chapter \ref chapterHalfedgeDS "Halfedge Data Structure"
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details, see the Chapter \ref chapterHalfedgeDS "Halfedge Data Structures"
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on the halfedge data structure design.
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Pulling all pieces together, the full example program illustrates how easy
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@ -167,7 +167,7 @@ The geometric traits for the segment Delaunay graph will be
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discussed in more detail in the next section.
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<LI>the *segment Delaunay graph data structure*. This is
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essentially the same as the Apollonius graph data structure (discussed
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in Chapter \ref secapollonius2design), augmented with some
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in Chapter \ref secapollonius2design of 2D Apollonius Graph), augmented with some
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additional operations that are specific to segment Voronoi
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diagrams. The corresponding concept is that of
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`SegmentDelaunayGraphDataStructure_2`, which in fact is a refinement
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@ -60,6 +60,6 @@ of triangulation data
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structure acting as a container for faces and vertices
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while taking care of the combinatorial aspects of the triangulation.
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The concepts and models relative to the triangulation data structure
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are described in Chapter \ref PkgTDS2.
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are described in Chapter \ref PkgTDS2 "2D Triangulation Data Structure".
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*/
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@ -1163,7 +1163,7 @@ The new solution to resolve the template dependency
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is based on a rebind mechanism similar to the mechanism used in the
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standard allocator class std::allocator. The rebind mechanism
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is described in Section \ref TDS_2D_default "The Default Triangulation Data Structure"
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of Chapter \ref Chapter_2D_Triangulation_Data_Structure "Triangulation Data Structure".
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of Chapter \ref Chapter_2D_Triangulation_Data_Structure "2D Triangulation Data Structure".
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For now, we will just notice that the design
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requires
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the existence in the vertex and face base classes
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@ -7,7 +7,7 @@ namespace CGAL {
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The class `Triangulation_data_structure_3` stores a 3D-triangulation data
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structure and provides the optional
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geometric functionalities to be used as a parameter for a
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3D-geometric triangulation (see Chapter \ref chapterTriangulation3).
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3D-geometric triangulation (see Chapter \ref chapterTriangulation3 "3D Triangulations").
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The vertices and cells are stored in two nested containers, which are
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implemented using `Compact_container`. The class may offer some
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@ -10,7 +10,7 @@ for a 3D-triangulation data structure, it is a model of the concept
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Note that if the triangulation data structure is used as a parameter of a
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geometric triangulation (Section \ref TDS3secdesign and
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Chapter \ref chapterTriangulation3), then the vertex base class has to
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Chapter \ref chapterTriangulation3 "3D Triangulations"), then the vertex base class has to
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fulfill additional geometric requirements, i.e. it has to be a model of the
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concept `TriangulationVertexBase_3`.
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@ -43,8 +43,7 @@ topological sphere \f$ S^d\f$ of \f$ \R^{d+1}\f$, for any \f$ d \in \{-1,0,1,2,3
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The second template parameter of the basic triangulation class
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(see Chapter \ref chapterTriangulation3
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)
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(see Chapter \ref chapterTriangulation3 "3D Triangulations")
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`CGAL::Triangulation_3` is a triangulation data structure class. (See
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Chapter \ref chapterTDS3.)
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|
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@ -14,7 +14,7 @@ geometric information related to the position of vertices.
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\cgal provides 3D geometric triangulations in which these
|
||||
two aspects are clearly separated.
|
||||
As described in Chapter \ref chapterTriangulation3, a geometric
|
||||
As described in Chapter \ref chapterTriangulation3 "3D Triangulations", a geometric
|
||||
triangulation of a set of points in \f$ \R^d\f$, \f$ d\leq 3\f$ is a partition of the
|
||||
whole space \f$ \R^d\f$ into cells having \f$ d+1\f$ vertices. Some of them
|
||||
are infinite, they are obtained by linking an additional vertex at
|
||||
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@ -27,7 +27,7 @@ topological sphere \f$ S^d\f$ in \f$ \R^{d+1}\f$.
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This chapter deals with 3D-triangulation data structures, meant to
|
||||
maintain the combinatorial information for 3D-geometric
|
||||
triangulations. The reader interested in geometric triangulations of
|
||||
\f$ \R^3\f$ is advised to read Chapter \ref chapterTriangulation3 "3D Triangulations.
|
||||
\f$ \R^3\f$ is advised to read Chapter \ref chapterTriangulation3 "3D Triangulations".
|
||||
|
||||
\section TDS3secintro Representation
|
||||
|
||||
|
|
@ -179,7 +179,7 @@ layer upon which a geometric layer can be built \cite k-ddsps-98. This
|
|||
geometric layer is typically one of the 3D-triangulation classes of \cgal:
|
||||
`Triangulation_3`, `Delaunay_triangulation_3` and
|
||||
`Regular_triangulation_3`. This relation is described in more details in
|
||||
Chapter \ref chapterTriangulation3, where the
|
||||
Chapter \ref chapterTriangulation3 "3D Triangulations", where the
|
||||
Section \ref Triangulation3secdesign explains other important parts of the
|
||||
design related to the geometry.
|
||||
|
||||
|
|
@ -209,7 +209,7 @@ or \f$ 2\f$-face. It also allows one, if the dimension of the triangulation is
|
|||
smaller than \f$ 3\f$, to insert a vertex so that the dimension of the triangulation
|
||||
is increased by one. The TDS is responsible for the combinatorial integrity of
|
||||
the eventual geometric triangulation built on top of it (the upper layer,
|
||||
see Chapter \ref chapterTriangulation3).
|
||||
see Chapter \ref chapterTriangulation3 "3D Triangulations").
|
||||
</UL>
|
||||
|
||||
The user has several ways to add his own data in the vertex and cell base classes used by the TDS. He can either:
|
||||
|
|
|
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Loading…
Reference in New Issue