CGAL 4.7 - 2D Minkowski Sums: CGAL Namespace Reference

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - 2D Minkowski Sums

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
Classes | Functions
CGAL Namespace Reference

## Classes

class | Greene_convex_decomposition_2
class | Hertel_Mehlhorn_convex_decomposition_2
class | Optimal_convex_decomposition_2
class | Polygon_triangulation_decomposition_2
class | Polygon_vertical_decomposition_2
class | Small_side_angle_bisector_decomposition_2

## Functions

template<class Kernel , class Container , class OutputIterator >
OutputIterator | approximated_inset_2 (const Polygon_2< Kernel, Container > &pgn, const typename Kernel::FT &r, const double &eps, OutputIterator oi)
| Provides a guaranteed approximation of the inset, or inner offset, of the given polygon `P` by a given radius `r`. More...
template<class Kernel , class Container >
Gps_circle_segment_traits_2 < Kernel > ::Polygon_with_holes_2 | approximated_offset_2 (const Polygon_2< Kernel, Container > &P, const typename Kernel::FT &r, const double &eps)
| Provides a guaranteed approximation of the offset of the given polygon `P` by a given radius `r` - namely, the function computes the Minkowski sum \( P \oplus B_r\), where \( B_r\) is a disc of radius `r` centered at the origin. More...
template<class Kernel , class Container >
Gps_circle_segment_traits_2 < Kernel > ::Polygon_with_holes_2 | approximated_offset_2 (const Polygon_with_holes_2< Kernel, Container > &wh, const typename Kernel::FT &r, const double &eps)
| Provides a guaranteed approximation of offset the given polygon with holes `pwh` by a given radius `r`, such that the approximation error is bounded by `eps`. More...
template<class Kernel , class Container , class DecompositionStrategy >
Gps_circle_segment_traits_2 < Kernel > ::Polygon_with_holes_2 | approximated_offset_2 (const Polygon_2< Kernel, Container > &P, const typename Kernel::FT &r, const double &eps, const DecompositionStrategy &decomp)
| Provides a guaranteed approximation of the offset of the given polygon `P` by a radius `r`, as described above. More...
template<typename Kernel , typename Container >
Polygon_with_holes_2< Kernel, Container > | minkowski_sum_2 (const PolygonType1< Kernel, Container > &P, const PolygonType2< Kernel, Container > &Q)
| Computes the Minkowski sum \( P \oplus Q\) of two given polygons (which may have holes). More...
template<typename Kernel , typename Container >
Polygon_with_holes_2< Kernel, Container > | minkowski_sum_by_reduced_convolution_2 (const PolygonType1< Kernel, Container > &P, const PolygonType2< Kernel, Container > &Q)
| Computes the Minkowski sum \( P \oplus Q\) of the two given polygons. More...
template<typename Kernel , typename Container >
Polygon_with_holes_2< Kernel, Container > | minkowski_sum_by_full_convolution_2 (const Polygon_2< Kernel, Container > &P, const Polygon_2< Kernel, Container > &Q)
| Computes the Minkowski sum \( P \oplus Q\) of the two given polygons. More...
template<typename Kernel , typename Container , typename PolygonConvexDecomposition_2 >
Polygon_with_holes_2< Kernel, Container > | minkowski_sum_2 (const PolygonType1< Kernel, Container > &P, const PolygonType2< Kernel, Container > &Q, const PolygonConvexDecomposition_2 &decomp, const Gps_segment_traits_2 &traits=Gps_segment_traits_2< Kernel, Container, Arr_segment_traits >())
| Computes the Minkowski sum \( P \oplus Q\) of the two given polygons. More...
template<class ConicTraits , class Container , class OutputIterator >
OutputIterator | inset_polygon_2 (const Polygon_2< typename ConicTraits::Rat_kernel, Container > &P, const typename ConicTraits::Rat_kernel::FT &r, const ConicTraits &traits, OutputIterator oi)

Computes the inset, or inner offset, of the given polygon `P` by a given radius `r` - namely, the function computes the set of points inside the polygon whose distance from \( P\)'s boundary is at least \( r\): \( \{ p \in P \;|\; {\rm dist}(p, \partial P) \geq r \}\). More...

template<class ConicTraits , class Container >
Gps_traits_2< ConicTraits > ::Polygon_with_holes_2 | offset_polygon_2 (const Polygon_2< typename ConicTraits::Rat_kernel, Container > &P, const typename ConicTraits::Rat_kernel::FT &r, const ConicTraits &traits)
| Computes the offset of the given polygon `P` by a given radius `r` - namely, the function computes the Minkowski sum \( P \oplus B_r\), where \( B_r\) is a disc of radius `r` centered at the origin. More...
template<class ConicTraits , class Container >
Gps_traits_2< ConicTraits > ::Polygon_with_holes_2 | offset_polygon_2 (const Polygon_with_holes_2< typename ConicTraits::Rat_kernel, Container > &pwh, const typename ConicTraits::Rat_kernel::FT &r, const ConicTraits &traits)
| Computes the offset of the given polygon with holes `pwh` by a given radius `r`. More...
template<class ConicTraits , class Container , class DecompositionStrategy >
Gps_traits_2< ConicTraits > ::Polygon_with_holes_2 | offset_polygon_2 (const Polygon_2< typename ConicTraits::Rat_kernel, Container > &P, const typename ConicTraits::Rat_kernel::FT &r, const DecompositionStrategy &decomp, const ConicTraits &traits)
| Computes the exact representation of the offset of the given polygon `P` by a radius `r`, as described above. More...