mirror of https://github.com/CGAL/cgal
Documentation additions
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Sebastian Morr
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2560066432
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@ -3,21 +3,21 @@ namespace CGAL {
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/*!
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\ingroup PkgMinkowskiSum2
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Computes the Minkowski sum \f$ P \oplus Q\f$ of the two given polygons.
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This method defaults to the reduced convolution method, see below.
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Note that as the input polygons may not be convex, their Minkowski
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sum may not be a simple polygon. The result is therefore represented
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as a polygon with holes.
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Computes the Minkowski sum \f$ P \oplus Q\f$ of two given polygons
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(which may have holes). `PolygonType1` and `PolygonType2` can be any combination of:
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\pre Both `P` and `Q` are simple, counterclockwise-oriented polygons.
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- `Polygon_2`
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- `Polygon_with_holes_2`
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This method defaults to the reduced convolution method, see below.
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\sa `CGAL::minkowski_sum_reduced_convolution_2()`
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\sa `CGAL::minkowski_sum_full_convolution_2()`
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*/
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template<class Kernel, class Container>
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Polygon_with_holes_2<Kernel,Container>
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minkowski_sum_2 (const Polygon_2<Kernel,Container>& P,
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const Polygon_2<Kernel,Container>& Q);
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minkowski_sum_2 (const PolygonType1<Kernel,Container>& P,
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const PolygonType2<Kernel,Container>& Q);
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/*!
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\ingroup PkgMinkowskiSum2
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@ -29,17 +29,17 @@ the Minkowsi sum. This method works very efficiently, regardless of whether `P`
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and `Q` are convex or non-convex. It is usually faster than the full
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convolution method, except in degenerate cases where the output polygon has
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many holes.
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Note that as the input polygons may not be convex, their Minkowski
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sum may not be a simple polygon. The result is therefore represented
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as a polygon with holes.
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\pre Both `P` and `Q` are simple, counterclockwise-oriented polygons.
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`PolygonType1` and `PolygonType2` can be any combination of:
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- `Polygon_2`
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- `Polygon_with_holes_2`
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*/
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template<class Kernel, class Container>
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Polygon_with_holes_2<Kernel,Container>
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minkowski_sum_reduced_convolution_2 (const Polygon_2<Kernel,Container>& P,
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const Polygon_2<Kernel,Container>& Q);
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minkowski_sum_reduced_convolution_2 (const PolygonType1<Kernel,Container>& P,
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const PolygonType2<Kernel,Container>& Q);
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/*!
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\ingroup PkgMinkowskiSum2
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@ -49,16 +49,16 @@ The function computes the (full) convolution cycles of the two polygons and
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extract the regions having positive winding number with respect to these
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cycles. This method work very efficiently, regardless of whether `P`
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and `Q` are convex or non-convex.
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Note that as the input polygons may not be convex, their Minkowski
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sum may not be a simple polygon. The result is therefore represented
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as a polygon with holes.
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\pre Both `P` and `Q` are simple polygons.
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`PolygonType1` and `PolygonType2` can be any combination of:
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- `Polygon_2`
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- `Polygon_with_holes_2`
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*/
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template<class Kernel, class Container>
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Polygon_with_holes_2<Kernel,Container>
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minkowski_sum_full_convolution_2(const Polygon_2<Kernel,Container>& P,
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const Polygon_2<Kernel,Container>& Q,
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minkowski_sum_full_convolution_2(const PolygonType1<Kernel,Container>& P,
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const PolygonType2<Kernel,Container>& Q,
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const Kernel& kernel = Kernel());
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/*!
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@ -72,62 +72,17 @@ decomposes them into convex sub-polygons \f$ P_1, \ldots, P_k\f$ and
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The decomposition is performed using the given decomposition method
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`decomp`, which must be an instance of a class template that models
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the concept `PolygonConvexDecomposition_2`.
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Note that as the input polygons may not be convex, their Minkowski
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sum may not be a simple polygon. The result is therefore represented
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as a polygon with holes.
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\pre Both `P` and `Q` are simple polygons.
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`PolygonType1` and `PolygonType2` can be any combination of:
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- `Polygon_2`
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- `Polygon_with_holes_2`
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*/
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template<class Kernel, class Container, class PolygonConvexDecomposition_2>
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Polygon_with_holes_2<Kernel,Container>
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minkowski_sum_2 (const Polygon_2<Kernel,Container>& P,
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const Polygon_2<Kernel,Container>& Q,
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minkowski_sum_2 (const PolygonType1<Kernel,Container>& P,
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const PolygonType2<Kernel,Container>& Q,
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const PolygonConvexDecomposition_2& decomp,
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const Gps_segment_traits_2& traits = Gps_segment_traits_2<Kernel,Container,Arr_segment_traits>());
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/*!
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\ingroup PkgMinkowskiSum2
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Computes the Minkowski sum \f$ P \oplus Q\f$ of polygon \f$ P\f$ and the
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polygon with holes \f$ Q\f$. If the input polygons `P` and `Q` are not
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convex, the function decomposes them into convex sub-polygons
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\f$ P_1, \ldots, P_k\f$ and \f$ Q_1, \ldots, Q_{\ell}\f$ and computes
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the union of pairwise sub-sums (namely \f$ \bigcup_{i,j}{(P_i \oplus Q_j)}\f$).
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The decomposition is performed using the given decomposition method
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`decomp`, which must be an instance of a class template that models the
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concept `PolygonWithHolesConvexDecomposition_2`.
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Note that as the input polygons may not be convex, their Minkowski
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sum may not be a simple polygon. The result is therefore represented
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as a polygon with holes.
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*/
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template<class Kernel, class Container,
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class PolygonWithHolesConvexDecomposition_2>
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Polygon_with_holes_2<Kernel,Container>
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minkowski_sum_2 (const Polygon_2<Kernel,Container>& P,
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const Polygon_with_holes_2<Kernel,Container>& Q,
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const PolygonWithHolesConvexDecomposition_2& decomp,
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const Gps_segment_traits_2& traits = Gps_segment_traits_2<Kernel,Container,Arr_segment_traits>());
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/*!
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\ingroup PkgMinkowskiSum2
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Computes the Minkowski sum \f$ P \oplus Q\f$ of the two given polygons with
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holes. If the input polygons `P` and `Q` are not convex, the function
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decomposes them into convex sub-polygons \f$ P_1, \ldots, P_k\f$ and
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\f$ Q_1, \ldots, Q_{\ell}\f$ and computes the union of pairwise sub-sums
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(namely \f$ \bigcup_{i,j}{(P_i \oplus Q_j)}\f$).
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The decomposition is performed using the given decomposition method
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`decomp`, which must be an instance of a class template that models the
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concept `PolygonWithHolesConvexDecomposition_2`.
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Note that as the input polygons may not be convex, their Minkowski
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sum may not be a simple polygon. The result is therefore represented
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as a polygon with holes.
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*/
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template<class Kernel, class Container,
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class PolygonWithHolesConvexDecomposition_2>
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Polygon_with_holes_2<Kernel,Container>
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minkowski_sum_2 (const Polygon_with_holes_2<Kernel,Container>& P,
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const Polygon_with_holes_2<Kernel,Container>& Q,
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const PolygonWithHolesConvexDecomposition_2& decomp,
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const Gps_segment_traits_2& traits = Gps_segment_traits_2<Kernel,Container,Arr_segment_traits>());
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} /* namespace CGAL */
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@ -6,6 +6,11 @@
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namespace CGAL {
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/*! \class
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* This class applies filter to a polygon with holes,
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* by removing all of its holes that cannot possibly contribute
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* to the Minkowski sum boundary.
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*/
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template <class Kernel_, class Container_>
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class Hole_filter_2
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{
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@ -185,6 +185,49 @@ minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
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return minkowski_sum_reduced_convolution_2(pgn1, pgn2);
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}
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/*!
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* Compute the Minkowski sum of two polygons with holes using the convolution
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* method. This function defaults to calling the reduced convolution method,
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* as it is more efficient in most cases.
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* Note that the result may not be a simple polygon. The result is therefore
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* represented as a polygon with holes.
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* \param pgn1 (in) The first polygon with holes.
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* \param pgn2 (in) The second polygon with holes.
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* \return The resulting polygon with holes, representing the sum.
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*
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* \sa `CGAL::minkowski_sum_reduced_convolution_2()`
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* \sa `CGAL::minkowski_sum_full_convolution_2()`
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
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const Polygon_with_holes_2<Kernel_, Container_>& pgn2)
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{
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return minkowski_sum_reduced_convolution_2(pgn1, pgn2);
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}
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/*!
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* Compute the Minkowski sum of a simple polygons and a polygon-with-holes
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* using the convolution method. This function defaults to calling the reduced
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* convolution method, as it is more efficient in most cases.
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* Note that the result may not be a simple polygon. The result is therefore
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* represented as a polygon with holes.
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* \param pgn1 (in) The polygon.
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* \param pgn2 (in) The polygon with holes.
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* \return The resulting polygon with holes, representing the sum.
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*
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* \sa `CGAL::minkowski_sum_reduced_convolution_2()`
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* \sa `CGAL::minkowski_sum_full_convolution_2()`
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
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const Polygon_with_holes_2<Kernel_, Container_>& pgn2)
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{
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Polygon_with_holes_2<Kernel_, Container_> pgnwh1(pgn1);
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return minkowski_sum_reduced_convolution_2(pgnwh1, pgn2);
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}
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/*!
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* Compute the Minkowski sum of two simple polygons by decomposing each
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* polygon to convex sub-polygons and computing the union of the pairwise
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