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template<class Kernel, class Container>
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typename Gps_circle_segment_traits_2<Kernel>::Polygon_with_holes_2
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approximated_offset_2 ( Polygon_2<Kernel, Container> P, typename Kernel::FT r, double eps)
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Provides a guaranteed approximation of the offset of the given polygon
P by a given radius r - namely, the function computes the
the Minkowski sum P ⊕ Br, where Br is a disc of radius
r centered at the origin.
The function actually outputs a set S that contains the Minkowski sum,
such that the approximation error is bounded by eps.
Note that as the input polygon may not be convex, its offset may not be a
simple polygon. The result is therefore represented as a polygon with
holes, whose edges are either line segments or circular arcs.
| Precondition: | P is a simple polygon. |
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template<class Kernel, class Container>
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typename Gps_circle_segment_traits_2<Kernel>::Polygon_with_holes_2
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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. It does so by offsetting outer boundary of pwh and insetting
its holes.
The result is represented as a generalized polygon with holes, such that the edges
of the polygon correspond to line segment and circular arcs.
| Precondition: | pwh is not unbounded (it has a valid outer boundary). |
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template<class Kernel, class Container, class DecompositionStrategy>
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typename Gps_circle_segment_traits_2<Kernel>::Polygon_with_holes_2
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Provides a guaranteed approximation of the offset of the given polygon
P by a radius r, as described above.
If the input polygon P is not convex, the function
decomposes it into convex sub-polygons P1, … , Pk and computes
the union of the sub-offsets (namely ∪i(Pi ⊕ Br)).
The decomposition is performed using the given decomposition strategy
decomp, which must be an instance of a class that models the
concept PolygonConvexDecomposition.
| Precondition: | P is a simple polygon. |
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