The function compute_outer_frame_margin computes the separation required between a polygon and the outer frame used to obtain an exterior skeleton suitable for the computation of outer offset polygons at a given distance.
#include <CGAL/compute_outer_frame_margin.h>
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Given a non-degenerate strictly-simple 2D polygon whose vertices are passed
in the range [first,beyond), calculates the largest euclidean distance
d between each input vertex and its corresponding offset vertex at
a distance offset. If such a distance can be approximately computed, returns an optional<FT> with the value d + (offset * 1.05). If the distance cannot be computed, not even approximately, due to overflow for instance, returns an empty optional<FT> (an absent result). This result is the required separation between the input polygon and the rectangular frame used to construct an exterior offset contour at distance offset (which is done by placing the polygon as a hole of that frame). Such a separation must be computed in this way because if the frame is too close to the polygon, the inward offset contour from the frame could collide with the outward offset contour of the polygon, resulting in a merged contour offset instead of two contour offsets, one of them corresponding to the frame. Simply using 2*offset as the separation is incorrect since offset is the distance between an offset line and its original, not between an offset vertex and its original. The later, which is calculated by this function and needed to place the frame sufficiently away from the polygon, can be thousands of times larger than offset. If the result is absent, any attempt to construct an exterior offset polygon at distance offset will fail. This will occur whenever the polygon has a vertex with an internal angle approaching 0 (because the offset vertex of a vertex whose internal angle equals 0 is at infinity ). Precondition: offset $$> 0. Precondition: The range [first,beyond) contains the vertices of a non-degenerate strictly-simple 2D polygon. |
The default traits class Default_traits is an instance of the class Polygon_offset_builder_traits_2<Kernel> parameterized on the kernel in which the type InputIterator::value_type is defined.