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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.
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| Precondition: | The range [first,beyond) contains the vertices
of a non-degenerate strictly-simple 2D polygon. |
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