Monday, April 07, 2014

[oyulkuqd] Perturbed polygons and polyhedra

Given a polygon, perturb its vertices while maintaining a constraint that none of the edges intersect.  Perhaps also keep all the vertices within a unit disc.  The motivation was to continuously sample among all possible polygons of a given number of vertices.

In three dimensions, easy is if all the faces are triangles.  If not triangles, then difficult seems to be, when a perturbation causes a face with 4 or more vertices to no longer be planar, to construct a minimal surface within a boundary of straight edges, then forbid those surface faces from intersecting.

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