Convexifying polygons with simple projections
It is known that not all polygons in 3D can be convexified when crossing edges are not permitted during any motion. in this paper we prove that if a 3D polygon admits a non-crossing orthogonal projection onto some plane, then the 3D polygon can be convexified. If an algorithm to convexify the planar projection exists and runs in time P, then our algorithm to convexify the 3D polygon runs in O(n + P) time. (C) 2001 Elsevier Science B.V. All rights reserved.
convexification of polygons linkage reconfiguration simple orthogonal projections computational geometry motion planning polymer physics computational biology