1 research outputs found
Reconstructing a Polyhedron between Polygons in Parallel Slices
Given two -vertex polygons, lying in the -plane
at , and lying in the -plane at , a
banded surface is a triangulated surface homeomorphic to an annulus connecting
and such that the triangulation's edge set contains vertex disjoint
paths connecting to for all . The surface
then consists of bands, where the th band goes between and
. We give a polynomial-time algorithm to find a banded surface
without Steiner points if one exists. We explore connections between banded
surfaces and linear morphs, where time in the morph corresponds to the
direction. In particular, we show that if and are convex and the
linear morph from to (which moves the th vertex on a straight line
from to ) remains planar at all times, then there is a banded
surface without Steiner points.Comment: preliminary version appeared in the Canadian Conference on
Computational Geometry (CCCG) 201