Star Unfolding Convex Polyhedra via Quasigeodesic Loops

Details Star Unfolding Convex Polyhedra via Quasigeodesic Loops Star Unfolding Convex Polyhedra via Quasigeodesic Loops

2007-07-28

arxiv.org/abs/0707.4258v4

Computer Science

Computational Geometry

10 pages, 7 figures. v2 improves the description of cut locus, and adds references. v3 improves two figures and their captions

Scientific paper

We extend the notion of star unfolding to be based on a quasigeodesic loop Q
rather than on a point. This gives a new general method to unfold the surface
of any convex polyhedron P to a simple (non-overlapping), planar polygon: cut
along one shortest path from each vertex of P to Q, and cut all but one segment
of Q.

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