6 citations · 29 across the 16 of their papers we have counts for
5 papers · 1 filter
Skeletal Cut Loci on Convex Polyhedra
Joseph O'Rourke, Costin Vilcu
On a convex polyhedron P, the cut locus C(x) with respect to a point x is a tree of geodesic segments (shortest paths) on P that includes every vertex. We say that P has a skeletal…
Cut Locus Realizations on Convex Polyhedra
Joseph O'Rourke, Costin Vîlcu
We prove that every positively-weighted tree T can be realized as the cut locus C(x) of a point x on a convex polyhedron P, with T weights matching C(x) lengths. If T has n leaves,…
Source Unfoldings of Convex Polyhedra via Certain Closed Curves
Jin-ichi Itoh, Joseph O'Rourke, Costin Vilcu
We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires…
Unfolding Convex Polyhedra via Quasigeodesic Star Unfoldings
Jin-ichi Itoh, Joseph O'Rourke, Costin Vîlcu
We extend the notion of a star unfolding to be based on a simple quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex po…
Star Unfolding Convex Polyhedra via Quasigeodesic Loops
Jin-ichi Itoh, Joseph O'Rourke, Costin Vîlcu
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…