6 citations · 29 across the 16 of their papers we have counts for
26 papers
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…
Simple Closed Quasigeodesics on Tetrahedra
Joseph O'Rourke, Costin Vilcu
Pogorelov proved in 1949 that every every convex polyhedron has at least three simple closed quasigeodesics. Whereas a geodesic has exactly pi surface angle to either side at each…
Reshaping Convex Polyhedra
Joseph O'Rourke, Costin Vilcu
Given a convex polyhedral surface P, we define a tailoring as excising from P a simple polygonal domain that contains one vertex v, and whose boundary can be sutured closed to a ne…
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,…
Tailoring for Every Body: Reshaping Convex Polyhedra
Joseph O'Rourke, Costin Vilcu
Given any two convex polyhedra P and Q, we prove as one of our main results that the surface of P can be reshaped to a homothet of Q by a finite sequence of "tailoring" steps. Each…
Locating diametral points
Jin-ichi Itoh, Costin Vîlcu, Liping Yuan +1
Let be a convex body in , with . We determine sharp sufficient conditions for a set composed of , , or points of , to contain a…