6 citations · 29 across the 16 of their papers we have counts for
15 papers · 1 filter
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…
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…
Some inequalities for tetrahedra
Jin-ichi Itoh, Joël Rouyer, Costin Vîlcu
We prove inequalities involving intrinsic and extrinsic radii and diameters of tetrahedra.
Farthest points on flat surfaces
Joël Rouyer, Costin Vîlcu
We consider the distance function from an arbitrary point on a flat surface, and determine the set of all \emph{farthest points} (i.e., points at maximal distance) from…