ﻻ يوجد ملخص باللغة العربية
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 that Q lives on a cone to both sides; it includes simple, closed quasigeodesics. Cutting a particular subset of the cut locus of Q (in P) leads to a non-overlapping unfolding of the polyhedron. This gives a new general method to unfold the surface of any convex polyhedron to a simple, planar polygon.
Let C be a simple, closed, directed curve on the surface of a convex polyhedron P. We identify several classes of curves C that live on a cone, in the sense that C and a neighborhood to one side may be isometrically embedded on the surface of a cone
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, P has (in general) n+1 vertices. We show there are in fact a continuu
The construction of an unbounded polyhedron from a jagged convex cap is described, and several of its properties discussed, including its relation to Alexandrovs limit angle.
We solve an open problem posed by Michael Biro at CCCG 2013 that was inspired by his and others work on beacon-based routing. Consider a human and a puppy on a simple closed curve in the plane. The human can walk along the curve at bounded speed and
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 new convex polyhedron via Alexandrovs Gluing Theorem. In particular, a d