Corpus ID: 1999009

Conical Existence of Closed Curves on Convex Polyhedra

  title={Conical Existence of Closed Curves on Convex Polyhedra},
  author={J. O'Rourke and C. V{\^i}lcu},
  • J. O'Rourke, C. Vîlcu
  • Published 2011
  • Mathematics, Computer Science
  • ArXiv
  • 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 Lambda, with the apex a of Lambda enclosed inside (the image of) C; we also prove that each point of C is "visible to" a. In particular, we obtain that these curves have non-self-intersecting developments in the plane. Moreover, the curves we… CONTINUE READING
    3 Citations
    Source Unfoldings of Convex Polyhedra via Certain Closed Curves
    • 1
    • PDF
    Development of Curves on Polyhedra via Conical Existence
    • 6
    • PDF
    A Generalization of the Source Unfolding of Convex Polyhedra
    • 4
    • PDF


    On the development of the intersection of a plane with a polytope
    • 16
    • PDF
    Star Unfolding Convex Polyhedra via Quasigeodesic Loops
    • 15
    • PDF
    Source unfoldings of convex polyhedra with respect to certain closed polygonal curves
    • In Proc. 25th European Workshop Comput. Geom.,
    • 2009
    Geometric Folding Algorithms: Linkages
    • 135
    On Convex Polyhedra
    • 172