Single-Vertex Origami and Spherical Expansive Motions

  title={Single-Vertex Origami and Spherical Expansive Motions},
  author={I. Streinu and W. Whiteley},
  • I. Streinu, W. Whiteley
  • Published in JCDCG 2004
  • Mathematics, Computer Science
  • We prove that all single-vertex origami shapes are reachable from the open flat state via simple, non-crossing motions. We also consider conical paper, where the total sum of the cone angles centered at the origami vertex is not 2π. For an angle sum less than 2π, the configuration space of origami shapes compatible with the given metric has two components, and within each component, a shape can always be reconfigured via simple (non-crossing) motions. Such a reconfiguration may not always be… CONTINUE READING
    48 Citations

    Figures and Topics from this paper

    Explore Further: Topics Discussed in This Paper

    Flattening single-vertex origami: the non-expansive case
    • 3
    • PDF
    Flattening single-vertex origami: The non-expansive case
    • 4
    Acute Triangulations of Polygons
    • I. Streinu
    • Mathematics, Computer Science
    • Discret. Comput. Geom.
    • 2005
    • 55
    • PDF
    On rigid origami I: piecewise-planar paper with straight-line creases
    • Zeyuan He, S. Guest
    • Mathematics, Computer Science
    • Proceedings of the Royal Society A
    • 2019
    • 6
    • Highly Influenced
    • PDF
    Modelling rigid origami with quaternions and dual quaternions
    • Weina Wu, Z. You
    • Mathematics
    • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    • 2010
    • 88
    • PDF
    Branches of Triangulated Origami Near the Unfolded State
    • 21
    • PDF
    Folding Equilateral Plane Graphs
    • 2
    • PDF
    A Generalized Carpenter's Rule Theorem for Self-Touching Linkages
    • 11
    • PDF
    Designing Freeform Origami Tessellations by Generalizing Resch's Patterns
    • 65
    • PDF
    • 13


    Blowing Up Polygonal Linkages
    • 52
    • PDF
    A combinatorial approach to planar non-colliding robot arm motion planning
    • I. Streinu
    • Mathematics, Computer Science
    • Proceedings 41st Annual Symposium on Foundations of Computer Science
    • 2000
    • 175
    • PDF
    Straightening polygonal arcs and convexifying polygonal cycles
    • 172
    • PDF
    Locked and Unlocked Polygonal Chains in Three Dimensions
    • 40
    • PDF
    On the Moduli Space of a Spherical Polygonal Linkage
    • 28
    • PDF
    Expansive Motions and the Polytope of Pointed Pseudo-Triangulations
    • 110
    • PDF
    A computational algorithm for origami design
    • 175
    • PDF