Paper by Erik D. Demaine

Reference:

Akira Baes, Erik D. Demaine, Martin L. Demaine, Elizabeth Hartung, Stefan Langerman, Joseph O'Rourke, Ryuhei Uehara, Yushi Uno, and Aaron Williams, “Rolling Polyhedra on Tessellations”, in Proceedings of the 11th International Conference on Fun with Algorithms (FUN 2022), Favignana, Italy, May 30–June 3, 2022, 5:1–5:16.

BibTeX

@InProceedings{Rolling_FUN2022,
  AUTHOR        = {Akira Baes and Erik D. Demaine and Martin L. Demaine and Elizabeth Hartung and Stefan Langerman and Joseph O'Rourke and Ryuhei Uehara and Yushi Uno and Aaron Williams},
  TITLE         = {Rolling Polyhedra on Tessellations},
  BOOKTITLE     = {Proceedings of the 11th International Conference on Fun with Algorithms (FUN 2022)},
  bookurl       = {https://sites.google.com/view/fun2022/home},
  ADDRESS       = {Favignana, Italy},
  MONTH         = {May 30--June 3},
  YEAR          = 2022,
  PAGES         = {5:1--5:16},

  withstudent   = 1,
  doi           = {https://dx.doi.org/10.4230/LIPIcs.FUN.2022.6},
  dblp          = {https://dblp.org/rec/conf/fun/BaesDDHLOUUW22},
  comments      = {This paper is also available from <A HREF="https://doi.org/10.4230/LIPIcs.FUN.2022.6">LIPIcs</A>.},
}

Abstract:

We study the space reachable by rolling a 3D convex polyhedron on a 2D periodic tessellation in the xy-plane, where at every step a face of the polyhedron must coincide exactly with a tile of the tessellation it rests upon, and the polyhedron rotates around one of the incident edges of that face until the neighboring face hits the xy plane. If the whole plane can be reached by a sequence of such rolls, we call the polyhedron a plane roller for the given tessellation. We further classify polyhedra that reach a constant fraction of the plane, an infinite area but vanishing fraction of the plane, or a bounded area as hollow-plane rollers, band rollers, and bounded rollers respectively. We present a polynomial-time algorithm to determine the set of tiles in a given periodic tessellation reachable by a given polyhedron from a given starting position, which in particular determines the roller type of the polyhedron and tessellation. Using this algorithm, we compute the reachability for every regular-faced convex polyhedron on every regular-tiled (≤ 4)-uniform tessellation.

Comments:

This paper is also available from LIPIcs.

Availability:

The paper is available in PDF (2971k).

See information on file formats.

[Google Scholar search]