Regular Meshes from Polygonal Patterns

Amir Vaxman, Christian Müller, Ofir Weber

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We present a framework for designing shapes from diverse combinatorial patterns, where the vertex 1-rings and the faces are as rotationally symmetric as possible, and define such meshes as regular. Our algorithm computes the geometry that brings out the symmetries encoded in the combinatorics. We then allow designers and artists to envision and realize original meshes with great aesthetic qualities. Our method is general and applicable to meshes of arbitrary topology and connectivity, from triangle meshes to general polygonal meshes. The designer controls the result by manipulating and constraining vertex positions. We offer a novel characterization of regularity, using quaternionic ratios of mesh edges, and optimize meshes to be as regular as possible according to this characterization. Finally, we provide a mathematical analysis of these regular meshes, and show how they relate to concepts like the discrete Willmore energy and connectivity shapes.
Original languageEnglish
Article number113
Number of pages15
JournalACM Transactions on Graphics
Volume36
Issue number4
DOIs
Publication statusPublished - 20 Jul 2017
EventSiggraph 2017 - Los Angeles, United States
Duration: 30 Jul 20173 Aug 2017
http://s2017.siggraph.org/

Keywords / Materials (for Non-textual outputs)

  • möbius transformations
  • polygonal patterns
  • architectural geometry
  • regular meshes

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