On linear spaces of polyhedral meshes

Roi Poranne, Renjie Chen, Craig Gotsman

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Polyhedral meshes (PM) -meshes having planar faces -have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate. Previous methods start with a smooth surface and then apply elaborate meshing schemes to create polyhedral meshes approximating the surface. In this paper, we describe a reverse approach: given the topology of a mesh, we explore the space of possible planar meshes having that topology. Our approach is based on a complete characterization of the maximal linear spaces of polyhedral meshes contained in the curved manifold of polyhedral meshes with a given topology. We show that these linear spaces can be described as nullspaces of differential operators, much like harmonic functions are nullspaces of the Laplacian operator. An analysis of this operator provides tools for global and local design of a polyhedral mesh, which fully expose the geometric possibilities and limitations of the given topology.

Original languageEnglish (US)
Article number7006805
Pages (from-to)652-662
Number of pages11
JournalIEEE Transactions on Visualization and Computer Graphics
Volume21
Issue number5
DOIs
StatePublished - May 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design

Keywords

  • Polyhedral meshes

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