Spectral surface quadrangulation

Shen Dong, Peer Timo Bremer, Michael Garland, Valerio Pascucci, John C Hart

Research output: Contribution to journalConference article

Abstract

Resampling raw surface meshes is one of the most fundamental operations used by nearly all digital geometry processing systems. The vast majority of this work has focused on triangular remeshing, yet quadrilateral meshes are preferred for many surface PDE problems, especially fluid dynamics, and are best suited for defining Catmull-Clark subdivision surfaces. We describe a fundamentally new approach to the quadrangulation of manifold polygon meshes using Laplacian eigenfunctions, the natural harmonics of the surface. These surface functions distribute their extrema evenly across a mesh, which connect via gradient flow into a quadrangular base mesh. An iterative relaxation algorithm simultaneously refines this initial complex to produce a globally smooth parameterization of the surface. From this, we can construct a well-shaped quadrilateral mesh with very few extraordinary vertices. The quality of this mesh relies on the initial choice of eigenfunction, for which we describe algorithms and hueristics to efficiently and effectively select the harmonic most appropriate for the intended application.

Original languageEnglish (US)
Pages (from-to)1057-1066
Number of pages10
JournalACM Transactions on Graphics
Volume25
Issue number3
DOIs
StatePublished - Jul 1 2006
EventACM SIGGRAPH 2006 - Boston, MA, United States
Duration: Jul 30 2006Aug 3 2006

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Eigenvalues and eigenfunctions
Fluid dynamics
Parameterization
Geometry
Processing

Keywords

  • Laplacian eigenvectors
  • Morse theory
  • Morse-Smale complex
  • Quadrangular remeshing
  • Spectral mesh decomposition

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

Cite this

Dong, S., Bremer, P. T., Garland, M., Pascucci, V., & Hart, J. C. (2006). Spectral surface quadrangulation. ACM Transactions on Graphics, 25(3), 1057-1066. https://doi.org/10.1145/1141911.1141993

Spectral surface quadrangulation. / Dong, Shen; Bremer, Peer Timo; Garland, Michael; Pascucci, Valerio; Hart, John C.

In: ACM Transactions on Graphics, Vol. 25, No. 3, 01.07.2006, p. 1057-1066.

Research output: Contribution to journalConference article

Dong, S, Bremer, PT, Garland, M, Pascucci, V & Hart, JC 2006, 'Spectral surface quadrangulation', ACM Transactions on Graphics, vol. 25, no. 3, pp. 1057-1066. https://doi.org/10.1145/1141911.1141993
Dong S, Bremer PT, Garland M, Pascucci V, Hart JC. Spectral surface quadrangulation. ACM Transactions on Graphics. 2006 Jul 1;25(3):1057-1066. https://doi.org/10.1145/1141911.1141993
Dong, Shen ; Bremer, Peer Timo ; Garland, Michael ; Pascucci, Valerio ; Hart, John C. / Spectral surface quadrangulation. In: ACM Transactions on Graphics. 2006 ; Vol. 25, No. 3. pp. 1057-1066.
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