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 language | English (US) |
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Pages (from-to) | 1057-1066 |
Number of pages | 10 |
Journal | ACM Transactions on Graphics |
Volume | 25 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2006 |
Event | ACM SIGGRAPH 2006 - Boston, MA, United States Duration: Jul 30 2006 → Aug 3 2006 |
Keywords
- Laplacian eigenvectors
- Morse theory
- Morse-Smale complex
- Quadrangular remeshing
- Spectral mesh decomposition
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design