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) |
|---|---|
| Title of host publication | ACM SIGGRAPH 2006 Papers, SIGGRAPH '06 |
| Pages | 1057-1066 |
| Number of pages | 10 |
| DOIs | |
| State | Published - Dec 1 2006 |
| Event | ACM SIGGRAPH 2006 Papers, SIGGRAPH '06 - Boston, MA, United States Duration: Jul 30 2006 → Aug 3 2006 |
Publication series
| Name | ACM SIGGRAPH 2006 Papers, SIGGRAPH '06 |
|---|
Other
| Other | ACM SIGGRAPH 2006 Papers, SIGGRAPH '06 |
|---|---|
| Country | United States |
| City | Boston, MA |
| Period | 7/30/06 → 8/3/06 |
Fingerprint
Keywords
- Morse theory
- Morse-Smale complex
- laplacian eigenvectors
- quadrangular remeshing
- spectral mesh decomposition
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Computer Vision and Pattern Recognition
- Software
Cite this
Spectral surface quadrangulation. / Dong, Shen; Bremer, Peer Timo; Garland, Michael; Pascucci, Valerio; Hart, John C.
ACM SIGGRAPH 2006 Papers, SIGGRAPH '06. 2006. p. 1057-1066 (ACM SIGGRAPH 2006 Papers, SIGGRAPH '06).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Spectral surface quadrangulation
AU - Dong, Shen
AU - Bremer, Peer Timo
AU - Garland, Michael
AU - Pascucci, Valerio
AU - Hart, John C
PY - 2006/12/1
Y1 - 2006/12/1
N2 - 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.
AB - 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.
KW - Morse theory
KW - Morse-Smale complex
KW - laplacian eigenvectors
KW - quadrangular remeshing
KW - spectral mesh decomposition
UR - http://www.scopus.com/inward/record.url?scp=34248397312&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34248397312&partnerID=8YFLogxK
U2 - 10.1145/1179352.1141993
DO - 10.1145/1179352.1141993
M3 - Conference contribution
AN - SCOPUS:34248397312
SN - 1595933646
SN - 9781595933645
T3 - ACM SIGGRAPH 2006 Papers, SIGGRAPH '06
SP - 1057
EP - 1066
BT - ACM SIGGRAPH 2006 Papers, SIGGRAPH '06
ER -