Designing Quadrangulations with Discrete Harmonic Forms

Tong, Y.; Alliez, P.; Cohen-Steiner, D.; Desbrun, M.

Designing Quadrangulations with Discrete Harmonic Forms

Files

201-210.pdf (1.1 MB)

Date

2006

Authors

Tong, Y.
Alliez, P.
Cohen-Steiner, D.
Desbrun, M.

Publisher

The Eurographics Association

Abstract

We introduce a framework for quadrangle meshing of discrete manifolds. Based on discrete differential forms, our method hinges on extending the discrete Laplacian operator (used extensively in modeling and animation) to allow for line singularities and singularities with fractional indices. When assembled into a singularity graph, these line singularities are shown to considerably increase the design flexibility of quad meshing. In particular, control over edge alignments and mesh sizing are unique features of our novel approach. Another appeal of our method is its robustness and scalability from a numerical viewpoint: we simply solve a sparse linear system to generate a pair of piecewise-smooth scalar fields whose isocontours form a pure quadrangle tiling, with no T-junctions.

        @inproceedings{:10.2312/SGP/SGP06/201-210
,
booktitle = {Symposium on Geometry Processing
},
editor = {Alla Sheffer and Konrad Polthier
},
title = {{Designing Quadrangulations with Discrete Harmonic Forms
}},
author = {Tong, Y. and 
Alliez, P. and 
Cohen-Steiner, D. and 
Desbrun, M.
},
year = {2006
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-24-X
},
DOI = {/10.2312/SGP/SGP06/201-210
}
}