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Designing Quadrangulations with Discrete Harmonic Forms

Tong, Y. and Alliez, P. and Cohen-Steiner, D. and Desbrun, M. (2006) Designing Quadrangulations with Discrete Harmonic Forms. In: SGP06: Eurographics Symposium on Geometry Processing. The Eurographics Association , Aire-la-Ville, Switzerland, pp. 201-210. ISBN 3-905673-36-3.

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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.

Item Type:Book Section
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Desbrun, M.0000-0003-3424-6079
Additional Information:© 2006 The Eurographics Association. The authors wish to thank Peter Schröder for his continuous help, and Alex McKenzie for his helpful comments. Sponsors include NSF (CAREER CCR-0133983, and ITR DMS-0453145), DOE (DE-FG02-04ER25657), and the EU Network of Excellence AIM@SHAPE (IST NoE No 506766).
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-04ER25657
European Research Council (ERC)506766
Record Number:CaltechAUTHORS:20170103-153308794
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73186
Deposited By: Kristin Buxton
Deposited On:04 Jan 2017 16:53
Last Modified:03 Mar 2020 13:01

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