Published July 2016
| public
Journal Article
Subdivision exterior calculus for geometry processing
Abstract
This paper introduces a new computational method to solve differential equations on subdivision surfaces. Our approach adapts the numerical framework of Discrete Exterior Calculus (DEC) from the polygonal to the subdivision setting by exploiting the refin-ability of subdivision basis functions. The resulting Subdivision Exterior Calculus (SEC) provides significant improvements in accuracy compared to existing polygonal techniques, while offering exact finite-dimensional analogs of continuum structural identities such as Stokes' theorem and Helmholtz-Hodge decomposition. We demonstrate the versatility and efficiency of SEC on common geometry processing tasks including parameterization, geodesic distance computation, and vector field design.
Additional Information
© 2016 ACM. We thank Daniel Garcia for his help in Fig. 7, and David Yu for his help in Fig. 8. We also acknowledge Noam Aigerman, Peter Schröder, Rasmus Tamstorf, and Ke Wang for early discussions, and Yiying Tong for his help with the final version. Meshes are courtesy of Bay Raitt (Car, Big guy, and MonsterFrog), Hugues Hoppe (Mannequin), and Giorgio Marcias (Torso). MD was partially supported through NSF grant CCF-1011944.Additional details
- Eprint ID
- 72346
- DOI
- 10.1145/2897824.2925880
- Resolver ID
- CaltechAUTHORS:20161128-155742047
- CCF-1011944
- NSF
- Created
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2016-11-29Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field