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Discrete multiscale vector field decomposition

Tong, Yiying and Lombeyda, Santiago and Hirani, Anil N. and Desbrun, Mathieu (2003) Discrete multiscale vector field decomposition. In: SIGGRAPH '03 ACM SIGGRAPH 2003 Papers. ACM , New York, NY, pp. 445-452. ISBN 1-58113-709-5. https://resolver.caltech.edu/CaltechAUTHORS:20170103-154427060

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Abstract

While 2D and 3D vector fields are ubiquitous in computational sciences, their use in graphics is often limited to regular grids, where computations are easily handled through finite-difference methods. In this paper, we propose a set of simple and accurate tools for the analysis of 3D discrete vector fields on arbitrary tetrahedral grids. We introduce a variational, multiscale decomposition of vector fields into three intuitive components: a divergence-free part, a curl-free part, and a harmonic part. We show how our discrete approach matches its well-known smooth analog, called the Helmotz-Hodge decomposition, and that the resulting computational tools have very intuitive geometric interpretation. We demonstrate the versatility of these tools in a series of applications, ranging from data visualization to fluid and deformable object simulation.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/1201775.882290DOIArticle
http://dl.acm.org/citation.cfm?doid=1201775.882290PublisherArticle
ORCID:
AuthorORCID
Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2003 ACM. The authors are extremely grateful to Peter Schröder for support, Konrad Polthier for inspiration, Rüdiger Westerman for data, John McCorquodale for feedback, and Alain Bossavit and Melvin Leok for collaboration. This work was supported in part by the NSF (CCR-0133983, DMS-0221666, DMS-0221669, EEC-9529152).
Funders:
Funding AgencyGrant Number
NSFCCR-0133983
NSFDMS-0221666
NSFDMS-0221669
NSFEEC-9529152
DOI:10.1145/1201775.882290
Record Number:CaltechAUTHORS:20170103-154427060
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170103-154427060
Official Citation:Yiying Tong, Santiago Lombeyda, Anil N. Hirani, and Mathieu Desbrun. 2003. Discrete multiscale vector field decomposition. In ACM SIGGRAPH 2003 Papers (SIGGRAPH '03). ACM, New York, NY, USA, 445-452. DOI: http://dx.doi.org/10.1145/1201775.882290
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73188
Collection:CaltechAUTHORS
Deposited By:INVALID USER
Deposited On:04 Jan 2017 16:48
Last Modified:11 Nov 2021 05:12

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