Huang, Jinghao and Schröder, Peter (2012) √3-Based 1-Form Subdivision. In: 7th International Conference, Avignon, France, June 24-30, 2010, Revised Selected Papers. Lecture Notes in Computer Science. No.6920. Springer-Verlag , Berlin, Germany, pp. 351-368. ISBN 978-3-642-27412-1. https://resolver.caltech.edu/CaltechAUTHORS:20120725-131858923
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Abstract
In this paper we construct an edge based, or 1-form, subdivision scheme consistent with √3 subdivision. It produces smooth differential 1-forms in the limit. These can be identified with tangent vector fields, or viewed as edge elements in the sense of finite elements. In this construction, primal (0-form) and dual (2-form) subdivision schemes for surfaces are related through the exterior derivative with an edge (1-form) based subdivision scheme, amounting to a generalization of the well known formulé de commutation. Starting with the classic √3 subdivision scheme as a 0-form subdivision scheme, we derive conditions for appropriate 1- and 2-form subdivision schemes without fixing the dual (2-form) subdivision scheme a priori. The resulting degrees of freedom are resolved through spectrum considerations and a conservation condition analogous to the usual moment condition for primal subdivision schemes.
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 2012 Springer-Verlag Berlin Heidelberg. | |||||||||
| Subject Keywords: | Discrete exterior calculus; √3-subdivision; 1- and 2-form subdivision; tangent vector field generation | |||||||||
| Series Name: | Lecture Notes in Computer Science | |||||||||
| Issue or Number: | 6920 | |||||||||
| DOI: | 10.1007/978-3-642-27413-8_22 | |||||||||
| Record Number: | CaltechAUTHORS:20120725-131858923 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120725-131858923 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 32721 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Aucoeur Ngo | |||||||||
| Deposited On: | 26 Jul 2012 23:35 | |||||||||
| Last Modified: | 09 Nov 2021 21:29 |
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