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√3-Based 1-Form Subdivision

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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/978-3-642-27413-8_22DOIArticle
https://rdcu.be/b3YgxPublisherFree ReadCube access
ORCID:
AuthorORCID
Schröder, Peter0000-0002-0323-7674
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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