$\sqrt{3}$-Based 1-Form Subdivision
Identifieur interne : 000025 ( Main/Exploration ); précédent : 000024; suivant : 000026$\sqrt{3}$-Based 1-Form Subdivision
Auteurs : Jinghao Huang [États-Unis] ; Peter Schröder [États-Unis]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2012.
Abstract
Abstract: In this paper we construct an edge based, or 1-form, subdivision scheme consistent with $\sqrt{3}$ 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 $\sqrt{3}$ 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.
Url:
DOI: 10.1007/978-3-642-27413-8_22
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