√3-Based 1-Form Subdivision
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.
Additional Information
© 2012 Springer-Verlag Berlin Heidelberg.Additional details
- Eprint ID
- 32721
- DOI
- 10.1007/978-3-642-27413-8_22
- Resolver ID
- CaltechAUTHORS:20120725-131858923
- Created
-
2012-07-26Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field
- Series Name
- Lecture Notes in Computer Science
- Series Volume or Issue Number
- 6920