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Erschienen in:
2012 | OriginalPaper | Buchkapitel
-Based 1-Form Subdivision
verfasst von : Jinghao Huang, Peter Schröder
Erschienen in: Curves and Surfaces
Verlag: Springer Berlin Heidelberg
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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.