A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Progressive geometry compression
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
CHARMS: a simple framework for adaptive simulation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Composite primal/dual √3-subdivision schemes
Computer Aided Geometric Design
Stationary subdivision and multiresolution surface representations
Stationary subdivision and multiresolution surface representations
Edge subdivision schemes and the construction of smooth vector fields
ACM SIGGRAPH 2006 Papers
Subdivision Surfaces
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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.