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- W1620001418 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 formule 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." @default.
- W1620001418 created "2016-06-24" @default.
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- W1620001418 date "2012-01-01" @default.
- W1620001418 modified "2023-09-28" @default.
- W1620001418 title "$sqrt{3}$ -Based 1-Form Subdivision" @default.
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- W1620001418 doi "https://doi.org/10.1007/978-3-642-27413-8_22" @default.
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