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A Hermite interpolatory subdivision scheme for C2-quintics on the Powell-Sabin 12-split

Lyche, Tom; Muntingh, Agnar Georg Peder
Journal article, Peer reviewed
Accepted version
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URI
http://hdl.handle.net/11250/2472670
Date
2014
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Original version
Computer Aided Geometric Design. 2014, 31 (7-8), 464-474.   10.1016/j.cagd.2014.03.004
Abstract
In order to construct a C1C1-quadratic spline over an arbitrary triangulation, one can split each triangle into 12 subtriangles, resulting in a finer triangulation known as the Powell–Sabin 12-split. It has been shown previously that the corresponding spline surface can be plotted quickly by means of a Hermite subdivision scheme (Dyn and Lyche, 1998). In this paper we introduce a nodal macro-element on the 12-split for the space of quintic splines that are locally C3C3 and globally C2C2. For quickly evaluating any such spline, a Hermite subdivision scheme is derived, implemented, and tested in the computer algebra system Sage. Using the available first derivatives for Phong shading, visually appealing plots can be generated after just a couple of refinements
Journal
Computer Aided Geometric Design

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