Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6876714 | Computer Aided Geometric Design | 2014 | 11 Pages |
Abstract
In order to construct a C1-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 C3 and globally C2. 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.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Graphics and Computer-Aided Design
Authors
Tom Lyche, Georg Muntingh,