A Hermite interpolatory subdivision scheme for $C^2$-quintics on the Powell-Sabin 12-split
Abstract
In order to construct a -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. In this paper we introduce a nodal macro-element on the 12-split for the space of quintic splines that are locally and globally . 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
Cite
@article{arxiv.1312.0030,
title = {A Hermite interpolatory subdivision scheme for $C^2$-quintics on the Powell-Sabin 12-split},
author = {Tom Lyche and Georg Muntingh},
journal= {arXiv preprint arXiv:1312.0030},
year = {2015}
}
Comments
17 pages, 7 figures