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arXiv · 1707.01255

Approximate Implicitization of Triangular B\'ezier Surfaces

Oliver J. D. Barrowclough·Tor Dokken
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Abstract

We discuss how Dokken's methods of approximate implicitization can be applied to triangular B\'ezier surfaces in both the original and weak forms. The matrices $\mathbf{D}$ and $\mathbf{M}$ that are fundamental to the respective forms of approximate implicitization are shown to be constructed essentially by repeated multiplication of polynomials and by matrix multiplication. A numerical approach to weak approximate implicitization is also considered and we show that symmetries within this algorithm can be exploited to reduce the computation time of $\mathbf{M}.$ Explicit examples are presented to compare the methods and to demonstrate properties of the approximations.

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BibTeXRIS

Oliver J. D. Barrowclough, Tor Dokken. 2017-07-05. Approximate Implicitization of Triangular B\'ezier Surfaces. https://doi.org/10.1145/1925059.1925084

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