Approximate implicitization of triangular Bézier surfaces

Oliver J. D. Barrowclough, Tor Dokken
2010 Proceedings of the 26th Spring Conference on Computer Graphics - SCCG '10  
We discuss how Dokken's methods of approximate implicitization can be applied to triangular Bézier surfaces in both the original and weak forms. The matrices D and 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
more » ... reduce the computation time of M. Explicit examples are presented to compare the methods and to demonstrate properties of the approximations.
doi:10.1145/1925059.1925084 dblp:conf/sccg/BarrowcloughD10 fatcat:r5zo6qxqmzc2fngdhc6wxu42tm