Farin, G.; Piper, B.; Worsey, A. J. The octant of a sphere as a non-degenerate triangular Bézier patch. (English) Zbl 0646.41011 Comput. Aided Geom. Des. 4, 329-332 (1987). Summary: We construct a symmetric rational quartic map from the standard triangle onto an octant of a sphere. The surface is non-degenerate: all Bézier points are distinct and their associated weights are positive. Cited in 17 Documents MSC: 41A20 Approximation by rational functions Keywords:stereographic projection; rational Bézier triangles; Bézier points; weights PDFBibTeX XMLCite \textit{G. Farin} et al., Comput. Aided Geom. Des. 4, 329--332 (1987; Zbl 0646.41011) Full Text: DOI References: [1] Farin, G., Triangular Bernstein-Bézier patches, Computer Aided Geometric Design, 3, 2, 83-127 (1986) [2] Farouki, R. T., Exact offset procedures for simple solids, Computer Aided Geometric Design, 2, 4, 257-279 (1985) · Zbl 0583.65095 [3] Piegl, L., The sphere as a rational Bézier surface, Computer Aided Geometric Design, 3, 1, 45-52 (1986) · Zbl 0631.65013 [4] Piegl, L., Less data for shapes, IEEE Computer Graphics and Applications, 7, 48-50 (1987) [5] Worsey, A. J.; Piper, B., A trivariate Powell-Sabin interpolant, Computer Aided Geometric Design (1987), submitted for publication · Zbl 0654.65008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.