Schumaker, Larry L.; Volk, Wolfgang Efficient evaluation of multivariate polynomials. (English) Zbl 0606.65007 Comput. Aided Geom. Des. 3, 149-154 (1986). The authors give an algorithm to evaluate a polynomial of total degree d defined on a triangle T in the plane, \[ p(r,s,t)=\sum^{d}_{i=0}\sum^{i}_{j=0}c_{d-i,i-j,j}\cdot r^{d- i}s^{i-j}t^ j, \] where \(c_{d-i,i-j,j}=(d!/(d-i)!(i-j)!j!)b_{d- i,i-j,j}\), \(0\leq j\leq i\), \(0\leq i\leq d\), and (r,s,t) are the barycentric coordinates of each point in T, and \(b_{ijk}\) are the coefficients in the algorithm of de Casteljau. This algorithm is significantly faster than de Casteljau. Reviewer: A.López-Carmona Cited in 1 ReviewCited in 25 Documents MSC: 65D10 Numerical smoothing, curve fitting 41A10 Approximation by polynomials 65D20 Computation of special functions and constants, construction of tables 41A63 Multidimensional problems Keywords:de Casteljau algorithm; data fitting; Bernstein-Bézier methods; surfaces; polynomial evaluation PDFBibTeX XMLCite \textit{L. L. Schumaker} and \textit{W. Volk}, Comput. Aided Geom. Des. 3, 149--154 (1986; Zbl 0606.65007) Full Text: DOI References: [1] Boehm, W.; Farin, G.; Kahmann, J., A survey of curve and surface methods in CAGD, Computer Aided Geometric Design, 1, 1-60 (1984) · Zbl 0604.65005 [2] de Casteljau, F., Courbes et surfaces à pôles (1963), André Citröen Automobiles: André Citröen Automobiles Paris [3] Schumaker, L. L., Numerical aspects of spaces of piecewise polynomials on triangulations, (Mason, J., Proceedings of Shrivenham Conference on Approximation Theory (1986)) · Zbl 0628.65008 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.