Efficient evaluation of multivariate polynomials
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.
scientific article; zbMATH DE number 3980352