Error analysis of efficient evaluation algorithms for tensor product surfaces

Backward stability of the Casteljau algorithm and two more efficient algorithms for polynomial tensor product surfaces with interest in CAGD is shown. The conditioning of the corresponding bases are compared. These algorithms are also compared with the corresponding Horner algorithm and their higher accuracy is shown. A running error analysis of the algorithms is also carried out providing algorithms which calculate “a posteriori” sharp error bounds simultaneously to the evaluation of the surface without increasing significantly the computational cost.