Accurate, Validated and Fast Evaluation of Bézier Tensor Product Surfaces

This paper proposes a compensated algorithm to evaluate Bézier tensor product surfaces with floating-point coefficients and coordinates. This algorithm is based on the application of error-free transformations to improve the traditional de Casteljau tensor product algorithm. This compensated algorithm extends the compensated de Casteljau algorithm for the evaluation of a Bézier curve to the case of tensor product surfaces. Forward error analysis and numerical experiments illustrate the accuracy and efficiency of the proposed algorithm.