Efficient and Accurate Evaluation of Bézier Tensor Product Surfaces

Abstract

This article proposes a bivariate compensated Volk and Schumaker (CompVSTP) algorithm, which extends the compensated Volk and Schumaker (CompVS) algorithm, to evaluate Bèzier tensor product surfaces with floating-point coefficients and coordinates. The CompVSTP algorithm is obtained by applying error-free transformations to improve the traditional Volk and Schumaker tensor product (VSTP) algorithm. We study in detail the forward error analysis of the VSTP, CompVS and CompVSTP algorithms. Our numerical experiments illustrate that the Comp-VSTP algorithm is much more accurate than the VSTP algorithm, relegating the influence of the condition numbers up to second order in the rounding unit of the computer.