Abstract: Triangular surface and progressive iterative algorithm have important application in fitting scatted data points and reverse engineering, this paper studies weighted progressive iterative algorithm for fourth-order triangular T-Bézier surface. It presents the weighted progressive iterative algorithm and analyzes the convergence of this algorithm, and the weighted progressive iterative algorithm approximation errors in [L1]-norm、[L2]-norm and [L∞]-norm are calculated. It also presents the extended weighted progressive iterative algorithm, according to that different control points give different weight factor to speed up the convergence speed. Some numerical examples are given to illustrate the effectiveness and its application of this algorithm.

Key words: computer aided design, weighted progressive iterative, triangular T-Bézier surface, fitting scatted data points, approximation error

摘要： 三角曲面和渐进迭代逼近在散乱点数据的拟合及逆向工程中有重要应用，研究了四阶T-Bézier三角曲面的带权渐进迭代算法。给出了带权渐进迭代算法，分析了算法的收敛性，并基于1-范数、2-范数和∞-范数分别给出了带权渐进迭代算法的逼近误差;针对不同的控制顶点赋予不同权值以加快收敛速度，给出了推广的带权渐进迭代算法;数值实例说明了算法的有效性及其应用。

关键词: 计算机辅助设计, 带权渐进迭代, T-Bé, zier三角曲面, 散乱点数据拟合, 逼近误差