In this thesis , basic subdivision schemes and its adaptive schemes in cad , together with the algorithm which is about triangle mesh model fitting loop subdivision surface , are studied in depth . then a software system based on subdivision surface is developed , and these algorithms are integrated in it . the main work is as follows : ( 1 ) subdivision theories and typical subdivision schemes are analyzed 本文先对基本细分算法及其在cad中的自适应细分算法和三角网格模型拟合loop细分曲面算法进行了比较深入的研究，最后将其集成开发出一个基于细分曲面的软件系统，主要内容包括： ( 1 )分析了细分理论和典型细分模式，阐述了细分曲面的极限点、切矢、法矢等基本几何量的精确计算方法。
2 . 4 linear convergence assumption ( h2 . 2 ) : let f ( x ) : rn - > r be twice continuously differ - entiable in some domain of x * which is the minimal point of f ( x ) , and exists e > 0 , m > m > 0 , if x - x * | | < holds , then the following inequality is satisfied , lemma 2 . 2 1若假设1成立，则算法或有限步终止于问题的稳定点，或产生无穷点列沁k其任意极限点都是问题的稳定点。 2 、 4线性收敛性假设2 2 ：设八）在极小点”的领域内二次连续可微，且玉0 ， m x 0 ，使得当iix ?工叫。
