自由曲线曲面的任意次非均匀细分

摘要

提出一种有效的建模自由曲线曲面的非均匀细分算法.首先在节点插入技术基础上推导出任意次自由曲线的非均匀细分规则,然后把它推广到张量积曲面得到任意次自由曲面的非均匀细分规则,最后对奇异点附近曲面采用类Doo-Sabin和Catmull-Clark的细分规则,从而使该算法可以实现建模任意次具有任意拓扑基网格的非均匀细分曲面.此外,该方法也实现了对传统细分格式的统一,例如,当次数为2并采用均匀节点矢量便转化为Doo-Sabin细分,当次数为3并采用均匀节点矢量便转化为Catmull-Clark细分.%In this paper, a new recursive non-uniform subdivision approach for modeling free-form curves and surfaces was presented. Based on the knot insertion technique, the non-uniform subdivision rules were provided for modeling arbitrarydegree curves and surfaces of arbitrary topology with non-uniform knot intervals. In particular, this approach generalized the traditional uniform subdivisions, such as Doo-Sabin and Catmull-Clark subdivision.