非均匀B样条曲面顶点及法向插值

POINTS AND NORMALS INTERPOLATION OF NON-UNIFORM B-SPLINE SURFACES

本文以非均匀Catmull-Clark细分模式下的轮廓删除法为基础,通过在细分网格中定义模板并调整细分网格的顶点位置,为非均匀B样条曲面顶点及法向插值给出了一个有效的方法．该细分网格由待插顶点形成的网格细分少数几次而获得．细分网格的顶点被分为模板内的顶点和自由顶点．各个模板内的顶点通过构造优化模型并求解进行调整,自由顶点用能量优化法确定．这一方法不仅避免了求解线性方程组得到控制顶点的过程,而且在调整顶点的同时也兼顾了曲面的光顺性．

Based on the skirt removed approach under the non-uniform Catmull-Clark subdivision scheme, an efficient algorithm is given for points and normals interpolation of non-uniform B-spline surfaces by defining templates in subdivision meshes and adjusting positions of subdivision mesh vertices. The subdivision mesh is obtained by subdividing the mesh several times, which is formed by given points. Vertices in templates are adjusted by solving optimization models. Free vertices are computed by the energy optimization method. The algorithm not only avoids computing control vertices by solving linear systems but also gives attention to the fairness of surfaces while adjusting control vertices.