基于顶点法向量约束的Catmull-Clark细分插值方法

提出一种基于顶点法向量约束实现插值的两步Catmull-Clark细分方法.第一步，通过改造型Catmull-Clark细分生成新网格.第二步，通过顶点法向量约束对新网格进行调整.两步细分分别运用渐进迭代方法和拉格朗日乘子法，使得极限曲面插值于初始控制顶点和法向量.实验结果证明了该方法可同时实现插值初始控制顶点和法向量，极限曲面具有较好的造型效果.

Catmull-Clark Subdivision Interpolation Based on Vertex Normal Vector Constraint

A new scheme for constructing a two steps Catmull-Clark subdivision surface with the vertex normal vector constraint interpolates the vertices of a quadrilateral mesh with arbitrary topology. Firstly, the new mesh is generated by the modified Catmull-Clark subdivision. Secondly, the new mesh is adjusted through vertex normal vector constraints. The two-phase scheme makes the limit surface interpolate all vertices and normal vector in the original mesh by applying the progressive iterative method and the Lagrange multiplier method respectively. The experimental examples are given to show that the method is effective both in interpolating initial control points and normal vector, the limit surface has good modeling effect.