可调节多约束Catmull-Clark细分曲面研究

提出了一种顶点和法向约束下的细分曲面构造方法。即在约束点网格基础上,先用带形状因子的Doo-Sabin方法对其细分一次,然后采用Lagrange乘子法优化求解顶点、法向和相似性约束下的最小顶点扰动量,并根据优化结果反复调整顶点位置,最终得到满足插值条件的细分曲面控制网格。该方法无需求解全局方程组,控制网格求解效率高;而求解过程中相似性约束的增加,保证了插值曲面的质量;形状因子的引入,则起到调节位置和法向约束影响范围的作用,从而给设计者提供更多的形状表达自由度。

Research on Adjustable Catmull-Clark Subdivision Surface with Multiple Constraints

A method for constructing subdivision surface with constraints of vertices and normal vectors is proposed.After subdividing the meshes consisting of constrained vertices using Doo-Sabin method with shape factor,the minimum perturbations of vertices are solved with Lagrange multiplier optimization method with constraints of vertices,normal vectors and similarity.Then,locations of vertices are modified repeatedly according to the optimum result.Finally,the control net of subdivision surface that satisfies the interpolation requirements is acquired.This method does not need to solve global equations,so it has high efficiency,and similarity constraint guarantees the quality of interpolation surface.The introduction of shape factor can adjust the influence region of the constraints of vertices and normal vectors,which gives designers more freedom to make shape expression.