基于细分模式与能量优化的曲面混合方法

Surfaces Blending Based on Subdivision Scheme and Energy Optimization

论述了用Catmull-Clark细分曲面及能量优化法对多张三次B样条曲面进行混合的方法。首先引入一种边界拓扑修改的细分规则,可生成逐段光滑的细分曲面,在此基础上构造多张三次B样条曲面的混合曲面,采用能量优化方法求解控制顶点。与现有方法相比,构造的混合曲面形状易于控制,能满足复杂的边界要求,且整个混合曲面除了在有限奇异点处为C1连续外均达到C2连续。

This paper describes a new method of blending cubic B-spline parametric surfaces using Catmull-Clark subdivision surfaces and energy optimization. Firstly, an approach based on boundary topological modifying is discussed to generate piecewise-smooth subdivision surfaces. The approach is then employed to blend parametric bicubic B-spline surfaces. The control vertices are computed based on energy optimization. Comparing with the current blending methods, it is easy to adjust the blending surfaces shape and satisfy the complex boundary conditions, and blending surfaces are guaranteed to be global C2continuous except at a finite number of extraordinary points where C1continuity is obtained.