用分片代数曲面构造管道曲面的过渡曲面

Blending Pipe Surfaces with Piecewise Algebraic Surfaces

借助围绕一个顶点处代数曲面的光滑拼接条件 ,提出并研究了用分片代数曲面构造三通管道的过渡曲面问题 .首先对空间区域进行适当的剖分以确定分片代数曲面的定义区域 .然后 ,通过求解一个线性方程组来构造出光滑拼接的分片代数曲面 .同时还讨论了在代数曲面片的 B- B表示下 ,Bézier纵标对过渡曲面的形状的局部控制问题 .结果表明 ,用分片代数曲面构造过渡曲面不仅可以降低曲面的次数 。

This paper derives a geometric continuity condition for algebraic surface patch complexes meeting at a common vertex. Based on the geometric continuity condition, a new scheme is presented to blend three cylinders with piecewise cubic algebraic surfaces. The algorithm starts with a suitable space partition for the defining domains of the piecewise algebraic surface patches. Then the piecewise algebraic surface is constructed by solving a linear system of equations. An intuitive and geometric means of controlling the shape of the blending surface is also discussed based on the Bernstein Bézier(B B) representation of algebraic surface patches. The results suggest that modeling with piecewise algebraic surfaces has two main advantages: (1) The degree of the algebraic surface patches is comparatively low; (2) The control over the shapes of the piecewise algebraic surfaces is much more intuitive and efficient.