基于混合子分方法的曲面网格顶点与法向插值

Vertex and Normal Interpolation of Surfaces Based on Control Net Generated by Mixed Subdivisions

顶点位置和法向插值是参数曲面造型的重要内容 .文中基于混合子分方法生成三次 B样条控制网格 ,使得相应的三次 B样条曲面插值初始网格中指定的顶点 ,并通过引入插值模板的概念 ,把法向的插值转化为对模板的旋转变换 ,使得曲面在不改变插值顶点的情况下插值法向 ,最后得到一张 C2 连续的插值指定顶点和法向的曲面 .与传统的逐片 Bézier或 Coons曲面片构造方法相比 ,此方法更为简洁且具有更高的连续阶 ,而且易于推广到高阶 B样条和任意拓扑情形 。

Interpolation to vertex positions and normals is one of important contents in parametric surface modeling. This paper presents an approach based on Catmull Clark and Doo Sabin subdivision schemes to generate the control net of bi cubic B spline surface interpolating the given vertices of initial net. The notion of stencils is introduced such that the normal interpolation is converted into the rotation transformation of stencils without influencing the effects of vertex interpolation, thus a C 2 continuous surface interpolating given vertices and normals is obtained. Compared to traditional methods through stitching patches piece by piece, our method is more compact and has smoothness of higher degree. In addition, the method can be easily extended to high degree B spline surfaces with arbitrary topology nets and it is also fairly useful for practical applications.