Zheng Jianmin, Cai Yiyu
School of Computer Engineering, Nanyang Technological University, Singapore.
IEEE Trans Vis Comput Graph. 2006 May-Jun;12(3):301-10. doi: 10.1109/TVCG.2006.49.
The construction of a smooth surface interpolating a mesh of arbitrary topological type is an important problem in many graphics applications. This paper presents a two-phase process, based on a topological modification of the control mesh and a subsequent Catmull-Clark subdivision, to construct a smooth surface that interpolates some or all of the vertices of a mesh with arbitrary topology. It is also possible to constrain the surface to have specified tangent planes at an arbitrary subset of the vertices to be interpolated. The method has the following features: 1) It is guaranteed to always work and the computation is numerically stable, 2) there is no need to solve a system of linear equations and the whole computation complexity is O(K) where K is the number of the vertices, and 3) each vertex can be associated with a scalar shape handle for local shape control. These features make interpolation using Catmull-Clark surfaces simple and, thus, make the new method itself suitable for interactive free-form shape design.
在许多图形应用中，构建一个对任意拓扑类型的网格进行插值的光滑曲面是一个重要问题。本文提出了一个两阶段过程，该过程基于控制网格的拓扑修改以及随后的Catmull-Clark细分，以构建一个对具有任意拓扑的网格的部分或所有顶点进行插值的光滑曲面。还可以约束曲面在要插值的顶点的任意子集中具有指定的切平面。该方法具有以下特点：1）保证始终有效且计算在数值上稳定；2）无需求解线性方程组，整个计算复杂度为O(K)，其中K是顶点数量；3）每个顶点可以与一个标量形状手柄相关联，用于局部形状控制。这些特点使得使用Catmull-Clark曲面进行插值变得简单，从而使新方法本身适用于交互式自由形式形状设计。
