Methods For Generation Of B-spline Surfaces From Triangle Meshes

Reconstruction of B-spline Surface is an important part of computer geometric modeling and plays an essential role in computer graphics. It is of a great interest for many applications such as animation, CAD, medicine image processing, reverse engineering and virtual environments. It is a basic step for the follow up processing, such as editing of surface, texture mapping. But a single B-spline surface can only represent rectangular topology type in essence. It is really a hard work that to generate smooth B-spline surfaces from arbitrary topological triangle meshes.Here two different methods of reconstructing B-spline surfaces from arbitrary topological triangle meshes are proposed, namely one method based on Catmull-Clark subdivision and the other based on partitioning and resampling. If smaller patches are required, the method based on Catmull-Clark subdivision is presented. Otherwise, the other method is used.The method based on Catmull-Clark subdivision is simple. It creates large, smoothly joining bicubic B-spline patches from a refined Catmull-Clark subdivision meshes.For arbitrary topological meshes, the method based on partitioning and resampling is very efficient. Firstly, the initial mesh is partitioned into patches homeomorphic to rectangles. Then, each patch is resampled into rectangular grid. Finally, we interpolate B-spline surface to the grid and smooth them. The contributions of our work are: 1) Partitions are performed interactively and boundaries of each patch are resampled uniformly. The extraction of boundaries is omitted. 2) For those patch boundaries without neighbors, corner vertices are determined by minimum interior angle, uniform choice or aspect ratio. 3) When computing the resultant force of each interior spring point, Farc andFfairare multiplied by a coefficient k. Thus, abnormal case will be avoided. 4) Smoothing betweenpatches is performed. The shared boundaries are very smooth.