Algorithms for Space Mapping Method on Spline Spaces over Modified Hierarchical T-Meshes

Abstract

The space-mapping method provides a novel method for dimension formulae explanation and basis construction for the spline space over hierarchical T-meshes. By the space-mapping method, we provide a unique basis construction framework that incorporates basis modification of the spline space over modified hierarchical T-meshes. The subdivision rules on the modified hierarchical T-meshes are given to prevent the redundant edges that exist on hierarchical T-meshes. In the basis construction framework, we describe the spline-modification mechanism over the modified hierarchical T-mesh when the cells of the corresponding crossing vertex relationship graph (CVR graph) are adjusted. We provide the framework’s algorithms for basis construction and modification. Moreover, we discuss the application of the splines that are constructed by the framework to surface reconstruction with adaptive refinement. In comparison to splines over hierarchical T-meshes, the modified hierarchical T-meshes have fewer cells subdivided when achieving similar accuracy.