Component-aware tensor-product trivariate splines of arbitrary topology

The fundamental goal of this paper aims to bridge the large gap between the shape versatility of arbitrary topology and the geometric modeling limitation of conventional tensor-product splines for solid representations. Its contribution lies at a novel shape modeling methodology based on tensor-product trivariate splines for solids with arbitrary topology. Our framework advocates a divide-and-conquer strategy. The model is first decomposed into a set of components as basic building blocks. Each component is naturally modeled as tensor-product trivariate splines with cubic basis functions while supporting local refinement. The key novelty is our powerful merging strategy that can glue tensor-product spline solids together subject to C² continuity. As a result, this new spline representation has many attractive advantages. At the theoretical level, the integration of the top-down topological decomposition and the bottom-up spline construction enables an elegant modeling approach for arbitrary high-genus solids. Each building block is a regular tensor-product spline, which is CAD-ready and facilitates GPU computing. In addition, our new spline merging method enforces the features of semi-standardness (i.e., ∑iwiBi(u,v,w)≡1 everywhere) and boundary restriction (i.e., all blending functions are confined exactly within parametric domains) in favor of downstream CAE applications. At the computational level, our component-aware spline scheme supports meshless fitting which completely avoids tedious volumetric mapping and remeshing. This divide-and-conquer strategy reduces the time and space complexity drastically. We conduct extensive experiments to demonstrate its shape flexibility and versatility towards solid modeling with complicated geometries and non-trivial genus.