The advent of isogeometric analysis has prompted a need for methods to generate Trivariate B-spline Solids (TBS) with positive Jacobian. However, it is difficult to guarantee a positive Jacobian of a TBS since the geometric pre-condition for ensuring the positive Jacobian is very complicated. In this paper, we propose a method for generating TBSs with guaranteed positive Jacobian. For the study, we used a tetrahedral (tet) mesh model and segmented it into sub-volumes using the pillow operation. Then, to reduce the difficulty in ensuring a positive Jacobian, we separately fitted the boundary curves and surfaces and the sub-volumes using a geometric iterative fitting algorithm. Finally, the smoothness between adjacent TBSs is improved. The experimental examples presented in this paper demonstrate the effectiveness and efficiency of the developed algorithm.
In this paper, we present a novel algorithm for constructing a volumetric T-spline from B-reps inspired by constructive solid geometry Boolean operations. By solving a harmonic field with proper boundary conditions, the input surface is automatically decomposed into regions that are classified into two groups represented, topologically, by either a cube or a torus. We perform two Boolean operations (union and difference) with the primitives and convert them into polycubes through parametric mapping. With these polycubes, octree subdivision is carried out to obtain a volumetric T-mesh, and sharp features detected from the input model are also preserved. An optimization is then performed to improve the quality of the volumetric T-spline. The obtained T-spline surface is C 2 everywhere except the local region surrounding irregular nodes, where the surface continuity is elevated from C 0 to G 1. Finally, we extract trivariate Bezier elements from the volumetric T-spline and use them directly in isogeometric analysis.