Volumetric T-spline construction using Boolean operations
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 Bzier elements from the volumetric T-spline and use them directly in isogeometric analysis.
volumetric t-spline boolean operations polycubes parametric mapping sharp feature isogeometric analysis