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 C2 everywhere except the local region surrounding irregular nodes, where the surface continuity is elevated from C0 to G1. Finally, we extract trivariate Bézier elements from the volumetric T-spline and use them directly in isogeometric analysis.

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