Isogeometric analysis-suitable trivariate NURBS models from standard B-Rep models

This paper presents an effective method to automatically construct trivariate spline models of complicated geometry and arbitrary topology required for NURBS-based isogeometric analysis. The input is a triangulation of the solid model's boundary. The boundary surface is decomposed into a set of cuboids in two steps: pants decomposition and cuboid decomposition. The novelty of our method is the pants-to-cuboids decomposition algorithm. The algorithm is completely automatic and very robust even for low-quality and noisy meshes. The set of cuboids composes a generalized polycube approximating very roughly the input model's geometry while faithfully replicating its topology. Due to its regular structure, the polycube is suitable for serving as the parametric domain for the tensor-product spline representation. Based on a discrete harmonic mapping between the cuboids' boundary and the polycube's boundary, surface and volume parameterizations are generated in order to fit the trivariate splines. The efficiency and the robustness of the proposed approach are illustrated by several examples.