Constructing volumetric parameterization based on directed graph simplification of ℓ_1 polycube structure from complex shapes

摘要

Volumetric spline parameterization of complex geometry plays a key role in isogeometric analysis (IGA). In this paper, we propose a general framework to construct volumetric parameterization from complex shapes based on directed graph simplification of the l(1) polycube structure. By minimizing the l(1)-norm of the normals on the input triangular meshes, a polycube structure can be generated with robustness, efficiency, and controllability. Then an algorithm is proposed for l(1) polycube structure simplification with a directed graph, which is an abstract structure generated from the polycube. After simplification, the vertex number of the directed graph will decrease, and the polycube structure will become more simple. From the simplified polycube structure, we construct a segmented surface by spline fitting techniques, and finally we fill each block with a trivariate B-spline volume with C-0-constraints. The proposed method can generate volumetric parameterization without an interior extraordinary vertex, and it has very high potential for constructing volumetric parameterization in IGA simulations. Some volume parameterization examples from complex shapes are presented to show the robustness and efficiency of the proposed method. (C) 2019 Elsevier B.V. All rights reserved.