A boundary element-based automatic domain partitioning approach for semi-structured quad mesh generation

Abstract In this paper, a boundary element-based approach is proposed for partitioning a planar domain automatically into a set of 4-sided regions, which is suitable for semi-structured quad mesh generation. The basic idea is to generate a smooth cross-field via solving PDEs with the boundary element method and then partition the input domain by extracting singular structures of the cross-field. Firstly, a cross is configured at each boundary vertex of the input domain. Then, two Laplacian equations are selected as the governing equation to smoothly propagate the crosses defined on the boundary into the interior of the domain. To obtain an accurate cross-field, the boundary element method is used to solve the governing equations. Then the singular vertices are identified by analyzing the structure of the cross-field, and the streamlines emanating from these points are traced and simplified as segmentation curves to partition the domain. Finally, to demonstrate the efficiency and effectiveness of the proposed approach, some quad mesh generation examples and comparison with previous approaches are presented.

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