A Regularization Approach for Automatic Quad Mesh Generation

Pure quadrilateral meshes are preferred when using shell-based structural analysis solvers since they provide more accurate results if compared to triangular or mixed meshes. Triangulations of complex trimmed surfaces (as con- structed in CAD) can be always generated and any triangle can be subdivided into three quadrilaterals by splitting the sides and introducing a new vertex at the centroid. Therefore, the conversion of a triangular mesh into a fully quadded conformal mesh is straightforward, and if the source triangulation is watertight, the resultant quad mesh maintains that property. However, triangle splitting implies that the quads inherit the original triangle shapes and the resulting mesh presents a very large number of irregular vertices. This paper describes a technique that recovers a significant amount of irregular vertices by performing iterative topological changes on the mesh and employs a modified Laplacian method for adjusting the vertex coordinates. The algorithm is robust, fast and produces a surface mesh of a BRep (where all vertices are on the geometry) that it is completely quadrilateral and semi-regular suitable for structural analysis and possibly other surface-based PDE solvers.