However, triangle splitting implies that the quads inherit the original triangle shapes and the resulting mesh presents a very large number of irregular vertices. 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. Triangulations of complex trimmed surfaces (as constructed 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.
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. The quad mesher, which is available in Gmsh, is validated and illustrated on two datasets of CAD models. Advantages of our approach include robustness, strict respect of the CAD features and support for user-prescribed size constraints. Validity of the quad mesh is guaranteed by monitoring element quality during all operations and reverting the changes when necessary. The topological modifications are either local and based on disk quadrangulations, or more global with the remeshing of patches of quads according to predefined patterns.
The idea is to preserve the irregular vertices matching cross-field singularities and to eliminate the others.
After triangle combination and midpoint-subdivision into an all-quadrilateral mesh, the topology of the mesh is modified to reduce the number of irregular vertices. An initial quad-dominant mesh is generated with frontal point insertion guided by a locally integrable cross field and a scalar size map adapted to the small CAD features. We propose an end-to-end pipeline to robustly generate high-quality quadrilateral meshes for complex CAD models.
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