A Novel Approach for Quad‐Dominant Mesh Generation Using Conformal Mapping Compressed Gradient Field

ABSTRACT The regular topological structure endows quadrilateral meshes with advantages such as high computational accuracy, reduced element requirements, and enhanced computational efficiency, granting them irreplaceable application value in high‐end engineering simulation domains. However, significant bottlenecks persist in the fully automatic generation technology of quadrilateral meshes for complex geometric models. Existing methods often encounter key issues such as high mesh distortion rates and insufficient algorithm stability when handling high‐curvature boundaries and multiscale feature regions, limiting their widespread application in engineering simulations. This article proposes a quad‐dominant mesh generation method based on gradient fields. Firstly, the three‐dimensional triangular mesh is transformed into a two‐dimensional parametric domain through conformal mapping. Subsequently, based on the compression ratio measured from three‐dimensional to two‐dimensional, the direction and size of the advancing front are calculated to draw contour lines in the parametric domain. A threshold is set to automatically generate high‐quality grids. Based on the extracted contour lines, high‐quality quadrilateral grids are generated pairwise along the gradient field directions. For regions that do not meet the threshold requirements, triangular mesh filling is employed to generate a two‐dimensional quad‐dominant grid. Due to the bijective nature of the mapping, the quad‐dominant surface mesh is obtained through the inverse transformation from the 2D parametric domain back to the 3D space.