A new quadtree-based approach for automatic quadrilateral mesh generation

In this paper, we present a new method for adaptive all-quadrilateral mesh generation for two-dimensional domains, including domains modeled by constraints with complex geometry or with varying scales. The method subdivides the domain's bounding box using a new extended quadtree scheme. In this subdivision process, the quadtree node corners are moved onto the geometrical constraints using local deformation criteria during the tree refinement steps. We define new subdivision patterns as part of our extended quadtree to add flexibility in the adaptation and guarantee that geometrical constraints are entirely modeled by tree edges. During the process, we ensure grid alignment with constraint accuracy and element quality at every scale. Our proposal converts the tree structure into a mesh with only quadrilateral elements. Results showed that our method generates elements of reasonable quality even for complex geometries and varying scales. The small number of parameters controlling the process is intuitive and makes our method efficient and user friendly.