αMST: A robust unified algorithm for quadrilateral mesh adaptation in 2D and 3D

The proposed αMST templates can also be used to improve surface quadrilateral meshes using conformal mapping of surface charts. Furthermore, rotating the templates in the direction of cross-fields allows mesh edges to align along curvature lines. The proposed 3D generalization is fast, scalable, and inexpensive while improving alignment, shape, size, and sparsely placing the singularities. Several examples (both in 2D/3D) are presented that demonstrate the robustness, efficiency, and versatility of the proposed concept and algorithm.