Automated Conversion of 2D Triangular Mesh into Quadrilateral Mesh with Directionality Control

This paper proposes an automated quadrilateral meshing technique based on the conversion of triangular meshes. Given a triangular mesh and a vector eld representing the desired directionality of quadrilateral elements, our new approach generates a well-shaped and well-aligned quadrilateral mesh. In the approach, the values of three scalar functions are rst calculated for each pair of adjacent triangular elements. These functions evaluate the following conditions: (1) directionality control, (2) optimization of the shapes of elements, and (3) reduction of the number of isolated triangular elements. Pairs of triangular elements are then converted into quadrilateral elements in order of the sum of the values of the three functions.