Automatic Conversion of Triangular Meshes into Quadrilateral Meshes with Directionality

This paper proposes a triangular-to-quadrilateral mesh conversion method that can control the directionality of an output quadrilateral mesh according to a user-specified vector field. Given a triangular mesh and a vector field, the method first scores all possible quadrilaterals that can be formed by pairs of adjacent triangles, according to their shape and directionality. It then converts the pairs into quadrilateral elements by order of the scores to form a quadrilateral mesh. Engineering analyses with finite element method occasionally require a quadrilateral mesh well-aligned along the boundary geometry or the directionality of physical phenomena, such as directions of streamline, shock boundary, and force propagation. The method we propose in this paper satisfies such directionality requirements because it can control the mesh directionality according to any desired vector fields.