Quad Mesh Generation Algorithm On Planar Regions

Quadrilateral meshes have been used for many years in computer-aided design and numerical simulation,and in recent years,quadrilateral meshes have become more and more widely used in computer graphics,geometric processing,animation simulation,and texture mapping.Compared with the traditional triangular mesh,the quadrilateral mesh has the superiority that the triangular mesh cannot match.Quadrilateral mesh generation has great practical value in the industry,but how to generate a high-quality quadrilateral mesh that meets user needs is still an open question.The main difficulties are: 1)The industrial model has many feature constraints that require the edges of the quadrilateral mesh to be aligned with the features.2)The existing quadrilateral mesh generation algorithm lacks control of singular points,and the position and number of singular points will fundamentally affect the quality of the quadrilateral mesh.In this paper,for a two-dimensional planar region with arbitrary boundaries,the design of the cross field is transformed into the minimization of the harmonic energy.Then,we use the streamline tracking method to divide the region into a number of quadrilateral blocks along the streamline of the cross field.Finally,we use the method of block parameterization to generate quad mesh with boundary alignment.In addition,we can control the position of the singular point of the generated cross field by adjusting the length of the initial vector on the boundary point and generate quadrilateral mesh with different singular points.