Quadrilateral Mesh Reconstruction Based On Directional Field

Polygonal meshes are widely used in engineering and medicine.It is also widely used in computer graphics,computer vision,geometric modeling,mechanical engineering,architectural design and medical images.Although triangular mesh has become the most popular form of representation because of its simplicity and ease of operation,quadrilateral mesh has irreplaceable advantages in capturing principal curvature direction,capturing sharp feature direction,high order surface modeling and texturing.In this paper,the quadrilateral mesh is reconstructed for the existing initial triangular meshes on the surface.The main method is based on the direction field.In a flat area or near the umbilical point,the direction of the principal curvature is often ill conditioned.Therefore,the direction of principal curvature can not be directly used as the guiding field of quadrilateral meshing.In this paper,a 4 symmetric directional field is used as the guiding field for quadrilateral meshing,and only a small number of stable,reliable and well defined principal curvatures are selected as the directional constraints.In the construction of 4 symmetric directional field,this paper uses mixed integer algorithm to interpolate and optimize the directional field.In the differential optimization,the search space should be reduced and the singular points should be optimized,so that a smooth 4 symmetric directional field can be obtained.Then the global parameterization is processed,and the global parameterization is locally oriented according to the smoothed orientation field.That is to say,the gradient direction of the parametric coordinates on the mesh model should be consistent with the orientation field direction.Mixed integer algorithm is still used to minimize the global energy function.Corresponding norm correction and boundary alignment are also carried out.Thus a seamless global smoothing parameterization is calculated.Finally,the quadrilateral mesh is extracted.Before extraction,parameterized optimization is carried out to avoid the problem of inaccurate numerical value,and then geometric extraction and connectivity extraction are carried out to obtain a concrete quadrilateral mesh.