Quadrilateral Meshing Algorithms Of Spline Surface

In industrial design area,spline modeling is the main technology of shaper at present.Due to the strong ability of shaper,spline can control the continuity of surface in order to help designer creating more complex and smoother surface shape.Finite element method is an effective tool to support numerical simulation in product analysis phase.Spline surface needs to be divided into finite element by finite element method,and this process is called mesh generation.Quadrilateral mesh is widely used for its higher calculation accuracy and efficiency in numerical calculation.At present,the quadrilateral mesh generation algorithm of spline surface can be divided into two types: one is to map quadrilateral mesh to spline surface by directly dividing quadrilateral mesh in the parameter domain.These methods are direct and easy to implement.However,it often causes large area distortion and generates quadrilateral mesh with poor quality;Another kind of method is to divide the spline model into triangular mesh model,and then calculate the quadrilateral mesh on the triangular mesh model.These methods are flexible and support a variety of mesh generation algorithms.However,it often loses the accuracy of the original model.By increasing the number of faces in the triangular mesh,the accuracy of the model will be improved,but the computational efficiency will be reduced.In order to solve above problem,two kinds of quadrilateral mesh generation algorithms of spline surface are practiced and improved in this thesis.The first algorithm located area distortion and then apply improved pattern method to spline so that distortion location will be adjustment.At the same time,the sampling points on the edge of the stitching edge are controlled to ensure the natural splicing of the quadrilateral mesh.The second algorithm is divided spline in to triangle mesh and calculate the quadrilateral mesh on the triangular mesh.In this thesis,an improved quadrilateral mesh algorithm based on graph-value harmonic map is proposed.The improved method computes foliation and meromorphic quadratic differentials by input poles to generate highly structured quadrilateral meshes.Finally,based on the idea of isogeometric analysis,this thesis proposes a quadrilateral mesh generation algorithm framework,which don’t introduce triangle mesh and support a variety of mesh generation algorithms.This method can directly calculate partial differential equations on spline surface to generate quadrilateral meshes.This thesis set an example of harmonic equation to practice and verify this algorithm framework.The algorithm ensures the accuracy of the quadrilateral mesh by implementing directly on the spline surface.At the same time,it also improves the efficiency of the algorithm because triangular mesh is not necessary to be generated.