Research On Mesh Parameterization Mapping With Low Distortion

Mesh parameterization is a research hotspot and difficulty in computer graphics and digital geometry processing.It can be used in texture mapping,shape analysis,mesh deformation,mesh editing and other fields.However,the current mesh parameterization method has low operating efficiency and serious mapping distortion.Therefore,this paper mainly studies the low-distortion parameterized mapping method,and finally designs and implements a low-distortion mapping verification system.Around this goal,the main research results of this article are as follows:(1)Aiming at the problems of easy distortion and long slit length when cutting the mesh model,the Seamster cutting method based on the pre-judgment mapping distortion area is researched and designed.Inputting the 3D mesh model and using the internal and external classification methods based on ray tracing to visually evaluate the triangular meshes one by one;evaluatting the easy-to-distortion points of the model according to the Gaussian curvature of the mesh vertices and generatting cuts;using the minimum spanning tree method to reduce the cuts seam length.The experimental verification shows that the visual area and the visual blind area of the method are reasonably distinguished,the high-distortion area of the model is accurately predicted,and the slit length is short.(2)Aiming at the problems of mapping distortion and computational complexity of the three-dimensional topological disc model,this paper studies and proposes a Tutte mapping calculation method with limiting the distortion.Inputting the cut three-dimensional grid model,calculatting the mesh object of the Tutte map,determining the boundary of the mapped model according to the slit,solving the mapping linear equation system to get the interior points of the model;measuring the mapping distortion of the model,using the improved Most Isometric Parameterizations distortion energy function measures the conformal distortion,and the symmetricDirichlet energy function is used to measure the isometric distortion;outputting the distortion measurement function and the distortion value.Experimental verification shows that the method has the advantages of accurate distortion measurement,high mapping efficiency and stable mapping quality.(3)To solve the problem of low efficiency of optimal coordinate points and unsatisfactory convergence quality,the optimal coordinate solution method combining agent function and assembly Newton is studied and proposed.Inputting the mapping distortion measurement function of the model;setting the iteration conditions,in the early stage of the iteration with large distortion energy,establishing the reference grid;using the gradient descent-based agent function method to solve the optimal coordinates;when the distortion energy is small at the later stage of the iteration,the assembly Newton method was used to solve the optimal coordinates.Experimental verification shows that the method has the advantages of fast distortion reduction speed,stable convergence quality,and high accuracy of optimal coordinate solution.(4)Designing and implementting a software system based on low distortion mesh parameterzation mapping.The system is divided into three modules: mesh parameterization,mesh model display module,mesh model texture mapping module.The mesh parameterization module of the system has high mapping efficiency and low distortion,and the texture mapping module with high texture rendering quality,fine and uniform stripe effect,real-time texture rendering,good user experience,and good system robustness.