Research On Parallelizable And Scalable Mesh Parameterization Methods

With the development of digital geometry processing technology,mesh has been widely used in animation,game,architecture,medical,industrial design,etc.Mesh pa-rameterization is an indispensable basic tool in the field of mesh processing,which plays an important role in mesh deformation,texture mapping and mesh compression.The existing parameterization methods have achieved good results in producing high-quality mesh without flipping,but these methods are often slow in processing large-scale mesh and not parallelizable,while some efficient algorithms can not meet the require-ments of non-inversion and high-quality,therefore it is of great significance to develop a parallelizable and scalable parameterization method which can take into account the efficiency of calculation,non-inversion and high quality simultaneously.In this paper,we propose a parallelizable and scalable parameterization method for triangular meshes,which can ensure that the parameterized results are free of inversion and low distortion.The main flow of our method is mesh disassemble,optimization and mesh restoration.First,we get the initial value of mesh parameterization by some simple parameterization methods.If the initial value is flipped,we can get the disjoint mesh by projecting the initial value to the feasible region.If the initial value is already in the fea-sible region,we do not need this step.Then the parameterization problem is constructed into a constrained optimization problem with respect to affine transformation on each triangular surface.Using ADMM algorithm to deal with the optimization problem,we introduce auxiliary variables and decompose the optimization problem into several par-allelizable local subproblems to obtain affine transformation on each triangular surface.After the algorithm converges,BFS method is used to recover the corresponding mesh from the affine transformations.Compared with the existing methods,Methods of this paper makes the parame-terization method highly parallel by introducing auxiliary variables,and can use GPU parallel acceleration.Our experiment on tasks such as mesh parameterization,mesh deformation will demonstrate the efficiency of our method,especially on large-scale mesh.