3D Mesh Parameterization Method Based On Average Normal Deformation

As a basic research problem in Computer Graphics,mesh parameterization plays a fundamental role in entertainment,industrial production,biomedicine,art,architecture and 3D urban model.The main driving force for the development of the initial parameterization method in Computer Graphics is texture mapping,which can improve the visual effect of the polygon model.Later,due to the rapid development of 3D scanning technology and the urgent need for efficient compression methods for increasingly complex triangulation,other applications including mesh deformation,remeshing,surface fitting,shape modeling,etc.,also rely on high-quality mesh parameterization.In this paper,we propose a parameterization method with extensive applicability and high efficiency.The effectiveness and robustness of this method are verified through sufficient experiments,and some applic ations of this method are analyzed and discussed.In recent years,with the development of parameter zation,researchers have proposed various mesh parameterization algorithms for different parameter domains and different parameterization properties.Generally,the methods of planar parameterization and spherical parameterization need to be discussed separately.Most algorithms can only focus on one of the parameter domains.This work proposes an algorithm for mesh parameterization based on average normal deformation,which can efficiently generate low-distortion parameterizations for bounded meshes and closed meshes with zero genus.Referring to the effect of the average curvature flow,a two-stage operation is used to push the vertices to the average position of its neighbors,thus deforming a mesh to a plane or a sphere.Instead of calculating the average coordinates of vertices directly,we compute the average normals of faces.In the first stage,we manipulate each triangle independently(local stage).The target normal vector of each face is calculated,and the triangle is rotated to a new position individually,updating the normal vector field.In the second stage,the whole mesh is processed(global stage).A simple Poisson system is used to compute the new positions of vertices while optimizing a stretch energy,and the scattered triangle is "stitched" to generate a new mesh.In order to accelerate the convergence and avoid the inversion or depression of the triangle,we dynamically adjust the weight of the average normal vector in the deformation.To make the deformation process more stable,we use a flexible curvaturerelated method to specify the rings of neighbors.Extensive experiments confirm that our algorithm can generate planar parameterization and spherical parameterization with low distortion in the same frame,and no user interaction is required.It can also achieve high quality results for multi-boundary meshes or high curvature models.In addition,the algorithm is insensitive to triangulation and is robust.Compared with the method based on convex combination,the algorithm proposed in this paper produces less distortion.Compared with the method based on energy optimization,the algorithm in this paper is faster and does not require additional initial parameterization.Compared with the method of geometric flow,it does not require embed the results into Euclidean space.Based on these advantages,our algorithm has high application value in mesh processing such as mesh deformation,planar parameterization of spherical topological mesh,and surface mapping.