Uniform Area Parameterization Of Triangulated Surface Meshes

Surface parameterization can be viewed as a one-to-one mapping from the surface to a suitable domain. Recently, there are lots of progresses in the 3D mesh parameterization. The ideal triangle mesh parameterization technology is that the mesh of the parameter domain should be topologically equivalent to the original 3D mesh and without any distortion (including the area, angle and length distortion). Mesh parameterization is a central issue in computer graphics. It has many applications such as texture mapping, remeshing, and repairing of CAD models and simulation.In computer, most of the 3D models are undevelopable, so there exists distortion in the processing of parameterization (planar embedding), and which is inevitable. The main concern of surface parameterization methods is the reduction of parametric distortion. Besides from providing a least-distorted mapping, a good parameterization method should be efficient for processing large surface meshes and robust.Based on available parameterization methods, a new distortion measure is proposed: it uses such a measure as the distortion measure, which is the ratio of the area of a neighboring vertex corresponding to a given inner vertex in a triangle mesh and the sum of the one-ring area. Then we give a so-called UAM (Uniform area Mapping) based on this distortion measure, the UAM is used in uniform texture mapping of complex 3D meshes in the end.Our steps are: firstly Mean Value Coordinates are used to map a 3D mesh into a square, and then the UAM, which is based on our proposed distortion measure, is used to map the non-uniform mesh square to a uniform mesh square. After calculating the texture coordinates in the uniform mesh, a fairly uniform texture mapping can then be realized for complex 3D meshes that only use one texture image. Experiments and comparisons are taken with representative 3D meshes, which reveals that our methods has obvious improvement in uniform texture mapping than available single parameterization methods. The algorithm is simple, fast and stable.