Abstract: Aiming at the parameterization problems for bounded and closed meshes, we proposed a mesh parameterization method based on local average  normal deformation. Taking the mean curvature flow as a reference, the vertices were pushed to the average position of their neighbors, thus deforming a mesh to a plane or a sphere. Firstly, the average normal of neighbor faces of each triangle was calculated and the rotation matrix of the normal was calculated. Secondly, based on Poisson system, the whole mesh were reconstructed by optimizing a stretching energy, the new coordinates of vertices were calculated. By alternating the above two steps, the original mesh was deformed to a constant mean curvature surface. The algorithm was different from the general methods based on energy optimization, which noly needed to solve a sparse linear system in each iteration, therefore, it could process large data sets quickly. By adding a penalty function during the deformation to dynamically adjust the weights of global average normals, the problem of triangle degeneration or flipping in the deformation process was avoided. The experimental results show that compared with other parameterization methods, the proposed method has the advantages of practical reliability and high efficiency, and can compute low-distortion plane parameterization and spherical parameterization in the same frame.

Key words: mesh parameterization, computation geometry, constrained deformation