Two-Manifold Triangular Mesh Remeshing

In computer graphics, a large number of graphics algorithms can only accept topology correctly, and high quality triangle mesh as input, the mesh with degenerate triangle may directly affect the reliability of the algorithm results, however, in practice, there are many problems in the input mesh, so triangle remeshing is a very basic and important work in computer graphics. Lots of existing remeshing algorithms have used global or local parameterization, so numerical instability problem would be caused when using these algorithms to process mesh with degenerate triangles, which leads to poor quality result or even worse algorithm dumped.Based on a locally parameterized remeshing algorithm, in this paper, a parameterized irrelevant triangle remeshing method has been introduced and was expanded for anisotropic remeshing. The algorithm can be roughly divided into the following three steps: preprocessing, resampling, and precise vertex relocation. In the first step, the feature of the mesh have been extracted if needed; In the second step, resampling the input mesh according to the vertex budget given by users, and the vertex distribution satisfy the isotropic properties; In the last step, using Lloyd relaxation algorithm to update the position of the vertex to constantly improve the quality of the result mesh.Due to the anisotropic remeshing is isotropic remeshing in Riemannian metric field, so we only need to change the calculation method of the measurement(such as angle, length, etc.) in the isotropic remeshing algorithm then the isotropic remeshing algorithm can be applied to the anisotropic remeshing. In anisotropic remeshing algorithm, we use the Riemannian metric field to represent the anisotropic properties of the mesh and present a method to calculate the Riemannian metric. For calculating the Riemannian metric field, we first calculate the curvature tensor field of the input mesh, then calculate Riemannian metric field with the error control from the curvature tensor field we got, and then smooth the stretching ratio of the Riemannian metric field. We will get a Riemannian metric field which can describe the anisotropic properties of the mesh more accurate in this way. The experimental results show that our algorithm is robust and efficient.