基於共形的最優網格參數化

A parameterization of a mesh refers to a bijective mapping that maps a simplicial 2- or 3-complex to a domain of simple shape. The mesh parameterization is a fundamental issue that has been extensively studied. It has been widely applied to carry out the 3D image processing tasks, such as surface registration and alignment as well as surface resampling and remeshing. Especially when the geometry is complicated, a parameterization of the surface can be used to simplify the shape of the domain. Practical applications arising from computer graphics can be smoothly carried out via the one-to-one correspondence between the surface and the domain of simple shape. The optimal distortion-balancing surface parameterization algorithm developed in this project can produce the surface mapping with balanced angle and area distortions. On the application of surface remeshing, the distortion-balancing parameterization can be used to effectively improve the quality of the triangular mesh. In summary, our conformal, area-preserving, and volume-preserving parameterization algorithms are the most efficient compared to other existing state-of-the-art algorithms. This helps the 3D mesh modeling and the manifold registration meet the real-time industrial standard.