Remeshing-assisted Optimization for Locally Injective Mappings - Jin, Y.; Huang, J.; Tong, R. (Computer graphics forum, 2014)
Constructing locally injective mappings for 2D triangular meshes is vital in applications such as deformations. In such a highly constrained optimization, the prescribed tessellation may impose strong restriction on the solution. As a consequence, the feasible region may be too small to contain an ideal solution, which leads to problems of slow convergence, poor solution, or even that no solution can be found. We propose to integrate adaptive remeshing into interior point method to solve this issue. We update the vertex positions via a parameter‐free relaxation enhanced geometry optimization, and then use edge‐flip operations to reduce the residual and keep a reasonable condition number for better convergence. For more robustness, when the iteration of interior point method terminates but leaves the positional constraints unsatisfied, we estimate the edges in the current tessellation that block vertices moving based on the convergence information of the optimization, and then split neighboring edges to break the restriction. The results show that our method has better performance than the solely geometric optimization approaches, especially for extreme deformations.