Naitsat, AlexanderZeevi, Yehoshua Y.Bommes, David and Huang, Hui2019-07-112019-07-112019978-3-03868-094-91727-8384https://doi.org/10.2312/sgp.20191214https://diglib.eg.org:443/handle/10.2312/sgp20191214We present a new unified algorithm for optimizing geometric energies and computing positively oriented simplicial mappings. Its major improvements over the state-of-the-art are: adaptive partition of vertices into coordinate blocks with the blended local-global strategy, introduction of new distortion energies for repairing inverted and degenerated simplices, modification of standard rotation-invariant measures, introduction of displacement norm for improving convergence criteria and for controlling the proposed local-global blending. Together these improvements form the basis for Adaptive Block Coordinate Descent (ABCD) algorithm aimed at robust geometric optimization. Our algorithm achieves state-of-the-art results in distortion minimization, even with highly distorted invalid initializations that contain thousands of inverted and degenerated elements. We show over a wide range of 2D and 3D problems that ABCD is more robust than existing techniques in locally injective mappings.Theory of computationNonconvex optimizationComputing methodologiesComputer graphics10.2312/sgp.201912143-4