2014/06/26 by Nikolay D. Dimitrov, Dimitrov, Nikolay · 1 citation
Engineering · Computer Science · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computer Graphics and Visualization Techniques
paper · pdf · doi:10.48550/arxiv.1406.6741
The main objective of this study is to understand how geometric hyper-ideal circle patterns can be constructed from given combinatorial angle data. We design a hybrid method consisting of a topological/deformation approach augmented with a variational principle. In this way, together with the question of characterization of hyper-ideal patterns in terms of angle data, we address their constructability via convex optimization. We presents a new proof of the main results from Jean-Marc Schlenker's work on hyper-ideal circle patterns by developing an approach that is potentially more suitable for applications.