High-quality planar NURBS parameterization of computational domain in IGA via control points and weights optimization
Date:日期：
Conference talk会议报告 at ，Mesh Generation and Applications Symposium (MEGAS 2021), Hangzhou, China
Slides, Photo 1, Photo 2, Conference Link
Constructing an analysis-suitable parameterization from a given boundary representation is a crucial step in isogeometric analysis (IGA). In this talk, I presented several sufficient conditions and a necessary condition for the injectivity of planar NURBS parameterizations, together with an injectivity-checking algorithm based on Bézier extraction. Building on these, I proposed a three-step unconstrained optimization approach: harmonic initialization, foldover elimination, and quality improvement that alternately optimizes the inner control points and weights with respect to a corrected Winslow functional plus a uniformity term. Comparisons with several state-of-the-art methods (nonlinear constrained optimization, variational harmonic, Teichmüller mapping and low-rank quasi-conformal methods) demonstrate the robustness and efficiency of the method, and tests with fixed weights show that optimizing the weights improves both the injectivity and quality of the parameterization.
Keywords: Isogeometric Analysis, Planar NURBS Parameterization, Injectivity, Control Points and Weights Optimization