High-quality planar NURBS parameterization based on alternating control points and weights optimization
Date:日期：
Lightning talk & poster快闪报告与海报 at ，13th National Conference on Geometric Design and Computing (第十三届全国几何设计与计算学术会议, GDC 2021), Changsha, China
Poster, Photo 1, Photo 2, Conference Link
In this lightning talk and poster, I presented a robust and efficient method for constructing high-quality planar NURBS parameterizations from four boundary NURBS curves by treating both the control points and the weights as variables. After deriving several injectivity conditions and a practical injectivity-checking algorithm, the method initializes the inner control points by a harmonic (Laplacian-energy) quadratic program with unit inner weights, eliminates foldovers via a ReLU-based unconstrained optimization, and then alternately optimizes the control points and the weights. Comparisons with the NCO, variational harmonic, Teichmüller mapping and low-rank quasi-conformal methods on several models demonstrate the effectiveness and advantages of the approach.
Keywords: Isogeometric Analysis, Planar NURBS Parameterization, Injectivity, Alternating Optimization