Analysis-suitable parameterization is a fundamental problem in IGA (IsoGeometric Analysis) implementation which significantly influences computational accuracy and efficiency. This paper proposes a variational framework to address the problem of producing a smooth parameterization of a computational domain represented in B-spline form. In order to control both angle and area distortions, a weighted and modified Liao functional is constructed. The weighting function is a modification of the Gaussian function used to penalize area distortion while a modified Liao functional is used to minimize the angle distortion. A Jacobian regularization scheme is adopted so that invalid initial solutions are acceptable and untangling of folding parameterization is made possible. An L-BFGS algorithm is applied to solve this unconstrained optimization problem. Experimental results show that the proposed objective functional could effectively untangle folding parameterization and further produce better results with lower area and angle distortions compared with other functionals and state-of-the-art parameterization techniques.

适合分析的参数化是 IGA（等几何分析）实现中的一个基本问题，它显着影响计算精度和效率。本文提出了一个变分框架来解决产生以 B 样条形式表示的计算域的平滑参数化的问题。为了控制角度和面积失真，构造了加权和修改的 Liao 泛函。加权函数是对用于惩罚区域失真的高斯函数的修改，而修改后的 Liao 函数用于最小化角度失真。采用雅可比正则化方案，因此可以接受无效的初始解，并使折叠参数化的解开成为可能。应用 L-BFGS 算法来解决这个无约束优化问题。