In this paper, we propose a new algorithm for computing planar multi-patch domain parameterizations which are suitable for consequent numerical computations based on isogeometric analysis. Firstly, a so-called fat skeleton of the given domain, represented by a multi-patch NURBS parameterization, is constructed, which determines the topology of a multi-patch NURBS parameterization suitable for the given domain. Then, we formulate an evolution process which successively transforms the initial shape represented by the fat skeleton to the target shape represented by the given domain. Moreover, a multi-patch optimization is applied in every time iteration to make the multi-patch NURBS parameterization as uniform and orthogonal as possible. The method is constructed such that it is fully automatic and it solves the biggest problems of the domain parameterization problem, i.e., it automatically determines a suitable topology of a multi-patch NURBS parameterization for the given domain and it also automatically solves the boundary correspondence problem. The functionality of the proposed method is demonstrated on several examples.

在本文中，我们提出了一种计算平面多面片域参数化的新算法，该算法适用于后续数值计算基于等几何分析。首先，构造由多面片 NURBS 参数化表示的给定域的所谓胖骨架，它确定了适合给定域的多面片 NURBS 参数化的拓扑结构。然后，我们制定了一个进化过程，该过程将脂肪骨架表示的初始形状依次转换为给定域表示的目标形状。此外，在每次迭代中应用多面体优化，使多面体 NURBS 参数化尽可能均匀和正交。该方法被构建为全自动的，它解决了域参数化问题的最大问题，即，它会自动确定给定域的多面片 NURBS 参数化的合适拓扑结构，并自动解决边界对应问题。所提出方法的功能在几个例子中得到了证明。