Planar multi-patch domain parameterization for isogeometric analysis based on evolution of fat skeleton

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. (C) 2021 Elsevier B.V. All rights reserved.