Constructing high-quality planar NURBS parameterization for isogeometric analysis by adjustment control points and weights

Parameterization of computational domains is a crucial step in isogeometric analysis (IGA). Non-Uniform Rational B-Spline (NURBS) is a standard tool in the CAD/CAM industry due to its powerful capability for shape representation. In this paper, we propose several sufficient conditions and a necessary condition for injective NURBS parameterizations of computational domains, taking into account both the control points and weights. Based on these conditions, an algorithm for the injectivity checking of NURBS parameterization is proposed. By taking both the internal control points and weights as optimization variables, we present an effective and robust approach for parameterizing planar computational domains. With the internal control points and weights updating alternately, the resulting parameterization is constructed by solving an unconstrained optimization problem whose objective function is a weighted sum of corrected Winslow functional and uniformity functional. Finally, the proposed checking algorithm is applied to verify the injectivity of the resulting parameterizations. Numerical examples demonstrate the effectiveness and robustness of the proposed method and show superior parameterization quality performance over the state-of-the-art approaches. (C) 2021 Elsevier B.V. All rights reserved.