NURBS-OT: An Advanced Model for Generative Curve Modeling

Abstract

This paper presents NURBS-OT (non-uniform rational B-splines—optimal transport), a new approach in the field of computer graphics and computer-aided design (CAD)/computer-aided manufacturing (CAM) for modeling complex free-form designs like aerodynamic and hydrodynamic structures, traditionally shaped by parametric curves such as Bézier, B-spline, and NURBS. Unlike prior models that used generative adversarial networks (GANs) involving large and complex parameter sets, our approach leverages a much lighter (0.37M versus 5.05M of BézierGAN), theoretically robust method by blending optimal transport with NURBS. This integration facilitates a more efficient generation of curvilinear designs. The efficacy of NURBS-OT has been validated through extensive testing on the University of Illinois Urbana-Champaign (UIUC) airfoil and superformula datasets, where it showed enhanced performance on various metrics. This demonstrates its ability to produce precise, realistic, and esthetically coherent designs, marking a significant advancement by merging classical geometrical techniques with modern deep learning.