Abstract
This paper presents NURBS-OT (Non-Uniform Rational B-Splines - Optimal Transport), a new approach in the field of computer graphics and CAD/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 vs. 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 UIUC airfoil and superformula datasets, where it showed enhanced performance on various metrics. This demonstrates its ability to produce precise, realistic, and aesthetically coherent designs, marking a significant advancement by merging classical geometrical techniques with modern deep learning.
