B\'ezierGAN: Automatic Generation of Smooth Curves from Interpretable Low-Dimensional Parameters

Many real-world objects are designed by smooth curves, especially in the domain of aerospace and ship, where aerodynamic shapes (e.g., airfoils) and hydrodynamic shapes (e.g., hulls) are designed. To facilitate the design process of those objects, we propose a deep learning based generative model that can synthesize smooth curves. The model maps a low-dimensional latent representation to a sequence of discrete points sampled from a rational Bézier curve. We demonstrate the performance of our method in completing both synthetic and real-world generative tasks. Results show that our method can generate diverse and realistic curves, while preserving consistent shape variation in the latent space, which is favorable for latent space design optimization or design space exploration. Keywords: Shape synthesis, aerodynamic design, hydrodynamic design, generative adversarial networks 1. Introduction Smooth curves are widely used in the geometric design of products, ranging from daily supplies like bottles and drinking glasses to engineering structures such as aerodynamic or hydrodynamic shapes.