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

arXiv: https://arxiv.org/abs/1808.08871 · HTML: https://mlsanity.com/paper/1808.08871/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2018.

## Built on by (most cited first, 11 of 11)

- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Constraining Generative Models for Engineering Design with Negative Data](https://mlsanity.com/paper/2306.15166/) (2023)
- [Airfoil GAN: Encoding and Synthesizing Airfoils for Aerodynamic Shape Optimization](https://mlsanity.com/paper/2101.04757/) (2021)
- [Inverse airfoil design method for generating varieties of smooth airfoils using conditional WGAN-gp](https://mlsanity.com/paper/2110.00212/) (2021)
- [Agentic Large Language Models for Conceptual Systems Engineering and Design](https://mlsanity.com/paper/2507.08619/) (2025)
- [Adversarial Latent Autoencoder with Self-Attention for Structural Image Synthesis](https://mlsanity.com/paper/2307.10166/) (2023)
- [Exploring the Potentials and Challenges of Deep Generative Models in Product Design Conception](https://mlsanity.com/paper/2407.11104/) (2024)
- [Tailoring Generative Adversarial Networks for Smooth Airfoil Design](https://mlsanity.com/paper/2404.11816/) (2024)
- [FuncGenFoil: Airfoil Generation and Editing Model in Function Space](https://mlsanity.com/paper/2502.10712/) (2025)
- [Language-Guided Trajectory Traversal in Disentangled Stable Diffusion Latent Space for Factorized Medical Image Generation](https://mlsanity.com/paper/2503.23623/) (2025)

## Abstract (arXiv)

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 B'ezier 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.