Sketch2MinSurf: Vision-Language Guided Generation of Editable Minimal Surfaces from Hand-Drawn Sketches

2026-05-20

AI Summary

This work addresses the challenging problem of converting hand-drawn sketches into structured, editable, and topologically consistent 3D surfaces under non-Euclidean representations. The authors propose a novel approach that integrates vision-language guidance with minimal surface theory, leveraging a spatial-topological tuple representation and a newly designed S2MS-Loss function to jointly optimize geometric reconstruction and topological fidelity. Evaluated on a test set of 100 sketches, the method achieves a topological similarity score of 0.844, significantly outperforming existing techniques. The generated surfaces are smooth, free of non-manifold artifacts, and directly editable, demonstrating practical utility in real-world applications such as public art installations.

Abstract

Converting hand-drawn sketches into structured 3D geometries remains challenging due to the difficulty of representing non-Euclidean surfaces and maintaining topological consistency. Existing generative models such as GANs, NeRFs, and diffusion architectures often fail to produce editable manifolds directly usable in downstream design workflows. We present Sketch2MinSurf, a hybrid vision-language and geometric optimization framework that integrates vision-language guidance with minimal-surface theory to generate smooth and editable 3D surfaces from hand-drawn sketches. The core of our approach is a spatial-topological encoding that represents geometry as tuples of node coordinates and real/virtual edge skeletons, enabling stable topological control during generation. We further introduce the Sketch2MinSurf Structural Loss (S2MS-Loss), a reward-modulated objective that jointly constrains geometric reconstruction and topological coherence. On a test set of 100 sketches, Sketch2MinSurf achieves a topological similarity score of 0.844, outperforming existing sketch-to-shape baselines. The generated manifolds are directly editable and free from non-manifold artifacts. A public art installation at a university showcases the method's potential for human-intent-driven 3D form generation. The dataset and code are available at https://anonymous.4open.science/r/Sketch2MinSurf/.

Problem

• sketch-to-3D
• minimal surfaces
• topological consistency
• editable manifolds
• non-Euclidean geometry

Innovation

• minimal surface
• topological consistency
• vision-language guidance
• editable 3D generation
• spatial-topological encoding