Organizations: National Cheng Kung University Tainan, Taiwan
Abstract
We present a unified framework for 3D geometric abstraction using a single continuous 4D wire, parameterized as a B-spline with spatial coordinates and variable width (x,y,z,w). Existing approaches typically represent shapes as collections of many independent curve segments, which often leads to fragmented structures and limited physical realizability. In contrast, we show that a single continuous spline is sufficiently expressive to capture complex volumetric forms while enforcing global topological coherence. By imposing continuity, our method transforms 3D sketching from a local density-accumulation process into a global routing problem, providing a strong inductive bias toward cleaner aesthetics and improved structural coherence. To enable gradient-based optimization, we introduce a differentiable rendering pipeline that efficiently rasterizes variable-width curves with bounded projection error. This formulation supports robust optimization using modern guidance signals such as Score Distillation Sampling (SDS) or CLIP. We demonstrate applications including image-to-3D abstraction, multi-view wire art generation, and differentiable stylized surface filling. Experiments show that our unified representation produces structures with higher semantic fidelity and improved structural coherence compared to approaches based on collections of discrete curves.
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/.
Differentiable rendering of planar rational splines remains largely underexplored, despite their widespread use in vector graphics and design. Existing differentiable vector renderers primarily focus on Bézier curves and rely on analytic rasterization, which can suffer from gradient instability and limited flexibility. We propose NURBS Splatting, a unified framework that represents planar rational curves as continuous Gaussian fields. By sampling Gaussians along the curve parameter domain and inside closed regions, rendering is reformulated as a smooth accumulation process with stable gradients. Our method naturally supports long splines, rational weights, non-uniform knots, and closed-region filling. We demonstrate its effectiveness in calligraphy reconstruction, vectorization frameworks, and long-spline image abstraction, showing improved stability and reconstruction quality over existing approaches.
Existing 3D generative models predominantly rely on implicit volumetric representations, which enforce watertight topology and struggle to represent thin-shell and non-manifold geometries such as garments. Geometry image-based approaches offer a surface-centric alternative, but existing methods rely on discrete binary occupancy maps whose resolution-dependent boundary encoding causes staircase artifacts and information loss upon downsampling, while surface reconstruction remains a non-differentiable post-processing step disconnected from the learning pipeline. To address this, we propose Differentiable Geometry Image (DiffGI), an end-to-end 3D-to-2D mapping framework that seamlessly integrates surface representation and geometric optimization. DiffGI replaces binary maps with a continuous 2D Truncated Signed Distance Function (TSDF), which encodes boundary position at subpixel precision within a fixed grid resolution, eliminating resolution-dependent staircase artifacts even under aggressive downsampling. Building on this continuous field, we introduce a differentiable Marching Squares algorithm based on analytical linear interpolation, allowing gradients from 3D surface losses to propagate back to the 2D latent space. Leveraging this differentiable pipeline, we train a DiffGI-VAE augmented with a geometry-aware normal rendering loss to compress complex 3D surfaces into an ultra-compact 32X32 latent space, and instantiate a transformer-based latent diffusion model with a flow-matching objective on top of this space for conditional 3D generation. Extensive experiments on garment and object datasets demonstrate that our method achieves superior reconstruction fidelity and boundary precision compared to prior geometry-image and voxel-based approaches, while requiring significantly fewer computational resources.