🤖 AI Summary
This work addresses the structural fragmentation and physical unrealizability inherent in traditional 3D sketching methods, which rely on numerous discrete curve segments. To overcome these limitations, the authors propose representing complex 3D geometry through a single, continuous, differentiable 4D B-spline that jointly encodes spatial coordinates and variable stroke width, thereby reformulating modeling as a global routing problem. This approach achieves, for the first time, topologically consistent sparse 3D abstractions and incorporates strong inductive biases to enhance structural coherence and aesthetic quality. Differentiable rendering is employed to rasterize width-varying curves, with optimization guided by projection error constraints and semantic signals from CLIP and Score Distillation Sampling (SDS). The method demonstrates significant improvements in semantic fidelity and structural integrity across tasks including image-to-3D abstraction, multi-view line drawing generation, and stylized surface filling.
📝 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.