# Optimizing 4D Wires for Sparse 3D Abstraction

arXiv: https://arxiv.org/abs/2605.11977 · HTML: https://mlsanity.com/paper/2605.11977/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 39 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 19 of 19)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [A Neural Representation of Sketch Drawings](https://mlsanity.com/paper/1704.03477/) (2017)
- [CLIPstyler: Image Style Transfer with a Single Text Condition](https://mlsanity.com/paper/2112.00374/) (2021)
- [CLIPDraw: Exploring Text-to-Drawing Synthesis through Language-Image Encoders](https://mlsanity.com/paper/2106.14843/) (2021)
- [VectorFusion: Text-to-SVG by Abstracting Pixel-Based Diffusion Models](https://mlsanity.com/paper/2211.11319/) (2022)
- [DreamTime: An Improved Optimization Strategy for Diffusion-Guided 3D Generation](https://mlsanity.com/paper/2306.12422/) (2023)
- [Towards Layer-wise Image Vectorization](https://mlsanity.com/paper/2206.04655/) (2022)
- [Word-As-Image for Semantic Typography](https://mlsanity.com/paper/2303.01818/) (2023)
- [DiffSketcher: Text Guided Vector Sketch Synthesis through Latent Diffusion Models](https://mlsanity.com/paper/2306.14685/) (2023)
- [3Doodle: Compact Abstraction of Objects with 3D Strokes](https://mlsanity.com/paper/2402.03690/) (2024)
- [Wired Perspectives: Multi-View Wire Art Embraces Generative AI](https://mlsanity.com/paper/2311.15421/) (2023)
- [CLIPAG: Towards Generator-Free Text-to-Image Generation](https://mlsanity.com/paper/2306.16805/) (2023)
- [Diff3DS: Generating View-Consistent 3D Sketch via Differentiable Curve Rendering](https://mlsanity.com/paper/2405.15305/) (2024)
- [Neural Image Abstraction Using Long Smoothing B-Splines](https://mlsanity.com/paper/2511.05360/) (2025)
- [Image-Space Collage and Packing with Differentiable Rendering](https://mlsanity.com/paper/2406.04008/) (2024)
- [WireBend-kit: A Computational Design and Fabrication Toolkit for Wirebending Custom 3D Wireframe Structures](https://mlsanity.com/paper/2509.24083/) (2025)

## Abstract (arXiv)

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.