arXiv:2605.11977cs.CV2026-05

用一根连续4D线统一抽象3D形状,结构更完整、可制造。

Optimizing 4D Wires for Sparse 3D Abstraction

论文配图:Optimizing 4D Wires for Sparse 3D Abstraction
图 1 · 摘自论文原文
  • 用参数化4D样条表示单根连续线条,支持宽窄变化。
  • 相比离散曲线段,生成结构语义更准、拓扑更连贯。
  • 适配图像到3D抽象、多视角线稿生成等任务。

我们提出一种统一的3D几何抽象框架,采用单个连续的4D线(参数化为带空间坐标和可变宽度$(x,y,z,w)$的B样条)来表示形状。现有方法通常将形状表示为多个独立的曲线段,常导致结构碎片化且难以物理实现。相比之下,我们证明单个连续样条足以捕捉复杂体积形态,并强制全局拓扑一致性。通过施加连续性约束,该方法将3D草图从局部密度累积过程转化为全局路径规划问题,提供更强的先验偏好,带来更优的美学效果与结构连贯性。为支持基于梯度的优化,我们设计了一种可微渲染管线,能高效对可变宽度曲线进行光栅化并保证投影误差有界。该形式支持现代引导信号如分数蒸馏采样(SDS)或CLIP。实验表明,相比基于离散曲线集合的方法,我们的统一表示在语义保真度与结构连贯性上均有提升。

原文摘要 · Abstract (English)

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.

3D抽象几何建模可微渲染

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