用高斯场统一渲染矢量图形，稳定且支持复杂曲线。
NURBS Splatting: A Unified Differentiable Rendering Framework for Vector Graphics
- 将平面有理样条转为连续高斯场采样渲染
- 支持长曲线、有理权重与闭合区域填充，梯度稳定
- 适合书法重建与矢量化任务，效果优于现有方法
平面有理样条的可微渲染仍鲜被研究，尽管其在矢量图形与设计中广泛应用。现有可微矢量渲染器多聚焦贝塞尔曲线，依赖解析光栅化，易出现梯度不稳定且灵活性有限。我们提出NURBS Splatting，将平面有理曲线表示为连续高斯场，沿曲线参数域及闭合区域内部采样高斯，并将渲染重构为平滑累积过程，实现稳定梯度。该方法天然支持长样条、有理权重、非均匀节点和闭合区域填充。我们在书法重建、矢量化框架及长样条图像抽象任务中验证其有效性，结果表明相比现有方法，具有更高的稳定性与重建质量。
原文摘要 · Abstract (English)
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.
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