NURBS Splatting: A Unified Differentiable Rendering Framework for Vector Graphics

2026-06-30

AI Summary

This work addresses the gradient instability and limited expressiveness of planar rational splines—such as NURBS—in differentiable rendering by introducing a continuous Gaussian field–based differentiable vector rendering framework. The method reformulates rendering as a smooth, differentiable accumulation process by sampling Gaussian kernels over both the curve parameter domain and the interior of closed regions. It is the first approach to jointly support long splines, rational weights, non-uniform knot vectors, and filled closed regions within a unified differentiable pipeline. Compared to conventional analytical rasterization techniques, the proposed framework substantially enhances gradient stability and geometric expressiveness, achieving superior reconstruction quality and robustness in tasks including calligraphy reconstruction, vectorization, and image abstraction with long splines.

Abstract

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.

Problem

• differentiable rendering
• vector graphics
• rational splines
• gradient instability
• NURBS

Innovation

• NURBS Splatting
• differentiable rendering
• vector graphics
• Gaussian splatting
• rational splines