NURBS Splatting: A Unified Differentiable Rendering Framework for Vector Graphics

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.