Windfoil: Closed-Form Coverage for Real-Time and Differentiable Vector Graphics

Matt DesLauriers

cs.GROct 1, 2026

Windfoil: Closed-Form Coverage for Real-Time and Differentiable Vector Graphics

Authors: Matt DesLauriers

Organizations: Creative Computing Institute University of the Arts London London, United Kingdom

Abstract

We present Windfoil, a GPU-friendly algorithm that treats rasterisation and differentiable vector graphics as two sides of the same problem by evaluating the box-filtered winding number of quadratic Bézier contours in closed form. We implement this in WebGPU, allowing it to run across a range of environments, including a web browser on a consumer laptop, and apply the system to real-time 2D rendering, high-resolution rasterisation for print media, and a differentiable renderer. We compare our renderer against Skia, a production-grade engine, and Slug, a popular GPU rasterisation algorithm for games and real-time applications, measuring fidelity to a reference box-filtered coverage. Our renderer matches the reference more closely than either, at performance comparable to Slug. We also compare our optimiser against DiffVG and Bézier Splatting, where it reaches equivalent or better reconstruction quality at a fraction of the per-step cost, scaling to tens of thousands of shapes at interactive rates.

Figures & tables


Ground Truth	$N{=}32$	$N{=}512$	$N{=}4{,}096$	$N{=}50{,}000$

Figure 1. Approximating a target photograph with 32 to 50,000 shapes, each a closed loop of quadratic Bézier curves, fitted by gradient descent on mean-squared pixel error. The renderer is differentiable and runs in WebGPU. Five images in a row, the first is a photo of a house in a field, and each subsequent image shows the same scene but painted with an increasing density of abstract coloured shapes.



(a) Ground Truth	(b) Ground Truth $2\times$	(c) Windfoil $2\times$	(d) $\|\Delta\|$ Windfoil	(e) $\|\Delta\|$ Slug	(f) $\|\Delta\|$ Skia	(g) $\|\Delta\|$ Figma

Figure 2. Coverage error against the box filter. Two scenes rendered at

512\times 512

pixels: the ‘@’ glyph from the Lato font, and a synthetic SVG rosette designed to highlight winding failures. (a) The box-filtered Ground Truth reference is estimated by point-sampling a

64\times 64

grid per pixel with winding ray-cast from the raw curves. (b) A nearest-neighbour scaled crop of the reference image. (c) Rendered with Windfoil, then also scaled and cropped. (d)–(g) Per-pixel

|\Delta|

from the reference crop as rendered by: Windfoil, Slug, Skia and Figma (v126.7.10), respectively. The error is amplified

\times 15

and clipped, so white pixels show differences. The (d) Windfoil column is mostly black, as the majority of rendered edges agree with the box filter. The rosette graphic exposes areas where averaging the winding before applying the fill rule leads to failures. Most notably, a bright vertical seam from winding cancellation at a self-crossing contour renders incorrectly as a hole with Windfoil and Slug, while Skia and Figma rasterise this edge correctly. A grid of two rows and seven columns. The top row is the glyph at-sign, the bottom a rosette graphic. The first column is the ground-truth reference, the next two are magnified crops of the reference and of Windfoil, and the last four are amplified error maps for Windfoil, Slug, Skia and Figma. Windfoil has smaller errors along ordinary edges, but both Windfoil and Slug show a bright seam at the rosette's self-crossing.


Windfoil (box)	Windfoil (tent)	Windfoil (cubic B-spline)	Skia	Figma	Photoshop

Figure 3. A sunburst scene of 256 thin strokes, rendered with different filter kernels and compared to existing production renderers. Six renderings of the same radial sunburst of thin black rays on white. The first three, rendered by Windfoil with box, tent, and cubic B-spline filters, resolve toward a smooth uniform grey at the centre. The last three, from Skia, Figma, and Photoshop, show strong moir'e interference and a progressively darker core.

Equal step budget
				final PSNR (dB)			$\Delta$ PSNR (dB)		optimise time (s)			parity speed-up
Benchmark	Opt. size	$N$	Budget	Windfoil	DiffVG	Bézier	DiffVG	Bézier	Windfoil	DiffVG	Bézier	DiffVG	Bézier
Kodak (24)	$768\times 512$	512	800 steps	26.60	26.41	22.80	$+0.19$	$+3.80$	2.57	269	23.0	$243\times^{\dagger}$	$196\times$
Färlev	$512\times 288$	256	800 steps	21.24	21.24	19.80	$0.00$	$+1.44$	1.22	138	17.2	—	$224\times$
Färlev	$512\times 288$	512	800 steps	21.83	21.79	20.73	$+0.04$	$+1.10$	1.85	220	22.3	$182\times$	$177\times$
Färlev	$512\times 288$	4096	800 steps	26.77	21.31	22.61	$+5.46$	$+4.16$	10.1	1658	132	$4901\times$	$214\times$

Table 1. Image fitting on an NVIDIA RTX 2000 Ada. Final PSNR is scored from saved PNGs, with DiffVG’s final render at

8\times 8

samples per pixel.

N

is the initial shape count;

\Delta

is Windfoil’s PSNR minus the baseline’s. Optimise time excludes setup, warm-up, final rendering, scoring, and output. Parity speed-up divides the baseline’s optimise time by Windfoil’s time to first reach that baseline’s final scored PSNR. Dashes mark unavailable or unreported comparisons. Bold marks the best value at the displayed precision, without implying statistical significance.


fishing boats in the harbour	a Paris café	a Tokyo street	a ballerina	a Ferris wheel

Figure 5. Text-to-SVG synthesis of scenes made of 256 white translucent rectangles, guided by CLIP. Each 2

\times

2 grid shows four optimisation runs using different random seeds. Five two-by-two grids of black-and-white generated scenes, one grid per text prompt. Each sketch is built from a few hundred overlapping semi-transparent white shapes on a black background.

Differentiable Rendering

Differentiable rendering makes image formation and its gradients computable, enabling visual scenes and graphics to be optimized from observations.

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(a) Ground Truth	(b) Ground Truth $2\times$	(c) Windfoil $2\times$	(d) $\|\Delta\|$ Windfoil	(e) $\|\Delta\|$ Slug	(f) $\|\Delta\|$ Skia	(g) $\|\Delta\|$ Figma

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Differentiable Rendering

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