Vectorizing hand-drawn logos

Overview

A hand-drawn logo is charming but unmeasurable: it lives as a flat image, or as an SVG of hundreds of hand-placed polyline points — smooth to the eye, but rough, impossible to edit, and not truly scalable. This skill turns each contour into a small set of smooth cubic Bézier curves — genuine parametric polynomials

B(t) = (1-t)³P₀ + 3(1-t)²t·C₁ + 3(1-t)t²·C₂ + t³P₃,   t ∈ [0,1]

The curve is fitted along the original outline (not replaced by idealized circles/rectangles), so the hand-drawn fullness and character — even an off-centre curl or a wobble you want to keep — survive. The output is fully mathematical: reproducible, infinitely scalable, parametrically tweakable, and diff-able in git. From one definition you fan out color/layout variants and rasterize to PNG/ICO.