Feaffer draws no bitmaps and stamps no textures. A feather is a few hundred thin strokes on an SVG, each one placed by the same handful of equations a real feather more or less obeys. What follows is the whole of it, plainly — because the pleasure of the thing is partly in seeing the grain of the maths through the finish, and because someone may want to grow their own.

The rachis is a single quadratic Bézier from the calamus at the base to the tip: B(t) = (1−t)²·base + 2(1−t)t·control + t²·tip, with the control point pushed sideways by the curvature, which is the wind the feather grew against. At any t along it we can take the tangent, and turn it a right angle for the normal — the across-vane direction the barbs comb out along. Under asymmetry the whole shaft drifts toward the leading edge (by asym · breadth · 0.22), the way a flight feather’s does. The visible quill stops at t = 0.9; the last tenth is closed by barbs, not by drawing the shaft to a point.

A single function width(t) gives the vane’s half-breadth all along the shaft. Below the widest point (peak ≈ 0.63) it eases up as sin(u·π/2)^0.85. Above it, a feather closes in one of three families— because a feather’s tip is categorical, not a slider, and the old continuous pointy-to-round blend always ran two closing mechanisms at once and lived in the lumps between them. Field guides know three, and each has its own mathematics:

• Rounded is a quarter of a superellipse, w = √(1 − uᵖ). For any power p ≥ 1 it is convex everywhere, so a dome has nowhere to dent inward — blunt or slender, never lumpy. And p is measured in pixels, not chosen in the abstract: it is set so the dome turns over as deep along the shaft as the vane is wide across, so a magpie’s long tail-feather stays as round at the tip as a short body feather. It closes by wrap (see the fan, below).
• Acuminate is a taper, w = (1−u)ᵏ. Raising k bends the edge concave — the sweeping hollow needle of a pheasant’s tail. Concavity is honest here; it is what acuminate means. It closes by taper alone: the vane shortens to nothing, and a fine sprig of bare quill carries the very point past where a drawable barb gives out.
• Truncate is the rounded body, cut. The barbs shear off along a growth contour — level with the cut at the shaft, drooping gently down each web — and the corner where the cut meets the side of the vane is rounded by a smooth minimum of the two edges, whose radius is the one degree of freedom: crisp square to soft-shouldered.

Asymmetry then steals breadth from the leading web and gives it to the trailing one, and cos(barb angle) sets how much of a barb’s length is spent reaching across the vane versus up it.

The barbs are combed in rows up the shaft (the rounded crown drinks extra half-step rows so its weave doesn’t thin where it turns over). Each barb leaves the shaft at the barb angle and has to be exactly long enough to land its tip on the vane’s outline — and here is the one properly subtle sum in the tool. A barb climbs as it reaches out, so it lands its tip higher up the edge than its root; reading the width at the root let a barb on a short broad feather climb clean past the crown at full breadth (a square-shouldered fat head). So the length is solved, not read — a damped fixed-point iteration, bl ← ½·bl + ½·width(t + bl·sinθ/L), a few turns until the tip sits on the envelope. Damped, because the envelope’s steep tip-end would otherwise make the bare iteration ring.

Two more honesties keep the vane silky: the tip jitter is scaled back by a barb’s slope (≈ 0.12 · min(1, tan46°/tanθ), 46° being the default comb), so a near-vertical barb’s shake doesn’t fling its tip wide of the edge; and on rounded tips a closing fan bends each near-apex barb so it leaves the shaft like its neighbours but arrivesskimming the crown — its arc’s control point placed where those two directions cross. Because only the rounded family fans, the fan can be served properly, and the old habit of every strand collapsing onto the axis (re- sharpening the tip into a central plume with a cleft down each web) dissolves.

The plumaceous down at the base is not strokes but wander: each strand is a chain of gentle turns around its own curl, with a whisper of gravity added every segment, and interior points sprout barbules — the micro-wisps that make downdown — all pooled into one shared path so a cloud of them costs the SVG almost nothing. Just above the down, each vane barb keeps a downy base for a short way (the afterfeather), so fluff eases into clean vane instead of hitting a hard waterline. The down draws from its own stream of dice, so faffing it never re-rolls the vane.

Age is more than missing barbs. A flown feather unzips: neighbouring barbs let go of one another and the edge bites in a V-shaped notch. The notches live on their own stream too, so a specimen’s wear is part of its fixed identity, not a thing that reshuffles every time you nudge another slider.