Stroke processing

Resampling: The drawn path is walked by arc length and one knot is taken per span. Everything the hand wobbled between the knots is discarded there, so the span is the smoothing strength.

Natural curve: A cubic spline through the knots with zero second derivative at the ends, parameterized by chord length so uneven knot spacing does not distort the shape.

Hobby curve: The interpolation METAFONT draws paths with: tangent directions come from a mock-curvature system and control handles from Hobby's velocity function. It swings wider through corners than the natural spline, which is the visible difference between the two.

Both take the same knots, so moving the span slider trades fidelity against smoothness for both at once. The curves are documented on Curves.

Why the others jump: The natural spline and Hobby's curve each solve one system over every knot, so a new knot re-solves the whole curve. The influence decays with distance, but it never reaches zero.

Local support: Each segment of these two depends only on its four surrounding knots. Appending a knot changes the last segments and nothing before them, which the readout measures as exactly zero.

The trade: The Catmull-Rom passes through every knot but is only C1, so its curvature can kink at knots. The B-spline is C2 and smoother, and pays for it by approximating the knots instead of passing through them, visibly cutting the corners.

Turn over a window: The turn at a point compares the incoming and outgoing directions, each measured over a fixed arc window rather than one segment, so the jitter of dense points does not trigger cuts.

One cut per corner: A cut cannot follow another within the window's arc, so a sharp corner yields exactly one cut. The boundary point is shared by both pieces, so the strokes stay connected end to end.

Rendering: The smoothed polyline becomes the stroke's control points, so a processed path draws with any renderer unchanged.

Span: A span of zero disables the resampling: every drawn point is a knot, and the stroke follows the hand exactly.

Per-piece processing: Each piece is resampled and smoothed on its own before rendering, so a corner ends one tapered stroke and starts the next instead of being rounded away.

The gate: hasSettledStart walks the drawn points and passes once the accumulated arc reaches a threshold. Distance, not a point count: a slow hand piles points onto one spot without adding direction.

A gesture released below the threshold draws nothing, and a piece split off below it stays hidden until its own arc passes.

The rule: smoothByWidth spaces the smoothing knots at width × gain, clamped to a working range, and interpolates them with the local Catmull-Rom, so the settled part of a growing stroke holds still.

The black pointer line stays unsmoothed, so the gap between the hand and the mark shows the smoothing at work: none when thin, wide arcs when thick.

The hull: The convex hull of the drawn points is the smallest convex region containing all of them. Its perimeter is resampled at the span for even knots, and the closed Catmull-Rom or B-spline rounds it into a blob.

Containment: Smoothing cuts inside the hull, so each knot is pushed outward along its edge normal by a fraction of the span. The curve then still contains every drawn point.

Filling: The closed polyline becomes a THREE.Shape and its triangulation fills the area.

Closing first: The path knots feed the closed spline, so the gesture becomes an enclosed loop before the offset. Without this, an open stroke offsets into a tube that follows the line; with it, the result is always a mass. The offset's distance field does not care if the closure crosses the stroke, so any gesture closes safely.

The outline: The distance field to the closed loop is stamped onto a grid, and the radius contour is extracted with marching squares. Its outer boundary keeps the loop's concavities, where the convex hull above spans them.

Smoothing: The contour is resampled at the span and rounded by the closed Catmull-Rom or B-spline. The contour already sits the radius out from the path, so the smoothing has room to cut inward without excluding any drawn point.

Radius: Small, the blob reads as a tube around the line; large, the concavities fill in and it approaches the hull.