Pressure curves — a shape, not an exponent

What was there, and why it was not enough

Three numbers: PressureSizeGamma, PressureFlowGamma, PressureHardnessGamma, each an exponent in p^γ. Cheap, one control each, and the tool bar called the slider "Response curve", which is the tell.

p^γ is monotone for every γ. So the whole family it can reach is "gentler" and "fiercer" — and there is no member of it that is thin at a feather touch, thick in the middle and thin again when leaned on. That is not an exotic request; it is what an ink brush that spreads and then floods actually does, and it is the first thing an artist tries to build.

A drawn curve reaches it, and reaches everything the exponents did.

The interpolant, and why not the obvious one

Monotone cubic, Fritsch–Carlson. The obvious choices both fail on a requirement that is easy to miss until it produces a bug report:

	What goes wrong
Straight segments	Visible corners at every handle. A response that changes slope in one step reads as the pen snagging.
Catmull–Rom / natural cubic	Overshoots. A curve whose handles all sit inside 0..1 evaluates past 1 between them.

The overshoot is the disqualifying one. For size it is a dab wider than the brush; for flow it is paint darker than the colour that was picked; and for either it happens at pressures the artist never placed a handle at, so it looks like the engine is broken rather than the curve.

Fritsch–Carlson is the same Hermite spline with two extra rules — zero tangent where the neighbouring secants disagree in sign, and a cap at three times the smaller of them — and those rules are exactly what makes the interpolant stay between its own handles.

They also set a floor on how sharply it can turn. FromGamma reproduces p^0.5 to about 2%, not to a byte of alpha, and no number of handles fixes that: 16 instead of 13 moves it by 0.003. This is the right trade rather than a shortfall, and the reason is that FromGamma is only ever a shape to start editing from — the render path still evaluates the exponent itself until a curve exists.

Sampling for it goes along whichever axis the exponent is well-behaved in: evenly in pressure above γ = 1, evenly in output below it, where the slope at zero is infinite and even pressure steps leave the whole knee to the interpolator.

The gamma is the curve's default shape, not a rival

Every file, preset and imported .abr in existence is written in gammas. Three options, and only one of them is safe:

1. Convert on load. Silently repaints art that is already finished, because the conversion is 2% off. No.
2. Two mechanisms at render time. Two code paths that must agree forever.
3. A target with no curve falls back to its own gamma. One evaluation path — PressureResponse.Factor — nothing to migrate, and old art renders byte-identically because it takes the same arithmetic it always did.

The editor hides the difference: it shows PressureResponse.Shape, which is the artist's curve or the one the gamma describes, so a brush made before curves existed opens on its real response rather than on a straight line that would flatten it at the first drag.

What pressure is allowed to drive

Seven targets, and the list is a judgement rather than an inventory.

Target	Why
Size, Flow, Hardness	The three that already had exponents
Scatter	Press harder, throw wider
Roundness	A flat brush pressed down spreads toward circular
Colour rate	A smudge that adds more of its own colour when leaned on
Smudge length	…and drags what it picked up further

Two deliberate absences:

• Opacity. It is a stroke-level cap that overlapping dabs never exceed, so "opacity follows pressure" would have to mean something different at every dab and could not mean anything at the stroke. Flow is the per-dab control and is what an artist means by transparency.
• Rotation. No pen gesture makes "press harder, turn the nib" a thing anybody does. Rotation follows the stroke's direction or it jitters; both exist.

Scatter keeps its direction

Pressure scales how far scatter throws, never which way. The angle stays the position hash's, so a harder press spreads the same pattern rather than picking a new one — dabs move outward instead of jumping about. That is invariant 2 seen from the artist's side: visual variation is wanted, logical randomness is forbidden, and a scatter that reshuffled under pressure would boil at 12 fps.

The control

Draws and reports; it does not decide. Every edit leaves as a whole new ResponseCurve on CurveChanged, so the change lands through the view model with the rest of the brush rather than mutating a record the view model believes it owns — which is also what lets undo see it.

The curve is drawn by sampling the same evaluator the engine uses, one sample per pixel, rather than by converting the handles into Avalonia's bezier primitives. A second implementation of the interpolant is a second thing to keep in step, and the failure mode — an editor that shows a shape the brush does not paint — is the worst one available here.

The ends keep their pressure: dragging the handle at full pressure sideways would leave the curve saying nothing about the top of the pen's range, where it is then flat, and the brush would read as having stopped responding rather than as having been edited.

Not in scope

Curves driven by anything other than pressure. Tilt and speed are the obvious candidates and neither is in the record yet — StrokePoint is (X, Y, Pressure) and nothing stores time. When they arrive, the shape of this is already right: BrushDynamic names the target, and the input would become a second key rather than a second mechanism.