A page that proves you understand colour

Two paints in daylight exactly the same (ΔE = 0.0). Under the bulb they separate, and under fluorescent light the difference ΔE = 19— in other words, obvious. The industry has a name for it: metameric mismatch — the reason behind the complaint "it looked right in the shop, wrong at home". Here real CIE colour matching functions and real light source spectra are used; the reflectance curves of two pigments are solved so that are produced.

Give a colour, and which pigments in what ratio should be mixed. What you see on screen is exactly the work done by the colour matching instrument in a paint laboratory: Kubelka-Munk computes the colour of the mixture, and the ratios are corrected step by step until ΔE shrinks. The numbers flow live — the solution is found on the spot, not read from a ready table.

The paint industry's way of measuring opacity: a film of increasing thickness is drawn across a black-and-white card, and the ratio of the readings over the black and the white ground is taken. The thickness at which the contrast ratio passes 98% is the point of "full coverage". Here that equation (Kubelka-Munk over a ground) is solved pixel by pixel.

Every colour the human eye can see lies inside this horseshoe-shaped area. The triangle is the part your screen can actually show. Every colour outside the triangle is lying on your screen — some real pigments sit exactly there. The most honest way to tell a customer "the colour you see on screen is not the thing itself".

"It went lighter as it dried" is the most frequent complaint, and it is not a fault of the paint: while wet, water and medium fill the space between the pigment grains, light scatters less, and the colour dark and saturated appears. As the water leaves, air takes its place, scattering rises, and the colour lightens and turns matt. Here the scattering coefficient rises over time; the rest is the equation's work.

On screen blue + yellow = grey. On the palette blue + yellow = green. The difference comes from light being absorbed and scattered inside the pigment grain; the paint industry has computed this with the Kubelka-Munk equation since 1931. That equation is running in the right half. For a paint brand there is no truer signature effect than this.

The signature of watercolour, the dark edge ring is not drawn here — it forms by itself as the water evaporates and the pigment is dragged to the edge and stays there. The texture of the paper is taken into account too: pigment collects in the hollows (granulation).

Here paint is not colour but volume. Every stroke leaves a height behind; the light refracts according to the slope of that surface and a ridge forms at the edge of the knife. The relief of an oil painting that you see when you look at it from the side.

A brush mark is not a "stamp". Each of the 420 bristles behaves like its own spring: press and it spreads, turn and it lags behind, lift and it gathers itself. The mark comes from where the bristles touch the paper — which is why no two strokes are alike.

Real marbling mathematics: every drop pushes the whole pattern beneath it outward in rings; the comb sweeps along a sine wave. Nobody else in the world has this — a signature effect out of our own culture.

The ray enters the glass and leaves through the back surface — and every colour at a different angle is refracted. That is where the rainbow fringe at the edges comes from; the same event as a prism splitting light. The shape of the bottle is defined as a single mathematical surface too, with no model file.

One 3D model, endless colours. Think what that means in a catalogue of 234 colours. Where: product heroes.

Not an imitation but physics: the fluid equations are solved on every frame (diffusion, pressure, vorticity). Where: hero openings — this is our signature.