What the Lambertian assumption costs a room, against how rough its walls are
Drawn at its defaults, in the room, with a lobe on its walls.
It reads 9 options and
no others: show, towards, conserve, centre, rough, rho, mix, lamp, reading.
Called by 17 essays
the blast radius of changing it
The solver had no slot for gloss
Every scene result in this collection is computed by radiosity, and radiosity is not an approximation that could be made more accurate. Its unknown is one number per surface, and a surface that returns light differently in different directions does not have one. A missing slot cannot be wrong by a small amount.
What a scene doesThirty unknowns instead of six
A directional transport solver is worth nothing until it reproduces the one it replaces. Setting every wall's bidirectional distribution to ρ over π collapses thirty ordered-pair radiances onto six radiosities and reproduces this collection's existing answer to 9.8 × 10⁻¹⁶ relative — which is the only reason anything else it says can be believed.
What a scene doesA lobe takes colour out of a bounce
A gloss wall sends more light to the floor and less colour. The extra light is a Fresnel reflection at the interface, it carries the lamp's spectrum rather than the paint's, and it arrives at the next surface white — so a green room in satin paint is less green than the same room in flat paint by nearly a colour difference of chroma.
What a scene doesThe floor is a different colour from the door
With a lobe on the walls the floor sends chroma 18.76 towards the front of the room and 20.94 towards the side walls, a spread of two colour differences. A radiosity solution assigns the floor one number, so the whole of that spread is a quantity the method has no slot for rather than one it estimates badly.
What a scene doesTwo ways to put a lobe on a wall
Take the interface's return out of the body term and a gloss wall makes the room less colourful. Add it beside the body term and the same wall makes the room more colourful. Same solver, same room, one line of energy accounting, and the two answers differ by nearly three units of chroma at the glossy end.
Where the model breaksWhere a patch stops being a point
A patch in a cube subtends a cone of 25.8° at the face opposite. A microfacet lobe of roughness 0.05 is about three degrees wide. Point-sampling the second inside the first returned a chroma of thirty-four thousand and a negative lightness, and the boundary between working and not working is measured rather than declared.
What a scene doesA tenth of the return arriving white
Nine per cent of what leaves a satin wall is a Fresnel reflection carrying no pigment. That nine per cent moves the room's colour by 4.89 ΔE₀₀ and its chroma by five per cent, because an interreflection multiplies and a small contribution with a different spectrum compounds into a large one.
What a scene doesEvery scene in this collection was matt
The green wall, the corner, the bounce series and the metamer separation are all computed on Lambertian surfaces, because the solver that produced them requires it. Each would move by between one and five colour differences on an ordinary satin finish, and none of those essays says what finish it means.
What a scene doesA gloss finish takes colour out of the whole room
A gloss wall makes the floor's return less colourful seen from the front of a room and more colourful seen from the coloured walls, which leaves open whether the lobe removes colour or only moves it. A ledger of every flux between the room's faces answers it. At an eggshell finish the room's reflected light gains 16 per cent in quantity and loses 8.3 per cent of its chroma, and the loss is nearly the same for blue, green and orange walls while the walls' own losses range from 13 to 25 per cent. Only the painted walls receive light as colourful as before.
What a scene doesA gloss room looks less colourful than it measures
A gloss finish takes 8.3 per cent of the chroma out of a green room's reflected light, and a viewer adapted to the room should discount a loss that affects everything alike. The appearance model says the opposite. Adaptation removes the colour the whole room shares, leaves the colour that differs from face to face, and the finish takes as large a share of that as of anything — so to a viewer standing in the room the faces lose 13.9 per cent of their chroma, not 8.6.
What a scene doesThe boundary belongs to the quadrature
The directional solver stops at a roughness of about 0.15, and below that its answers are not imprecise but unphysical. The boundary is where the lobe stops being resolved by the sampling, so it belongs to the discretisation rather than to the room — and moving it is a purchase. Measured across six quadratures the reachable roughness falls as the cost to the power of a third, so a finish twice as glossy costs seven times the work and a polished varnish costs two hundred and thirty-six times.
What a scene doesA finish adds colour only to a daylight meter
Measured against daylight's white, a satin finish under six lamps and six wall colours takes anything from −6 to 42 per cent of a room's colour, and one room reads as more colourful glossy than matt. Measured against the white of the lamp each room is actually lit by, the same thirty-six rooms lose between 7.7 and 12.9 per cent and none gains. The whole spread was the lamp's own colour, and the finish does one simple thing to every room: it pulls the room's colour a tenth of the way towards the lamp's white.
What a scene doesWhat an adapted viewer loses is set by the wall
A satin finish takes about a tenth of a room's colour, measured on the room's light against its lamp's white. Read through an appearance model by a viewer adapted to the room, the same thirty-six rooms lose between 12.8 and 30.9 per cent — 1.4 to 2.4 times as much — and the wall colour decides the multiplier: a deep red room loses twice what a green one does, under every lamp. A test on the bare wall predicts it. Add a little of the lamp's white to the wall's own colour and ask the model what that costs: the answer orders the thirty-six multipliers at 0.95.
What a scene doesA dark wall pays for a finish
A satin finish takes about a tenth of a room's colour, and the tenth varies. The natural explanation is that a weak colour loses a larger share of itself to the white light a glossy surface adds. Over seventy-two paints under one lamp that explanation orders nothing: the loss runs from 2.5 to 15.5 per cent, it follows how much light the wall returns at a rank correlation of −0.89, and it follows how colourful the wall is at −0.04. Two rooms equally colourful matt lose shares nearly six times apart, and the one that loses more is the darker.
What a scene doesThe finish adds the room's own colour
Among dark walls a more saturated paint loses a smaller share of its colour to a gloss finish, and among pale walls a larger one. The mechanism proposed for that reversal was spectral concentration — a narrow tall band — and the census that found it already contained four families of paints whose bands are all the same width. Holding lightness still, the band's width orders the losses at a rank correlation of 0.01. What does order them is that the light a finish adds has already bounced off the walls.
What a scene doesAn open room hands over sooner
A gloss finish takes the least colour from a saturated dark wall and the most from a saturated pale one, and in a closed cube the sign changes at a wall returning about a third of the light. The prediction was that a less enclosed room would move that point up the lightness scale and that a room with a window would have no pale end. Opening one wall moves it down, from a luminance factor of 0.36 to 0.29, and opening a second to 0.24; stretching the room into a corridor or flattening it nudges it slightly up. The ambient does whiten, as predicted. A whiter ambient does not delay the colour term — it weakens it, so the other term takes over sooner.
What a scene doesA probe at the wall prices the finish
The light arriving at a painted wall from the rest of its room is what a gloss finish hands back, and a small probe held against the wall reads it. It lies on the line from the lamp's white to the wall's own colour, a fraction of the way along, and the fraction is set by how much light the wall returns, not by how colourful it is — as predicted. It is not the fixed fraction the prediction said: it runs from 2 to 46 per cent across seventy-two paints in one room. That variation is what makes it useful. Read in the matt room, it orders what a satin finish would cost more tightly than the paint's own lightness does, in every room tried.