Area lights — lights with a size

Area lights — lights with a size

Status: shipped in v0.47.0. Diffuse direction is analytic; the terminator wrap and the specular representative point are fitted approximations, and this page says which is which.

A point light is a mathematical convenience. Nothing in the world is one — a window is two metres of glass, a strip light is a metre of tube, a bulb has a bulb. The difference shows up in three places at once: the shape of a highlight, the softness of a terminator, and the direction light arrives from when the emitter is close and wide.

Every placeable light now carries the surface it emits from. Point is the default and the zero-size case, and the whole implementation collapses to max(dot(n,l),0) × (1 - d/range)² when the emitter has no size — the expression that was inline before, reached numerically and not approximately.

#The shapes

A rect and a disk are one-sided by default — a window lights the room, not the wall it is set into. Turning lights both ways on makes it a panel that glows from both faces.

The node's scale multiplies the emitter, so dragging a scale handle on a window does what it looks like it does.

#Diffuse: the part that is exact

The vector irradiance of a polygon,

w = (1/2π) Σᵢ θᵢ ûᵢ

(θᵢ is the angle edge i subtends at the shading point, ûᵢ the unit normal of the wedge it sweeps) is linear in the surface normal. That is the useful fact: one loop over the edges gives a single vector, and the emitter's own lighting direction is ŵ. It is not the direction of the emitter's centre — for a four-metre strip standing beside a wall those differ by a lot, and that difference is exactly why the wall lights evenly instead of showing a hot spot opposite the middle.

area_light_probe checks this against quadrature over the emitter's real surface, at three different surface normals, and it agrees to within 8-bit quantisation.

The terminator softening is a fit. Once the direction is known, the response is clamp((n·ŵ + s) / (1 + s), 0, 1) where s is the emitter's apparent angular half-size. It is the right shape — a big light wraps past the horizon, a small one does not, and s = 0 is exactly max(n·ŵ, 0) — but it is not the clipped polygon integral, and a very large emitter very close to a surface will be a few percent off.

Range falloff measures to the emitter's nearest point, not its centre, and that measurement is view-independent. A three-metre bar whose centre is out of range still has an end beside you; a light that dimmed as you walked around it without moving would be unplaceable.

#Specular: the representative point

For the highlight, each shape reports the point on itself nearest the mirror direction, and the lobe is widened by the emitter's apparent size and re-normalised so growing a light spreads its highlight rather than adding energy to it.

• a sphere gives the classic disc highlight
• a rect gives a broad soft rectangle, clipped to its own extents
• a tube streaks along its own length — measured in the probe as a highlight more than twice as wide as it is tall, against a point light's round one

This is an approximation and a well-known one. It is not LTC: there are no fitted lookup tables, the energy is not exact, and a rect seen at a grazing angle does not horizon-clip its highlight properly. What it buys is that every shading path in the engine gets it — the raster PBR path, the Blinn-Phong path, the raymarched terrain and blobs and .flsl materials — from one function, with no tables to ship and nothing to bind.

#In the fog

Volumetric fog reads the emitter too, but takes only its distance and direction — there is no surface in mid-air to be facing anything, so there is no N·L term to replace. The visible consequence is that a long bar lights the air along its whole length rather than from a point at its middle. See ./volumetrics.md.

#Editing it

The Inspector's light node: pick emits from, then its dimensions. Switching shape carries the size across, so trying rect against disk is one click rather than a re-measure.

The Scene view draws the emitter at its real size and facing, with an arrow out of the emitting face. That matters more than it sounds: a rect light aimed at the wall behind it lights nothing, and there is no way to see that in the finished picture — the room is simply dark and the light looks like it is on.

From Lua, on node:getcomponent("PointLight"): shape (0 point, 1 sphere, 2 rect, 3 disk, 4 tube), plus width, height, radius, length, thickness, twoSided. A dimension reads 0 on a shape that has no such dimension, and writing one only lands on a shape that has it. Assigning shape keeps the size the emitter had, so cross-fading a window into a bulb does not flash.

#Cost

Per light per fragment: a point costs what it always did. A sphere or disk adds a handful of arithmetic. A rect adds four acos calls and four cross products; a tube adds one segment projection. All sixteen slots are shared with point lights and the same contribution ranking chooses them, so an area light is not a separate budget.

#Verified by

cargo run -p floptle-render --example area_light_probe -- <dir> — six checks:

1. a zero-size emitter reproduces the point light's closed form
2. a four-metre rect lights the far end of a wall a point at its centre leaves dark (measured as evenness, 0.95 against 0.62)
3. the analytic direction matches quadrature over the emitter's surface, at three different surface normals
4. a one-sided emitter does not light what is behind it — and both the two-sided version and the same emitter turned around do, so the facing test is not simply rejecting everything
5. a three-metre sphere reaches around onto a face a pinpoint leaves dark
6. a bar streaks its highlight along its own length and only along it

Runs under lavapipe in CI.

#Not in this one

• LTC. Linearly-transformed cosines would make the specular energy-exact and horizon-correct, at the cost of two fitted lookup textures. The seam is one function (area_terms), so it can be swapped without anything above it changing.
• Shadows shaped by the emitter. An area light still casts through the same sun/field shadow machinery as everything else; its softness comes from the penumbra setting, not from its own width.
• Textured emitters. A rect light emits one colour, not an image.
• Emitter geometry. The light does not draw itself — put a mesh with an emissive material where the emitter is if you want to see it in the frame.