Radiosity

C481 B581 Computer Graphics
Dana Vrajitoru

Radiosity

A global illumination method that also needs a lot of computations.
Based on the interaction between all of the surfaces in the scene, and on the conservation of the global light energy.
We can choose to compute the light intensity in each point of the scene, then use this information to render the scene from any point of view.

General idea: we must have an equilibrium of the amount of light produced by each light source and the total amount of light reflected by each surface.

Notations

Radiosity b: the total amount of light energy that we can find in each point, i.e. that is visible in this point in a solid angle in a unit of time.
Emitted light e: part of the radiosity that is produced by the point, if it belongs to a light source.
Reflected light R: part of the radiosity that is reflected by the surface containing the point depending on a factor r.
Note. b = e + R.
Form factor f: part of the radiosity produced by one object that is reflected by another one.

The System of Equations

In general, e = 0 for a point in the scene that is not a light source, and r = 0 for the light sources.
The radiosity in each point must be equal to the light emitted by it plus the total light it reflects from all of the other objects in the scene.

Numerically the integral becomes a sum over all the polygons in the scene.
This is a system of equations where the unknowns are b_i.

The Form Factor
If j corresponds to a light source, f_i-j depends on the angle between the ray of light from the source to the surface and the normal to the surface.
If the objects i and j are both reflecting surfaces, then f_i-j depends on the angles made by the normals to the surface in i and j with the line segment from i to j.
f_i-i = 0, for i=1 to n.

Gauss-Seidel Method
Iteratively compute b_i :
Initialize

Compute b_i for the light sources based on the emitted energy.
For all the other polygons, assign b_i = 0 (or sum the components from the light sources).

Recalculate each b_ibased on the previously computed b₁, b₂, ... b_n.
If the scene is made of complex surfaces, discretize it as a mesh of polygons.

http://www.cg.tuwien.ac.at/research/rendering/rays-radio/