Solving the radiosity equation

Rendering a 3D scene with a radiosity engine means solving the radiosity equation for each patch (remember they have been subdivided). This means solving a N by N linear system, where N is the number of patches. Our computers are not able to solve this in a humanly acceptable time, cause often N is near thousands of hundreds.

Of course, there is a way to obtain faster results : iterative solving methods like Jacobi or Gauss-Seidel. The principle of iterative methods is to proceed step by step, with a partial solution on each step. On each step, you approach more and more the final result. For the end user, this means you progressively see the image appear. The correct solution is never reached. You stop the calculation process wether manually or automatically, when the amount of energy that has not yet been dispatched is under a fixed value. Actually, the iterative methods have a physical meaning : the repartition of the whole light energy in the scene, until it has been absorbed by all the patches.