Gradient Space Projection
This image is rendered using my global illumination renderer plug-in for 3D Studio Max R4 (native renderer of R4 did not have global illumination support). Only a single light source is used in this scene (the lamp in the corner), and almost all of the scene is illuminated by the reflected illumination from the ceiling.
Gradient Space Projection is a simple method for handling projections on the hemisphere. The proposed method defines a coordinate system on the hemisphere surface that effectively converts the hemisphere to an infinite plane tangent to the top of the hemisphere, which is called the gradient space. Using this coordinate system, projections onto the hemisphere are replaced by simple perspective projections onto the gradient space. This approach totally eliminates the non-linearities caused by the spherical surface and permits exact hemisphere projection computations using only a single projection operation.
Gradient Space Projection can easily be used in different global illumination algorithms. This image shows Gradient Space Projection used for gathering illumination from a photon map.
Here is another scene illuminated by a skylight rendered using my old renderer plug-in for 3D Studio Max R4.
This is another image rendered using my old renderer plug-in for 3D Studio Max R4. The Chevy model is illuminated by a uniform skylight.
A simple animation showing the gradient space project in action. The motion is hand animated in 3ds Max R4 and rendered using my renderer plugin with global illumination support using gradient space projection in 2003.