Gradient Space Projection Projections onto the Hemisphere

In this paper we present 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. We present different sampling techniques on the gradient space and provide qualitative comparisons.