A Spherical Cap Preserving Parameterization for Spherical Distributions

We introduce a novel parameterization for spherical distributions that is based on a point located inside the sphere, which we call a pivot. The pivot serves as the center of a straight-line projection that maps solid angles onto the opposite side of the sphere. By transforming spherical distributions in this way, we derive novel parametric spherical distributions that can be evaluated and importance-sampled from the original distributions using simple, closed-form expressions. Moreover, we prove that if the original distribution can be sampled and/or integrated over a spherical cap, then so can the transformed distribution. We exploit the properties of our parameterization to derive efficient spherical lighting techniques for both real-time and offline rendering. Our techniques are robust, fast, easy to implement, and achieve quality that is superior to previous work.

[IvoPavlik]

Does it mean that for any spherical distribution with analytical sampling it is possible to construct a sampling method for the distribution clipped to an arbitrary spherical cap?

[iamtanmay]

So, the source code of the Unity Engine itself was modified for this paper ? Or what role did Unity Technologies play ? Its not entirely clear.

[renzocoppola]

Will this see the light? I mean in Unity.