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Sampling
Monte Carlo Sampling: Generate random points according to a distribution and evaluate


Nusselt Analogon
Given sender patch with area .
Project sender patch onto hemisphere of receiving patch:

where is the angle between sending patch normal and projection direction and is the distance between the two patches.
Project result into plane:


The form factor is the covered portion of the unit circle.



Problem: Assumptions only hold for patches that are sufficiently far away.

Hemicube
Rasterize 5 sides of a hemicube placed around a point on .
Denote by the set of pixels that see patch . Then,

where are pre-calculated form factors for the individual pixels of the hemicube.