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Heightfield Driven Microfact-based BRDF Generation

The main idea is to develop a BRDF based on a heightfield.
This work discusses the number of problems which occur when
extending Ashikhmin's work in SIGGRAPH 2000 to arbitrary heightfields. As
the normal distributions become non-continuous, and table based.
What are the proper bounds for such a distribution - what types of
heightfields can be properly be displayed in such a formulation - and what
sizes are needed for these tables are all questions answered by this
research.
My formulation has some start-up cost for large heightfields
producing large numbers of normals, but it runs in real-time ray tracing
with several table look-ups and minor calculations.
Thoughts on how to extend this work to diffuse surfaces has been
given and is a topic of possible future research.