[Algorithms] applying precomputed and/or sampled lighting to dynamic objects

[Charles B. <cb...@cb...>]

The basic idea here is an old one :

encoding the specular and diffuse lighting incident in a point in an
environment map.  To light an object near that point, you use the 
reflection vector to look up the specular map and the normal to look
up the diffuse map.  The final color is then :

Out =  (1 - Gloss) * Diffuse(normal) * Texture
       + Gloss * Specular(reflection) * (BRDF Texture)

(the Gloss map may just be a function of position, or it may also be a
function of angle (eg. the Fresnel term)).  The (BRDF Texture)
could be 1 in the simplest case.  The normal and reflection vector might
come from the vertices, or from a normal map (you need EMBM for the reflection
vector to come from the normal map).  All of this can be done with vertex +
pixel shaders.

This can produce very high quality lighting by including radiosity
contributions
in the environment map.  The problem is that only a single environment map is
used, and the lighting environment is actually location dependent.

To address this, I propose that you lay down several environment map sample
points
(you create a new map as a preprocess when you detect that the old one is a
bad
approximation there).  All the environment map points are joined by a
tetrahedral
net (simplicial complex).

At run time, the center of the object is used to find its environment maps.
 That
center point selects a tetrahedron, which in turn selects four environment
maps.
You can find "barycentric" coordinates in the tetrahedron by using volumes of
sub-tetrahedra just the same way you use areas of triangles.  You use a
"virtual"
environment map by alpha-blending together the four maps at the corners of the
tetrahedron using their barycentric coordinates as alpha values.  Thus the
Diffuse and Specular terms in the above lighting equation are replaced with
four
alpha-blended terms.

This can be done with 7 passes using two-multitexture hardware.
First precompute a "Specular Response" texture as BRDF * Gloss.

1) render two diffuse environment maps
2) alpha blend in two more diffuse environment maps
3) multiply by (1-Gloss) * Texture
4 - 7) add on Specular(i) * (Specular Response) for i = 1 to 4

To use normal maps requires three-simultaneous texture hardware, I believe.

I don't think there's any way to use fewer environment maps without severe
transitioning
artifacts.  If your game has strongly constrained environments, then you
can use the walls
of the game as boundaries of the graph of environment maps, so that few (or
no) tetrahedrons
are created (for example, you could have just a linear set of nodes down a
hallway).


Very cool little BRDF note I just learned : almost all materials reflect
more strongly
at glancing angles (this is obvious for glass and chrome and whatnot) -
it's even true
for paper!  Hold a piece of paper at a very glancing angle to a light
source, and you
will observe a strong specular reflection!!  Whether or not this affects
the typical
illumination of paper at all is another question...


--------------------------------------
Charles Bloom           www.cbloom.com