RE: [Algorithms] Lightmap Terrain

[Fredo D. <fr...@gr...>]

It is a classical misunderstanding to believe that radiosity needs
closed environments.
There is no problem (neither theoretical nor practical) with unbounded
scenes.

Francois Sillion has a paper about hierarchical radiosity for terrains
and sky:
Hierarchical Lighting Simulation for Outdoor Scenes 
http://www-imagis.imag.fr/Membres/Francois.Sillion/Papers/Index.html

I had also seen some work that simulated the interreflexions between
mountains to simulate the snow coverage. Can't remember where though.

if you want radiosity code:
http://www.graphics.lcs.mit.edu/~fredo/Book/code.html
under global illumination

But this won't give you real-time.
I guess you could accelerate this by doing only one bounce, and by
gathering light only from nearby vertices.

See also the paper by Heidrich et al. at Siggraph this year, it is in
fact very related (they compute interreflections for bump maps, and bump
maps are height fields). It is also quite related to the horizon map
idea discussed in a previous e-mail.
http://www.ag2.mpi-sb.mpg.de/~heidrich/

But, as already said, there is no way you can in a cheap way integrate
smoothly the illumination coming from the sky.

I guess you could use a simple heuristic for the sky illumination from a
vertex. What you want to do is to integrate the light coming from the
whole sky, that is, a hemisphere, taking shadowing into account.
Assume that only the adjacent faces and the global terrain hide the sky.
Thus, for each face you subtract the corresponding wedge from the
hemisphere (I have made a figure at
http://graphics.lcs.mit.edu/~fredo/sky.jpg)
I'm sure that this has been already used somehere, but I have no idea
where.

For the shadowing of direct lighting from the sun, I don't know if
Musgrave describes such an optimization, but you could also sweep
"shadowing horizons" from the parallel light source direction to compute
the illumination along parallel lines on the terrain. Sounds not clear?
See the figure http://graphics.lcs.mit.edu/~fredo/shadow.jpg
Note that because the light direction is not a multiple of 45 degrees,
the sweep lines don't fall on all the vertices. Well, I'm sure that you
can find a way to deal with that with weights or something else.

To summarize, you have three problems:
- illumination from the sun (the most important light source): use the
cosine law, parallel light source and maybe try my sweep idea
- illumination from the sky (very important for overcast days), nasty
but intersecting the wedges from the hemisphere may give you something.
- interreflexion from the neighbouring terrain: I propose to consider
only one bounce from the adjacent vertices. Of course add an ambient
term too.

Fredo

--
Fredo Durand,  MIT-LCS Graphics Group
NE43-255, Cambridge, MA 02139 
phone : (617) 253 7223  fax : (617) 253 4640 
http://graphics.lcs.mit.edu/~fredo/