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What is the process of creating geometry data to assist on NPCs movements and such on a 3D world to avoiding having them from going through the ground, etc? Are there specific modelling programs that can create the world and the collision geometry to be used?

The map I made has caves, lakes with deep water, varying terrains heights, mountains, etc.

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Are you meaning a navmesh; the grid of nodes that NPCs can follow? –  The Communist Duck Dec 19 '10 at 11:51
    
Does your world have caves/overhangs, or is it a pure heightmap? –  Martin Dec 19 '10 at 14:44
    
It has caves, lower and highs lands, mountains. So when I sent some random walk ai for the NPCS they often go underground, behind walls andso forth. –  Prix Dec 19 '10 at 18:06
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Check out recast: http://code.google.com/p/recastnavigation/

It has a lot of good starting points. You'd have to extend it for how you want things like water to be treated, but it's probably the closest thing to a free out of the box solution out there that I know of.

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A very nice Open Source project Recast and Detour. Recast creates the Nav Mesh and Detour creates pathing on the mesh. The project was created by Mikko Mononen, the Lead AI Programmer on Crysis. His personal blog has development information on the project digestingduck.blogspot.com –  David Young Dec 21 '10 at 0:09
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