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3D navigation mesh algorithm?


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This is a question for the people that have a degree in mathematics or computer science;

The following is based on Valve's Navigation Mesh system;

In my gamemode I plan on including smart AI bots. Before the AI bots can be used, a navigation mesh needs to be generated. Does anybody have any ideas of what algorithm would be used to split the map into rectangles (collisions) that the bots can walk around on? It needs to involve virtually walking around the map, and linking together sections that can be walked on.

The second half of the problem is calculating when the bots should carry on, and when they should turn to go down another path. In certain circumstances, the bots will have a target (a capture point or a flag), and in most cases, they will have no target, and be expected to simply roam around the map looking for non-allied players to kill.

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