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Character Movement on 3D (Polygonal) Surface

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Ok, so I''ve kinda gotten into the 3D game programming a little late (2nd year of college). It''s always hard trying to figure out what you need to know in order to do what you want (and also having the funds to do so). I really love it. A couple friends and I have decided to make a game before next years game developer''s conference (or at least a demo). Nothing too fancy, but something to show off to try and sack a coop in the business. At the moment, I''m having trouble figuring out how to calculate a character''s movement along a surface of polygons. The problem I have is that I can''t figure out how to get the character to move across multiple polygons without keeping track of all the vertices. What I was doing was treating the character as a point on the surface...and it''s easy doing just one surface, but the problem is doing many connected surfaces. Any suggestions? Any better way of doing it? Any other help would be great also.

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