Perspective Texture maping


I'm trying to understand the algoritm to perspective texture maping for a poligonal mesh. Actualy i'm trying to understand about texture maping at all.

I get som sites which are presenting the algorithm but i have few questions about it.

1.) In all the examples they are useing the u, v coordinates. I'm confused if they are the vectors which are representing texture or they are coordinates for vertex in the texture space.
2.) should i have the texture coordinates for every vertex setup before maping or compute it from the mesh vertex and texture coordinates.

let asume that i have convex polygon A[-10, -10, 10] B[0, 10, 0] C[10, -10, 0]
and texture coordinates are P[0,0,0] T[0,10,0] S[10,0,0]

How should i compute the u, v for the polygon vertex ABC and for the point X in the polygon plane?

I REALLY need help about it, pleas.
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