Mathematical Topics from 3D Graphics - 3D Math Primer for Graphics and Game Development - page 394

In principle, it doesn't matter how
we determine the UV coordinates for a
given point on the surface. However,
even when UV coordinates are calcu-
lated dynamically, rather than edited
by an artist, we typically compute or
assign UV coordinates only at the ver-
tex level, and the UV coordinates at an
arbitrary interior position on a face are
obtained through interpolation. If you
imagine the texture map as a stretchy
cloth, then when we assign texture-
mapping coordinates to a vertex, it's
like sticking a pin through the cloth at
those UV coordinates, and then pinning
the cloth onto the surface at that ver-
tex. There is one pin per vertex, so the
whole surface is covered.

Figure 10.16
An example texture map, with labeled
UV coordinates according to the DirectX
convention, which places the origin in
the upper-left corner.

Figure 10.17
A texture-mapped quad, with different UV coordinates assigned to the vertices