3D triangle's (U, V) to (X, Y, Z)

[Maciej]

Hello

Could you please help me with the following?
Basically, I need to find the coordinates in space (X, Y, Z) of any POINT belonging to a 3D triangle, given that POINTS's two dimensional (U, V) coords. The UV pair is always between (0, 0) and (1, 1), however the answer should not rely on this assumption.

The data I have is:
- three sets of (X, Y, Z) coordinates, one for each triangle's vertex
- three sets of corresponding (U, V) coordinates, one for each triangle's vertex

Example data:
v1 = (0, 0, 0); uv1 = (0, 0)
v2 = (10, 0, 0); uv2 = (1, 0)
v3 = (10, 10, -10); uv3 = (1, 1)

I need to find:
- the (X, Y, Z) coordinates of any point belonging to that triangle given the UV pair.

For example, given the
UV = (1, 0.5)
in this case the result should be:
XYZ = (10, 5, -5)

I will really appreciate if you find any solution for this problem.
It sounds pretty easy and obvious, however I haven't managed to find any formula for this for over a week.

Thank you in advance.