Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Maciej
Posts:
1
Registered:
10/28/10


3D triangle's (U, V) to (X, Y, Z)
Posted:
Oct 28, 2010 6:37 PM


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.



