Transforming Triangle in 3 Space with z = 1-x-y

[albert281]

I am trying to transform a triangle in 3 space with the constraint that z = 1-x-y. At this point I have the following transformation matrix A, and three vector equations:

| a1 a2 a3 |
A = | a4 a5 a6 |
| a7 a8 a9 |



A*x1 = k1*y1
A*x2 = k2*y2
A*x3 = k3*y3




I know the vertices of both triangles, before and after the transformation. The problem is that I can't put the above description in a manner that is solveable...without some input to clarify the issue.

The transformed triangle points can move in a manner to suggest stretching and translation, but not rotation. Given that z is dependent on x and y, how can I constrain this problem such that I can generate n equations in n unknowns?

 

[albert281]

I figured out how to solve for a7, a8 and a9 by using the constraint x+y+z=1 and solving for 3 equations in 3 unknowns. I found k1=k2=k3=1. I only have 6 equations in 6 unknowns left! Yay!