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Transform triangle

  1. May 26, 2010 #1
    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?
     
  2. jcsd
  3. May 26, 2010 #2
    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!
     
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