This is my first post on Mathematics Exchange, so I hope you'll be easy on me!
I'm trying to project points in one 2-d coordinate space into another 2-d coordinate space using a simple matrix transform (Python/Numpy code here).
By solving the matrix problem in the way indicated in that snippet, I get a 3x3 matrix. I now wish to use that matrix to project 2d points from the input space to the output space (lines 129-140 of the code).
My trouble is, given a 2d point in the input coordinates like 0, 347.04001, when I compose the point in 3x1 notation [0, 347.04001, 1] and multiply the point by my translation matrix, the point is not correctly positioned in the output space.
My question is: After I translate my input point to the output space (e.g. line 129), how should I interpret the third value of the output vector (row 3 column 1 of the output vector)? More generally, how should I interpret the values in the third row of the translation matrix? Any help others can provide on this question will be tremendously appreciated!