Finding IFS Rules from Images of Points

Background: Matrix Formulation

The equations

ax1 + by1 + e = u1 ax2 + by2 + e = u2 ax3 + by3 + e = u3 cx1 + dy1 + f = v1 cx2 + dy2 + f = v2 cx3 + dy3 + f = v3

can be written in matrix form as

and

Note both equations have the same coefficient matrix, so if that matrix is invertible, the solutions are easy.

and

Here is a proof that the matrix is invertible if and only if the points p1, p2, and p3 are non-collinear.

Here is the solution.

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