I am given two triangles which can be seen here, we'll take the values of $D_0$ and $D_1$ to be 0 for simplicity. From these two triangles, I am supposed to decompose it and find a Translation matrix $T$, a Scaling matrix $S$ and a Rotation matrix $R$ such that $TSR$ = $M$ where $M$ is the full transformation matrix. I believe I was able to find the translation matrix by finding the center of mass of each triangle and then subtracting to find the translation matrix. Now I am not sure how to find the scaling and rotation matrix. Could someone please guide me into achieving this.
2026-04-12 03:11:34.1775963494
Finding the translation, scaling and rotation matrices between two triangles.
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Some thoughts:
$TSR$ applies in this order on the triangle: $R$ first, then $S$ then $T$.
AB is still 1 unit in length, R and T wouldn't change the length of AB, so can you decide anything about $S$ from this?
T doesn't change the orientation of AB, and ABs orientation is unchanged, can you then deduce anything about $R$ and $S$?