How can I chain rotate and scale operations (each with different origins) while keeping each operation origin in relation to the original local component space?
Using matrix denotation (i.e. T for translation matrix, R for the rotation matrix, and S for the scaling matrix) I'm performing the following operations on my object:
\begin{gather*} T*R*S \end{gather*}
$T$ takes us from a global to local coordinate frame, then $R$ and $S$ rotate and subsequently scale our object. Since we are rotating and scaling around unique points in the object, the operation breaks down to:
mat= $I$mat=mat$*$ $T$mat=mat$*$ translation matrix to $R$ origin $*$ $R$ $*$ translation matrix to $-R$ originmat=mat$*$ translation matrix to $S$ origin $*$ $S$ $*$ translation matrix to $-S$ origin
However, this produces an object that is both scaled and rotated with respect to the original object. For example, if we scale by $2$x about the bottom-left corner $(0,0)$ and rotate $45^{\circ}$ about the center $(1.5, 1.5)$ we produce the following:
What operation(s) need to be edited in order to achieve rotating about the newly scaled object's center:
