I've been making a lot of effort over the past few hours to gain some intuition into the art of geometric transformation but to little avail. I would really like to be able to look at a transformation matrix and have a pretty good idea of what it does to a shape (or at least a vector)
I sketched a simple box on a graph, and applied two simple transformations to them. After doing the first, I expected the second to produce a sort of mirror, or opposite of it, but that didn't happen (and I suppose it makes sense now thinking about it).
However, I would really appreciate if someone could give me an approach to thinking of these things intuitively and understanding where inside the matrix does the magic happen.
Below is my simple box (all drawn in Microsoft Publisher :) and the transformation matrix I used on each point (only one is labeled, the others are obvious)
I applied a very similar transformation in the second case but got a very different result.