I've wanted to write a page about coordinate transforms, but I've started it and abandoned it several times.
The first version was about matrices. I had seen Nicky Case's interactive explanation and Max Goldstein's animated explanation but I wanted to write something more basic. I wrote out an outline showing how matrices could be used for translate, scale, rotate, and shear transformations, and how those could be combined or inverted to generate all the effects we want.
After struggling with this for a few weeks, I put the page on hold.
I returned to it after a friend of mine suggested that I take matrices out completely. I had to ponder that for a while. Surely, the whole point of the page was to show how matrices worked. How could I do that if I took out matrices?
I came up with a new outline that pushed matrices to the very end. I covered all the transforms first, with simple code to implement each. If you have a series of transforms
C, and you want to transform point
p, you can call
C(B(A(p))). At the end I introduced matrices as a uniform representation of all the different types of transforms. They also offer a way to combine transforms together, so that you can call
(C ∘ B ∘ A)(p).
I had implemented lots of interactive diagrams for this page (see the draft version), but in the end I was unhappy with that version too.
There's a technique called 5 Whys (or 3 Whys) that I should've tried.
Why do I want to explain matrices? Because they are a nice way of implementing transformations.
Why do I want to explain transformations? Because they are a uniform way of thinking about operations we need in games: translate, scale, rotate.
Why do I want to explain translate, scale, rotate? Because they are a clean way to solve problems with game cameras: scrolling, zooming, rotating, and isometric views.
Aha! Maybe that's the real problem: game cameras. Instead of starting with matrices and then explaining how they represent transformations and then explaining how transformations can be combined, I could start with game cameras and then work my way up to transformations and then matrices.
I'm going to make another attempt at an outline for this page starting with game cameras.
Update: [2016 Aug] Well, I failed. I lost motivation to work on this so I've put it on hold … again. I think I may take a long break from tutorials.