Matrix Math (and an error in the Actionscript docs)
I'm working on a project that uses [an algorithm similar to] texture mapping, for which I want to precalculate the .invert() of a whole bunch of .transform.matrix objects. I'll post something about that in the next coupla days. Meanwhile, I found something perplexing in the Actionscript documentation but the possibility exists that I am just a dope so please point out an error in my reasoning. As you may know, you can represent any arbitrary combination of 2-D scalings, skews, rotations and translations using standard matrix operations. The Actionscript docs for the Matrix class mention this in passing, but has elements .b and .c switched: it should be
and not![right: [ [a,c,tx] [b,d,ty] [0,0,1] ]](theory/genericMatrix.png)
I whipped up a MatrixMathDemo in flex to demonstrate the issue and a writeup on Mathematical matrices and the actionscript Matrix transformations [PDF/nb]. The 2d, 3d, 4th tabs compare the Matrix methods concat(), invert() and (deltaP/p)ointTransform() respectively with an explicit calculation of the corresponding Matrix operation: they show that in fact the documentation has b and c switched. (The code is free to reuse or modify (but give credit) in case that's useful.) Some references:![wrong: [ [a,c,tx] [c,d,ty] [0,0,1] ]](theory/genericMatrix-wrong.png)
- This flash-specific tutorial at senocular.com is good, though the matrices are transposed from what is typically presented.
- The posts on the flashcoders list A little matrix.invert() mystery and followup are explained by b and c being switched; they link to post on a french blog that is helpful if you parlez.
- To brush up on matrix mathematics, please see the Matrix and Quaternion FAQ or Wikpedia.