On Jun 17, 2009, at 4:37 PM, Graham Cox wrote:
It's fair to say that transforms can be a bit unintuitive - you expect them to perform the operations in the order you set. In fact, the reverse order is what it will actually do. (The explanation for this lies in the maths, but it sounds like you're not interested in that, in which case this might be a struggle).
For people with a background closer to programming and farther from math, it might be easier to think of matrix multiplication as a stack (the LIFO kind of data structure). What you write last is what gets done first when it comes to using matrices as operations on geometrical objects. So, the result of applying ABC to an object o (where A, B, and C are matrices) is that first C is applied to o, then B is applied to the result of that, then A is applied to the result of *that*. In reality, behind the curtains, it may be and often is the case that A, B, and C get multiplied together first and then the result of that is applied to o, but conceptually you can think of it as I described.
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