From: Boris Zbarsky <bzbarsky@MIT.EDU>
Date: Thu, 12 Aug 2010 11:27:16 -0400
Message-ID: <4C6412D4.2070106@mit.edu>
```On 8/12/10 10:59 AM, David Flanagan wrote:
> But if you don't talk about the algebraic operations then you haven't
> really defined what a transformation is, have you?

Given that the input is in coordinates, we need to talk about algebraic
operations to define the transformation on vectors those coordinates
produce.  That is, we need a clear definition of what the output vector
is given an input vector and a list of 6 numbers.

But once we have that, composition of transformation can be described
simply as composition (thinking of them as functions), without reference
to algebraic manipulation of their particular matrix representations.

> I suppose it does. So to be complete, the spec would have to show the
> math required to transform a point (x,y) using the CTM.

Yes, indeed.

> Are you suggesting that there is some way that the spec can be written
> generically without any assumptions about row vector or column vector
> format?

No, I'm just saying that the definition of transform composition doesn't
need to make such assumptions.

> Note that the matrix shown above already appears in the current
> version of the transform() method description. I don't see how to avoid
> picking one form or another unless you want to define a CTM as an array
> of 6 numbers and show the formulas for updating each of those numbers
> without referring to matrix multiplication at all.

While that would be a viable course of action, I don't think there's a
need for that.  Defining the CTM as a matrix and defining how the 6
numbers produce the matrix and exactly how the matrix acts on vectors is
fine; while it's actually a bit more text than the other it produces a
simpler conceptual picture.

-Boris
```
Received on Thursday, 12 August 2010 08:27:16 UTC

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