Re: Help with understanding matrices
Re: Help with understanding matrices
- Subject: Re: Help with understanding matrices
- From: Doug McNutt <email@hidden>
- Date: Tue, 12 Feb 2008 21:16:25 -0700
At 22:04 -0500 2/12/08, deivy petrescu wrote:
>As Doug pointed out earlier, this is a matrix that tells us that the x- axis is the usual x-axis, but the y-axis is reflected. That is y -> -y.
Actually, I was wrong about that unless you are programming in quickdraw and need to reverse that, which has +y pointing down. Postscript does honor "standard" math rules for graphics.
>This is absolutely bogus. Scaling is a conformal map, that is, it preserve angles. So this matrix does not represent a rotation, however, tx and ty are scaled by 1/2 and therefore suggest size. But no guarantees.
Postseript once had to account for displays and printers that have rectangular - as opposed to square - pixels. That's likely the reason for scaling independently in the two coordinates.
As for being conformal. . . Does a circle scaled into an ellipse along a 45 degree line rotate in the process?
For a simple rotation - without the (0,0,1) column on the right - a rotation is described by an orthonormal matrix. The dot product of any row or column vector with any of it's neighbors is zero and the dot product of each row and column vector with itself is unity. For two dimensional drawings that probably applies to the 2 x 2 matrix in the upper left corner of a Postscript matrix.
--
--> From the U S of A, the only socialist country that refuses to admit it. <--
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