Re: Help with understanding matrices
Re: Help with understanding matrices
- Subject: Re: Help with understanding matrices
- From: Simon Topliss <email@hidden>
- Date: Tue, 12 Feb 2008 20:12:37 +0000
On 12 Feb 2008, at 19:46, Doug McNutt wrote:
At 18:41 +0000 2/12/08, Simon Topliss wrote:
Hello everyone. Is there a maths genius in the room?
I never studied matrices at school and I'm having a great deal of
difficulty understanding how to do matrix calculations.
and some more.
First: What you might have learned in school about matrix
transformations would have been useless. Adobe's idea of matrix
multiplication and other operations does not match the textbooks.
A 2 dimensional rotation is a 2 x 2 matrix multiplication in "maths"
but a 3 x 3 operation with one column always (0,0,1) in Adobe's
graphics. That's a bit like homogeneous equations in the mathematics
of projective geometry but not quite. The a, b, c, d, tx, and ty
values are the 6 values that are not the left column of the 3 x 3
matrix. The upper left 2x2 square:
a = cos phi b = sin phi
c = -sin phi d = cos phi
Is pretty much a real mathematical rotation but you'll be bothered
because it's not centered on the object and the angles are not
measured the way mathematicians think about it
The bottom row represents translation by tx and ty with a 1 at the
right end
tx ty 1
Two zeros complete the matrix in the upper two thirds of the right
column.
Scaling is accomplished as a rotation of zero degrees with the trig
functions multiplied by the scale factor. The cosines of a zero
degree rotation are 1 and the sines are zero.
Adobe's "Postscript Language Reference Manual - the red book - by
Addison Wesley ISBN 0-201-18127-4 is the bible and you will need it.
Page 155 in the 2nd edition.
Postscript also does things differently than does open GL which uses
4 x 4 matrices to describe 3 D images in a manner that more closely
resembles projective geometry.
And matrix multiplication begins with dot products. Each element of
the result is the dot product of a row vector from the left matrix
and a column vector from the right. The result is not commutative so
A * B is not necessarily the same as B * A. The dot product is the
some of the products of the components of two vectors.
AppleScript is not the right tool for extensive matrix manipulations.
Wuh? Meh? Fuh? Guh? Duh?
Thanks for the reply, Doug. Unfortunately, that raised more questions
than answers!
Is what I'm trying to do even possible with the data I have from
Illustrator?
There are Scripting Additions for advanced maths, but I've no idea
what to look for to solve the equation. Satimage.osax has a COS and
SIN function. I afraid to admit that I've no idea what "phi" relates to.
Please be gentle with me. It's my first time!
Simon
_______________________________________________
Do not post admin requests to the list. They will be ignored.
AppleScript-Users mailing list (email@hidden)
Help/Unsubscribe/Update your Subscription:
Archives: http://lists.apple.com/archives/applescript-users
This email sent to email@hidden