Re: Help with understanding matrices
Re: Help with understanding matrices
- Subject: Re: Help with understanding matrices
- From: deivy petrescu <email@hidden>
- Date: Tue, 12 Feb 2008 22:04:51 -0500
Simon;
On Feb 12, 2008, at 13:41, 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.
I tried to read the wikipedia entry but it was way over my head!
http://en.wikipedia.org/wiki/Matrix_(mathematics)
What I'm trying to work out is the rotation and/or scale of an image
placed in Adobe Illustrator CS3.
Getting to matrix of an image when first placed into returns the
result:
{class:matrix, mvalue_a:1.0, mvalue_b:0.0, mvalue_c:0.0,
mvalue_d:-1.0, mvalue_tx:-7598.0, mvalue_ty:9058.275390625}
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.
I assume tx and ty are related to the size of the image, but I am not
sure (read below why).
If I rotate the image by 45 degrees clockwise, the matrix is now:
{class:matrix, mvalue_a:0.707106769085, mvalue_b:-0.707106769085,
mvalue_c:-0.707106769085, mvalue_d:-0.707106769085,
mvalue_tx:-1.14441533203125E+4, mvalue_ty:821.1611328125}
This matrix indeed corresponds to a rotation of 45 degrees clockwise
for a system of coordinates (x,-y). I have no clue as why tx and ty
are changed.
And, if I then scale it by 50%, the matrix is now:
{class:matrix, mvalue_a:0.353553384542, mvalue_b:-0.353553384542,
mvalue_c:-0.353553384542, mvalue_d:-0.353553384542,
mvalue_tx:-5511.07666015625, mvalue_ty:559.08056640625}
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.
Unless there is an algorithm, probably based on the tangent of the
angle, this matrix above is pure garbage.
To see if you can get anything out of this, rotate 30 and 60 degrees,
scale and also scale without any rotation.
Send the matrices.
However, this weekend does not seem very promising, if you have some
time to wait...
So, how would I work out what the rotation and scale of the image is
given the values in the second and third results?
What do the "mvalue" numbers define? Is there even a way to get the
rotation and scale from these numbers?
TIA for anyone willing to help me with this.
Simon
Deivy
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