How to read a PDF text matrix

Question

I am writing a program to create PDF file directly from my Program. I have used the PDF Reference manual and managed to figure out everything except for 1 thing. The Text Matrix

Answer 1

Point definition

[x, y, 1]

This is a one dimensional vector (array) which places the point at the coordinates x and y. 1 is not needed to specify the point location, but it is helpful for the calculation of the location of a point in a different coordination system, like from device independent pixels to device depended pixels.

Translation calculation

x_new = a*x + c*y + e;
y_new = b*x + d*y + f;

Written as matix, the calculation looks like this:

Matrix for translation

A translation moves a point.

[1, 0, 0, 1, tx, ty]

x_new = 1*x + 0*y + tx;
y_new = 0*x + 1*y + ty;

or

x_new = x + tx;
y_new = y + ty;

Matrix for rotation

[cos(theta), sin(theta), -sin(theta), cos(theta), 0, 0]

x_new = cos(theta)*x - sin(theta)*y + 0;
y_new = sin(theta)*x + cos(theta)*y + 0;

0 degree rotation, cos(0)=1, sin(0)=0: [1, 0, -0, 1, 0, 0]

x_new = 1*x + 0*y + 0;
y_new = 0*x + 1*y + 0;

or

x_new = x;
y_new = y;

90 degree rotation, cos(90)=0, sin(90)=1: [0, 1, -1, 0, 0, 0]

x_new = 0*x + -1*y + 0;
y_new = 1*x + 0*y + 0;

or

x_new = -y;
y_new = x;

180 degree rotation, cos(180)=-1, sin(180)=0: [-1, 0, -0, -1, 0, 0]

x_new = -1*x + 0*y + 0;
y_new = 0*x + -1*y + 0;

or

x_new = -x;
y_new = -y;

270 degree rotation, cos(270)=0, sin(270)=-1: [0, -1, 1, 0, 0, 0]

x_new = 0*x + 1*y + 0;
y_new = -1*x + 0*y + 0;

or

x_new = y;
y_new = -x;

Example text matrix

[0 1 -1 0 07 07]

0 1 -1 0: Rotation by 90 degrees 07 07: Translation (offset) by 7 in each x and y direction

Answer 2

Also interesting for you could be Chapter 4.2.2 Common Transformations in PDF developer reference https://www.adobe.com/content/dam/acom/en/devnet/pdf/pdfs/pdf_reference_archives/PDFReference.pdf

Answer 3

The matrices used in PDFs are Affine transforms.

tm loads the parameters into:

|a b 0|
|c d 0|
|e f 1|

Where:

a is Scale_x
b is Shear_x
c is Shear_y
d is Scale_y
e is offset x
f is offset y

A good introduction can be found at http://docstore.mik.ua/orelly/java-ent/jfc/ch04_11.htm

Hope this helps someone.