I see some familiar motifs. Since this all is about scribblings in 2D plane, to quote PDF (same with Postscript) Reference (relevant pages are very simple and concise, no math):

PDF represents coordinates in a two-dimensional space. The point (x, y) in such a space can be expressed in vector form as [ x y 1 ]. The constant third element of this vector (1) is needed so that the vector can be used with 3-by-3 matrices in the calculations described below.

The transformation between two coordinate systems is represented by a 3-by-3 transformation matrix written as follows:

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

Because a transformation matrix has only six elements that can be changed, it is usually specified in PDF as the six-element array [ a b c d e f ].

Coordinate transformations are expressed as matrix multiplications:

                          | a b 0 |
[ x' y' 1 ] = [ x y 1 ] x | c d 0 |
                          | e f 1 |

[download]

"e f" are to translate, "a d" to scale (let's omit rotation and skewing for simplicity). Suppose I want to translate by (32,64) and then scale by factor of 3:

pdl> p $m = pdl '3 0 0 ; 0 3 0 ; 32 64 1'

[
 [ 3  0  0]
 [ 0  3  0]
 [32 64  1]
]

[download]

And I have this dumb set of points:

pdl> p $points = rint transpose cat sequence(10),sequence(10)/3

[
 [0 0]
 [1 0]
 [2 1]
 [3 1]
 [4 1]
 [5 2]
 [6 2]
 [7 2]
 [8 3]
 [9 3]
]

[download]

Then:

pdl> p $points->append(1) x $m

[
 [32 64  1]
 [35 64  1]
 [38 67  1]
 [41 67  1]
 [44 67  1]
 [47 70  1]
 [50 70  1]
 [53 70  1]
 [56 73  1]
 [59 73  1]
]

[download]

See? Coordinates were modified as requested.

"Six numbers per row/point" are six numbers (3 x,y pairs) required to append a cubic bezier curve segment to path -- this is another one which rings the bell, but maybe it's false alarm and I misread what they are trying to accomplish.

In reply to Re: Translating python math to Perl by Anonymous Monk
in thread Translating python math to Perl by cavac

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