How to interpret graph-paper generating svg? - svg

Question

I need help interpreting the svg which generates this graph paper.
I think I understand the general idea behind the code:
there are 3 layers/groups being created, one of which has the original rectangle
translation and transform operations appear to be used to replicate this rectangle all over the canvas.
but I'm having a hard time understanding some details behind the svg code.
I also don't understand how the layers interact with each other.
Questions
How do you interpret the transform="matrix(0,1,-1,0,400,0)" operation?
Can you explain the implied for-loop that's in this svg code which copies the rectangles?
What does the path tag do in the context of this code?
I am trying to understand this svg code well enough so I can modify it for my own uses.
Thank you.
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
<svg
xmlns:svg="http://www.w3.org/2000/svg"
xmlns="http://www.w3.org/2000/svg"
xmlns:xlink="http://www.w3.org/1999/xlink"
version="1.0"
width="400"
height="400"
id="svg2180">
<defs
id="defs2182" />
<g
style="opacity:1;display:inline"
id="layer1">
<g
style="stroke:#a9a9a9;stroke-opacity:1"
id="g8191">
<path
d="M 20,0 L 20,400"
style="fill:none;fill-rule:evenodd;stroke:#a9a9a9;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
id="path1872" />
<use
transform="translate(20,0)"
style="stroke:#a9a9a9;stroke-opacity:1"
id="use8185"
x="0"
y="0"
width="400"
height="400"
xlink:href="#path1872" />
<use
transform="translate(40,0)"
style="stroke:#a9a9a9;stroke-opacity:1"
id="use8187"
x="0"
y="0"
width="400"
height="400"
xlink:href="#path1872" />
<use
transform="translate(60,0)"
style="stroke:#a9a9a9;stroke-opacity:1"
id="use8189"
x="0"
y="0"
width="400"
height="400"
xlink:href="#path1872" />
</g>
<use
transform="translate(100,0)"
id="use8197"
x="0"
y="0"
width="400"
height="400"
xlink:href="#g8191" />
<use
transform="translate(200,0)"
id="use8199"
x="0"
y="0"
width="400"
height="400"
xlink:href="#g8191" />
<use
transform="translate(300,0)"
id="use8201"
x="0"
y="0"
width="400"
height="400"
xlink:href="#g8191" />
<use
transform="matrix(0,1,-1,0,400,0)"
id="use8203"
x="0"
y="0"
width="400"
height="400"
xlink:href="#g8191" />
<use
transform="translate(0,100)"
id="use8205"
x="0"
y="0"
width="400"
height="400"
xlink:href="#use8203" />
<use
transform="translate(0,200)"
id="use8207"
x="0"
y="0"
width="400"
height="400"
xlink:href="#use8203" />
<use
transform="translate(0,300)"
id="use8209"
x="0"
y="0"
width="400"
height="400"
xlink:href="#use8203" />
</g>
<g
style="display:inline"
id="layer2">
<g
style="stroke:#366;stroke-opacity:1"
id="g8225">
<path
d="M 100,0 L 100,400"
style="fill:none;fill-rule:evenodd;stroke:#366;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
id="path8215" />
<use
transform="translate(100,0)"
style="stroke:#366;stroke-opacity:1"
id="use8217"
x="0"
y="0"
width="400"
height="400"
xlink:href="#path8215" />
<use
transform="translate(200,0)"
style="stroke:#366;stroke-opacity:1"
id="use8219"
x="0"
y="0"
width="400"
height="400"
xlink:href="#path8215" />
</g>
<use
transform="matrix(0,1,-1,0,400,0)"
id="use8232"
x="0"
y="0"
width="400"
height="400"
xlink:href="#g8225" />
</g>
<g
id="layer3">
<rect
width="399"
height="399"
x="0.5"
y="0.5"
style="fill:none;stroke:#366;stroke-opacity:1"
id="rect10078" />
</g>
</svg>

Answer 1

Don't misinterpret the "layers" in this document. They aren't really about layering, they're about grouping.
How do you interpret the transform="matrix(0,1,-1,0,400,0)" operation?
That is a transformation matrix for an affine transform. It's a fancy way to combine rotation, skew, and translation into one function. They can be difficult to wrap one's mind around though, and I usually only see them used in code generated by a drawing application.
Can you explain the implied for-loop that's in this svg code which copies the rectangles?
In SVG, you can re-use any object that you have given an id to, using the <use .../> tag. This can be used as a sort of DRY, to keep repetition low in the code. In this case, a group of horizontal lines is created, then copies are made by referencing them with use tags. each use has it's own transform attribute to move it into place. Halfway down the list, the line group get rotated 90 degrees (using the transform matrix) and then copied across the image.
What does the path tag do in the context of this code?
It just draws the thick line. This could have been done with a line element, but drawing software output that, and it wasn't smart enough to replace it, I guess. Usually path elements are used for more complex shapes, since they support arcs and bezier curves.