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This page explains, step-by-step, how we generate our SVG logo, using the above expression<ref>[https://codegolf.stackexchange.com/users/78410/bubbler "Bubbler"], message [https://chat.stackexchange.com/transcript/message/52389201#52389201 "52389201"] in ''The Nineteenth Byte'' chat room. Stack Exchange network, 2019-10-31 23:57</ref> | This page explains, step-by-step, how we generate our SVG logo, using the above expression<ref>[https://codegolf.stackexchange.com/users/78410/bubbler "Bubbler"], message [https://chat.stackexchange.com/transcript/message/52389201#52389201 "52389201"] in ''The Nineteenth Byte'' chat room. Stack Exchange network, 2019-10-31 23:57</ref>. This demonstrates quite a few APL features. | ||
We will follow APL's evaluation from [[Evaluation order|right to left]]. | We will follow APL's evaluation from [[Evaluation order|right to left]]. | ||
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</source> | </source> | ||
Those are our radii! Let's save them: | |||
<source lang=apl> | |||
r←⌊∘.+⍨.5×4!⍨⍳5 | |||
</source> | |||
== Towards an SVG == | |||
=== Placing the circles === | |||
Now that we have our radii, we need to figure out where to put our circles. The horizontal pair-wise sum shows how much adjacent circles "reach out" towards each other. [[N-wise Reduce]] solves that. Here, <source lang=apl inline>/</source> is an operator which takes the plus function and applies it in-between the elements of each horizontal run of length ''N'' (the left argument) in the right argument: | |||
<source lang=apl> | |||
2+/sizes | |||
3 5 5 3 | |||
6 9 9 6 | |||
8 11 11 8 | |||
6 9 9 6 | |||
3 5 5 3 | |||
</source> | |||
Since the circles line up on a grid, we need the maximum for each horizontal space, that is for each column. APL uses [[dyad]]ic <source lang=apl inline>a⌈b</source> as the [[maximum]] of ''a'' and ''b''. <source lang=apl inline>⌈⌿</source> is the columnar maximum-[[reduce|reduction]]: | |||
<source lang=apl> | |||
⌈⌿2+/sizes | |||
8 11 11 8 | |||
</source> | |||
But obviously, we can't let the circles touch, so we add 1. Finally, we prepend a 0 which is the offset of the first circle: | |||
<source lang=apl> | |||
⊢offsets←0,+\1+⌈⌿2+/sizes | |||
0 9 21 33 42 | |||
</source> | |||
<source lang=apl inline>⊢</source> is the [[identity]] function, which is just used here get the pass-though value from the assignment, as it would otherwise be hidden. (We call assignment ''shy''.) | |||
<source lang=apl inline>⍴</source> is the [[shape]] and <source lang=apl inline>⍳</source> generates the [[index of|indices]] of an array of that size. | |||
<source lang=apl> | |||
⍴r | |||
5 5 | |||
⊢indices←⍳⍴r | |||
┌───┬───┬───┬───┬───┐ | |||
│0 0│0 1│0 2│0 3│0 4│ | |||
├───┼───┼───┼───┼───┤ | |||
│1 0│1 1│1 2│1 3│1 4│ | |||
├───┼───┼───┼───┼───┤ | |||
│2 0│2 1│2 2│2 3│2 4│ | |||
├───┼───┼───┼───┼───┤ | |||
│3 0│3 1│3 2│3 3│3 4│ | |||
├───┼───┼───┼───┼───┤ | |||
│4 0│4 1│4 2│4 3│4 4│ | |||
└───┴───┴───┴───┴───┘ | |||
</source> | |||
Now we take each coordinate (i.e. each [[rank]] 0 cell) from that and use it to [[Squad index|index]] into the list (a [[rank]] 1 array) of offsets. The result is has shape… | |||
<source lang=apl> | |||
⍴xy←indices⌷⍤0 1⊢offsets | |||
5 5 2 | |||
</source> | |||
that is, it is a 3D array with 5 layers, 5 rows in each layer, and 2 columns in each row. Each row represents an <math>(x,y)</math> value. The first and last layers, which represents the leftmost and rightmost columns of the logo, are: | |||
<source lang=apl> | |||
(1↑xy) (¯1↑xy) | |||
┌────┬─────┐ | |||
│0 0│42 0│ | |||
│0 9│42 9│ | |||
│0 21│42 21│ | |||
│0 33│42 33│ | |||
│0 42│42 42│ | |||
└────┴─────┘ | |||
</source> | |||
E.g. the second row in the first layer is <math>(x,y)=(0,9)</math> | |||
<source lang=apl> | |||
</source> | |||
=== Making <code><circle/></code> tags === | |||
<source lang=apl> | |||
</source> | |||
<source lang=apl> | |||
</source> | |||
<source lang=apl> | |||
</source> | |||
== References == | == References == | ||
<references /> | <references /> | ||