Math::...elRings(3pm)

💖 Math::PlanePath::PixelRings 💖

okay bestie, welcome to the User Contributed Perl Documentation for Math::PlanePath::PixelRings(3pm) — it's a Perl module and it makes pixellated concentric circles and honestly? iconic behavior. ✨

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🌸 NAME 🌸

Math::PlanePath::PixelRings — pixellated concentric circles 🎀

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✨ SYNOPSIS ✨

use Math::PlanePath::PixelRings;
my $path = Math::PlanePath::PixelRings->new;
my ($x, $y) = $path->n_to_xy (123);

that's it. three lines. you're already slaying. 💅

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🦋 DESCRIPTION 🦋

so what this path does is it drops points onto the pixels of concentric circles, using the midpoint ellipse drawing algorithm. it's giving geometry, it's giving rasterization, it's giving art. 🎨

                       63--62--61--60--59                     5
                     /                    \
                   64  .   40--39--38   .  58                 4
                 /       /            \       \
               65  .   41  23--22--21  37   .  57             3
             /       /   /            \   \       \
           66  .   42  24  10-- 9-- 8  20  36   .  56         2
            |    /   /   /            \   \   \     |
           67  43  25  11   .   3   .   7  19  35  55         1
            |   |   |   |     /   \     |   |   |   |
           67  44  26  12   4   1   2   6  18  34  54       Y=0
            |   |   |   |     \   /
           68  45  27  13   .   5   .  17  33  53  80        -1
            |    \   \   \            /   /   /     |
           69  .   46  28  14--15--16  32  52   .  79        -2
             \       \   \            /   /       /
               70  .   47  29--30--31  51   .  78            -3
                 \       \            /       /
                   71  .   48--49--50   .  77                -4
                     \                    /
                       72--73--74--75--76                    -5

           -5  -4  -3  -2  -1  X=0  1   2   3   4   5

the way this algorithm works means the rings don't overlap. periodt. each ring is 4 or 8 pixels longer than the one before it. if the ring follows the preceding one super tightly then it's 4 longer — for example N=18 to N=33. if it goes wider then it's 8 longer — for example the N=54 to N=80 ring. the average extra is approximately 4*sqrt(2). math is mathing fr fr. 😌

you can think of the rings as being part-way between the diagonals like "DiamondSpiral" and the corners like "SquareSpiral".

            *           **           *****
             *            *              *
              *            *             *
               *            *            *
                *           *            *

           diagonal     ring         corner
           5 points    6 points     9 points

for example the N=54 to N=80 ring has a vertical part N=54,55,56 like a corner, then a diagonal part N=56,57,58,59. in bigger rings the verticals are all intermingled with the diagonals but the principle stays the same, no cap. the number of vertical steps determines where it crosses the 45-degree line, which is at R*sqrt(2) but rounded according to the midpoint algorithm. 🧚

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💜 FUNCTIONS 💜

go read "FUNCTIONS" in Math::PlanePath for the behavior that's common to all the path classes, bestie — that's the shared lore. 📚

• $path = Math::PlanePath::PixelRings->new () — make a new path object and hand it back to you. fresh out the box. 🎁
• ($x,$y) = $path->n_to_xy ($n) — for "$n < 1" the return is an empty list, because it's considered there are no negative points. 🚫 the behaviour for fractional $n is unspecified as yet — so like, don't count on it, it's still figuring itself out. 🙈
• $n = $path->xy_to_n ($x,$y) — returns an integer point number for coordinates "$x,$y". every integer N is considered the centre of a unit square, and an "$x,$y" inside that square returns N. 🎯 not every point of the plane is covered (like those ones marked with a "." in the sample above). if "$x,$y" is not reached then the return is "undef". 💀

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🌈 SEE ALSO 🌈

• Math::PlanePath
• Math::PlanePath::Hypot
• Math::PlanePath::MultipleRings

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👑 HOME PAGE 👑

<http://user42.tuxfamily.org/math-planepath/index.html>

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🎀 LICENSE 🎀

Copyright 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Kevin Ryde

This file is part of Math-PlanePath.

Math-PlanePath is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-PlanePath is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.

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fr fr, that warranty disclaimer is not a vibe, it's a legal document, and it means what it says. 🙏

and that's the whole page, bestie!! this one's from perl v5.32.0, dated 2021-01-23 — go forth and draw your little circles, you absolute main character. 💖✨🦋🌸💅🫶