--- name: "Math::PlanePath::GreekKeySpiral" section: "3pm" platform: "linux" package: "libmath-planepath-perl" version: "129-1" release: "Debian 13 (Trixie)" platforms: ["linux"] url: "https://new.carta.tech/Math::PlanePath::GreekKeySpiral" --- # Math::PlanePath::GreekKeySpiral(3pm) ## NAME Math::PlanePath::GreekKeySpiral -- square spiral with Greek key motif ## SYNOPSIS ``` use Math::PlanePath::GreekKeySpiral; my $path = Math::PlanePath::GreekKeySpiral->new; my ($x, $y) = $path->n_to_xy (123); ``` ## DESCRIPTION This path makes a spiral with a Greek key scroll motif, ``` 39--38--37--36 29--28--27 24--23 5 | | | | | | 40 43--44 35 30--31 26--25 22 4 | | | | | | 41--42 45 34--33--32 19--20--21 ... 3 | | | 48--47--46 5---6---7 18 15--14 99 96--95 2 | | | | | | | | | 49 52--53 4---3 8 17--16 13 98--97 94 1 | | | | | | | 50--51 54 1---2 9--10--11--12 91--92--93 <- Y=0 | | 57--56--55 68--69--70 77--78--79 90 87--86 -1 | | | | | | | | 58 61--62 67--66 71 76--75 80 89--88 85 -2 | | | | | | | | 59--60 63--64--65 72--73--74 81--82--83--84 -3 ^ -3 -2 -1 X=0 1 2 3 4 5 6 7 8 ... ``` The repeating figure is a 3x3 pattern ``` | * *---* | | | right vertical *---* * going upwards | *---*---* | ``` The turn excursion is to the outside of the 3-wide channel and forward in the direction of the spiral. The overall spiralling is the same as the `"SquareSpiral"`, but composed of 3x3 sub-parts. ### Sub-Part Joining The verticals have the "entry" to each figure on the inside edge, as for example N=90 to N=91 above. The horizontals instead have it on the outside edge, such as N=63 to N=64 along the bottom. The innermost N=1 to N=9 is a bottom horizontal going right. ``` *---*---* | | bottom horizontal *---* * going rightwards | | --*---* *--> ``` On the horizontals the excursion part is still "forward on the outside", as for example N=73 through N=76, but the shape is offset. The way the entry is alternately on the inside and outside for the vertical and horizontal is necessary to make the corners join. ### Turn An optional `"turns => $integer"` parameter controls the turns within the repeating figure. The default is `"turns=>2"`. Or for example `"turns=>4"` begins ``` turns => 4 105-104-103-102-101-100 79--78--77--76--75 62--61--60--59 | | | | | | 106 119-120-121-122 99 80 87--88--89 74 63 66--67 58 | | | | | | | | | | | | 107 118 115-114 123 98 81 86--85 90 73 64--65 68 57 | | | | | | | | | | | | 108 117-116 113 124 97 82--83--84 91 72--71--70--69 56 | | | | | | 109-110-111-112 125 96--95--94--93--92 51--52--53--54--55 | | 130-129-128-127-126 17--18--19--20--21 50 37--36--35--34 | | | | | | 131 144-145-146-147 16 9-- 8-- 7 22 49 38 41--42 33 | | | | | | | | | | | | 132 143 140-139 148 15 10--11 6 23 48 39--40 43 32 | | | | | | | | | | | | 133 142-141 138 149 14--13--12 5 24 47--46--45--44 31 | | | | | | 134-135-136-137 150 1-- 2-- 3-- 4 25--26--27--28--29--30 | ..-152-151 ``` The count of turns is chosen to make `"turns=>0"` a straight line, the same as the `"SquareSpiral"`. `"turns=>1"` is a single wiggle, ``` turns => 1 66--65--64 61--60 57--56 53--52--51 | | | | | | | | 67--68 63--62 59--58 55--54 49--50 | | 70--69 18--17--16 13--12--11 48--47 | | | | | | 71--72 19--20 15--14 9--10 45--46 | | | | ... 22--21 2-- 3 8-- 7 44--43 | | | | | 23--24 1 4-- 5-- 6 41--42 | | 26--25 30--31 34--35 40--39 | | | | | | 27--28--29 32--33 36--37--38 ``` In general the repeating figure is a square of turns+1 points on each side, spiralling in and then out again. ## FUNCTIONS See "FUNCTIONS" in Math::PlanePath for behaviour common to all path classes. - "$path = Math::PlanePath::GreekKeySpiral-\>new ()" - "$path = Math::PlanePath::GreekKeySpiral-\>new (turns =\> $integer)" Create and return a new Greek key spiral object. The default `"turns"` is 2. - "($x,$y) = $path-\>n\_to\_xy ($n)" Return the X,Y coordinates of point number `$n` on the path. For `"$n < 1"` the return is an empty list, it being considered the path starts at 1. - "$n = $path-\>xy\_to\_n ($x,$y)" Return the point number for coordinates `"$x,$y"`. `$x` and `$y` are each rounded to the nearest integer, which has the effect of treating each N in the path as centred in a square of side 1, so the entire plane is covered. ## SEE ALSO Math::PlanePath, Math::PlanePath::SquareSpiral Jo Edkins Greek Key pages `"http://gwydir.demon.co.uk/jo/greekkey/index.htm"` ## HOME PAGE \ ## 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 \.