1Math::PlanePath::GreekKUesyeSrpiCroanlt(r3i)buted Perl DMoactuhm:e:nPtlaatnieoPnath::GreekKeySpiral(3)
2
6 Math::PlanePath::GreekKeySpiral -- square spiral with Greek key motif
7
9 use Math::PlanePath::GreekKeySpiral;
10 my $path = Math::PlanePath::GreekKeySpiral->new;
11 my ($x, $y) = $path->n_to_xy (123);
12
14 This path makes a spiral with a Greek key scroll motif,
15 39--38--37--36 29--28--27 24--23 5
17 | | | | | |
18 40 43--44 35 30--31 26--25 22 4
19 | | | | | |
20 41--42 45 34--33--32 19--20--21 ... 3
21 | | |
22 48--47--46 5---6---7 18 15--14 99 96--95 2
23 | | | | | | | | |
24 49 52--53 4---3 8 17--16 13 98--97 94 1
25 | | | | | | |
26 50--51 54 1---2 9--10--11--12 91--92--93 <- Y=0
27 | |
28 57--56--55 68--69--70 77--78--79 90 87--86 -1
29 | | | | | | | |
30 58 61--62 67--66 71 76--75 80 89--88 85 -2
31 | | | | | | | |
32 59--60 63--64--65 72--73--74 81--82--83--84 -3
33 ^
35 -3 -2 -1 X=0 1 2 3 4 5 6 7 8 ...
37 The repeating figure is a 3x3 pattern
39 |
41 * *---*
42 | | | right vertical
43 *---* * going upwards
44 |
45 *---*---*
46 |
47 The turn excursion is to the outside of the 3-wide channel and forward
49 in the direction of the spiral. The overall spiralling is the same as
50 the "SquareSpiral", but composed of 3x3 sub-parts.
51 Sub-Part Joining
53 The verticals have the "entry" to each figure on the inside edge, as
54 for example N=90 to N=91 above. The horizontals instead have it on the
55 outside edge, such as N=63 to N=64 along the bottom. The innermost N=1
56 to N=9 is a bottom horizontal going right.
57 *---*---*
59 | | bottom horizontal
60 *---* * going rightwards
61 | |
62 --*---* *-->
63 On the horizontals the excursion part is still "forward on the
65 outside", as for example N=73 through N=76, but the shape is offset.
66 The way the entry is alternately on the inside and outside for the
67 vertical and horizontal is necessary to make the corners join.
68 Turn
70 An optional "turns => $integer" parameter controls the turns within the
71 repeating figure. The default is "turns=>2". Or for example
72 "turns=>4" begins
73 turns => 4
75 105-104-103-102-101-100 79--78--77--76--75 62--61--60--59
77 | | | | | |
78 106 119-120-121-122 99 80 87--88--89 74 63 66--67 58
79 | | | | | | | | | | | |
80 107 118 115-114 123 98 81 86--85 90 73 64--65 68 57
81 | | | | | | | | | | | |
82 108 117-116 113 124 97 82--83--84 91 72--71--70--69 56
83 | | | | | |
84 109-110-111-112 125 96--95--94--93--92 51--52--53--54--55
85 | |
86 130-129-128-127-126 17--18--19--20--21 50 37--36--35--34
87 | | | | | |
88 131 144-145-146-147 16 9-- 8-- 7 22 49 38 41--42 33
89 | | | | | | | | | | | |
90 132 143 140-139 148 15 10--11 6 23 48 39--40 43 32
91 | | | | | | | | | | | |
92 133 142-141 138 149 14--13--12 5 24 47--46--45--44 31
93 | | | | | |
94 134-135-136-137 150 1-- 2-- 3-- 4 25--26--27--28--29--30
95 |
96 ..-152-151
97 The count of turns is chosen to make "turns=>0" a straight line, the
99 same as the "SquareSpiral". "turns=>1" is a single wiggle,
100 turns => 1
102 66--65--64 61--60 57--56 53--52--51
104 | | | | | | | |
105 67--68 63--62 59--58 55--54 49--50
106 | |
107 70--69 18--17--16 13--12--11 48--47
108 | | | | | |
109 71--72 19--20 15--14 9--10 45--46
110 | | | |
111 ... 22--21 2-- 3 8-- 7 44--43
112 | | | | |
113 23--24 1 4-- 5-- 6 41--42
114 | |
115 26--25 30--31 34--35 40--39
116 | | | | | |
117 27--28--29 32--33 36--37--38
118 In general the repeating figure is a square of turns+1 points on each
120 side, spiralling in and then out again.
121
123 See "FUNCTIONS" in Math::PlanePath for behaviour common to all path
124 classes.
125 "$path = Math::PlanePath::GreekKeySpiral->new ()"
127 "$path = Math::PlanePath::GreekKeySpiral->new (turns => $integer)"
128 Create and return a new Greek key spiral object. The default
129 "turns" is 2.
130 "($x,$y) = $path->n_to_xy ($n)"
132 Return the X,Y coordinates of point number $n on the path.
133 For "$n < 1" the return is an empty list, it being considered the
135 path starts at 1.
136 "$n = $path->xy_to_n ($x,$y)"
138 Return the point number for coordinates "$x,$y". $x and $y are
139 each rounded to the nearest integer, which has the effect of
140 treating each N in the path as centred in a square of side 1, so
141 the entire plane is covered.
142
144 Math::PlanePath, Math::PlanePath::SquareSpiral
145 Jo Edkins Greek Key pages
147 "http://gwydir.demon.co.uk/jo/greekkey/index.htm"
148
150 <http://user42.tuxfamily.org/math-planepath/index.html>
151
153 Copyright 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
154 2020 Kevin Ryde
155 This file is part of Math-PlanePath.
157 Math-PlanePath is free software; you can redistribute it and/or modify
159 it under the terms of the GNU General Public License as published by
160 the Free Software Foundation; either version 3, or (at your option) any
161 later version.
162 Math-PlanePath is distributed in the hope that it will be useful, but
164 WITHOUT ANY WARRANTY; without even the implied warranty of
165 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
166 General Public License for more details.
167 You should have received a copy of the GNU General Public License along
169 with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
170perl v5.34.0 2021-07-22Math::PlanePath::GreekKeySpiral(3)