1Math::PlanePath::DiamonUdsAerrmsC(o3n)tributed Perl DocuMmaetnht:a:tPiloannePath::DiamondArms(3)
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NAME

6       Math::PlanePath::DiamondArms -- four spiral arms
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SYNOPSIS

9        use Math::PlanePath::DiamondArms;
10        my $path = Math::PlanePath::DiamondArms->new;
11        my ($x, $y) = $path->n_to_xy (123);
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DESCRIPTION

14       This path follows four spiral arms, each advancing successively in a
15       diamond pattern,
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17                        25   ...                    4
18                    29  14  21  36                  3
19                33  18   7  10  17  32              2
20            ... 22  11   4   3   6  13  28          1
21            26  15   8   1   2   9  24 ...      <- Y=0
22                30  19  12   5  20  35             -1
23                    34  23  16  31                 -2
24                      ...   27                     -3
25
26                         ^
27            -3  -2  -1  X=0  1   2   3   4
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29       Each arm makes a spiral widening out by 4 each time around, thus
30       leaving room for four such arms.  Each arm loop is 64 longer than the
31       preceding loop.  For example N=13 to N=85 below is 84-13=72 points, and
32       the next loop N=85 to N=221 is 221-85=136 which is an extra 64, ie.
33       72+64=136.
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35                        25          ...
36                       /  \           \
37                     29  . 21  .  .  . 93
38                    /        \           \
39                  33  .  .  . 17  .  .  . 89
40                 /              \           \
41               37  .  .  .  .  . 13  .  .  . 85
42              /                 /           /
43            41  .  .  .  1  .  9  .  .  . 81
44              \           \  /           /
45               45  .  .  .  5  .  .  . 77
46                 \                    /
47                  49  .  .  .  .  . 73
48                    \              /
49                     53  .  .  . 69
50                       \        /
51                        57  . 65
52                          \  /
53                           61
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55       Each arm is N=4*k+rem for a remainder rem=0,1,2,3, so sequences related
56       to multiples of 4 or with a modulo 4 pattern may fall on particular
57       arms.
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59       The starts of each arm N=1,2,3,4 are at X=0 or 1 and Y=0 or 1,
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61                      ..
62                        \
63                    4    3  ..          Y=1
64                  /        /
65                ..  1    2           <- Y=0
66                     \
67                      ..
68                    ^    ^
69                   X=0  X=1
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71       They could be centred around the origin by taking X-1/2,Y-1/2 so for
72       example N=1 would be at -1/2,-1/2.  But the it's done as N=1 at 0,0 to
73       stay in integers.
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FUNCTIONS

76       See "FUNCTIONS" in Math::PlanePath for behaviour common to all path
77       classes.
78
79       "$path = Math::PlanePath::DiamondArms->new ()"
80           Create and return a new path object.
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82       "($x,$y) = $path->n_to_xy ($n)"
83           Return the X,Y coordinates of point number $n on the path.  For "$n
84           < 1" the return is an empty list, as the path starts at 1.
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86           Fractional $n gives a point on the line between $n and "$n+4", that
87           "$n+4" being the next point on the same spiralling arm.  This is
88           probably of limited use, but arises fairly naturally from the
89           calculation.
90
91   Descriptive Methods
92       "$arms = $path->arms_count()"
93           Return 4.
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SEE ALSO

96       Math::PlanePath, Math::PlanePath::SquareArms,
97       Math::PlanePath::DiamondSpiral
98

HOME PAGE

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

103       Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 Kevin Ryde
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105       This file is part of Math-PlanePath.
106
107       Math-PlanePath is free software; you can redistribute it and/or modify
108       it under the terms of the GNU General Public License as published by
109       the Free Software Foundation; either version 3, or (at your option) any
110       later version.
111
112       Math-PlanePath is distributed in the hope that it will be useful, but
113       WITHOUT ANY WARRANTY; without even the implied warranty of
114       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
115       General Public License for more details.
116
117       You should have received a copy of the GNU General Public License along
118       with Math-PlanePath.  If not, see <http://www.gnu.org/licenses/>.
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122perl v5.32.0                      2020-07-28   Math::PlanePath::DiamondArms(3)
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