1Math::PlanePath::FilledURsienrgsC(o3n)tributed Perl DocuMmaetnht:a:tPiloannePath::FilledRings(3)
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6 Math::PlanePath::FilledRings -- concentric filled lattice rings
7
9 use Math::PlanePath::FilledRings;
10 my $path = Math::PlanePath::FilledRings->new;
11 my ($x, $y) = $path->n_to_xy (123);
12
14 This path puts points on integer X,Y pixels of filled rings with radius
15 1 unit each ring.
16 110-109-108-107-106 6
18 / \
19 112-111 79--78--77--76--75 105-104 5
20 | / \ |
21 114-113 80 48--47--46--45--44 74 103-102 4
22 | / | | \ |
23 115 81 50--49 27--26--25 43--42 73 101 3
24 / / | / \ | \ \
25 116 82 52--51 28 14--13--12 24 41--40 72 100 2
26 | | | / / \ \ | | |
27 117 83 53 29 15 5-- 4-- 3 11 23 39 71 99 1
28 | | | | | | | | | | | |
29 118 84 54 30 16 6 1-- 2 10 22 38 70 98 <- Y=0
30 | | | | | | / / / / / /
31 119 85 55 31 17 7-- 8-- 9 21 37 69 97 137 -1
32 | | | \ \ / / | | |
33 120 86 56--57 32 18--19--20 36 67--68 96 136 -2
34 \ \ | \ / | / /
35 121 87 58--59 33--34--35 65--66 95 135 -3
36 | \ | | / |
37 122-123 88 60--61--62--63--64 94 133-134 -4
38 | \ / |
39 124-125 89--90--91--92--93 131-132 -5
40 \ /
41 126-127-128-129-130
42 ^
44 -6 -5 -4 -3 -2 -1 X=0 1 2 3 4 5 6
45 For example the ring N=22 to N=37 is all the points
47 2.5 < hypot(X,Y) < 3.5
49 where hypot(X,Y) = sqrt(X^2+Y^2)
50 N Start
52 The default is to number points starting N=1 as shown above. An
53 optional "n_start" can give a different start with the same shape. For
54 example to start at 0,
55 26-25-24 n_start => 0
57 / \
58 27 13-12-11 23
59 / / \ \
60 28 14 4--3--2 10 22
61 | | | | | |
62 29 15 5 0--1 9 21
63 | | | / / /
64 30 16 6--7--8 20 36
65 \ \ / /
66 31 17-18-19 35
67 \ /
68 8 32-33-34
69 The only effect is to push the N values by a constant amount but can
71 help match N on the axes to counts of X,Y points < R or similar.
72
74 See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path
75 classes.
76 "$path = Math::PlanePath::FilledRings->new ()"
78 "$path = Math::PlanePath::FilledRings->new (n_start => $n)"
79 Create and return a new path object.
80
82 Entries in Sloane's Online Encyclopedia of Integer Sequences related to
83 this path include,
84 <http://oeis.org/A036704> (etc)
86 A036705 first diffs of N on X axis,
88 being count of X,Y points n-1/2 < norm <= n+1/2
89 A036706 1/4 of those diffs
90 n_start=1 (the default)
92 A036707 N/2+X-1 along X axis,
93 being count norm <= n+1/2 in half plane
94 A036708 (N(X,0)-N(X-1,0))/2+1,
95 first diffs of the half plane count
96 n_start=0
98 A036704 N on X axis, from X=1 onwards
99 count of X,Y points norm <= n+1/2
100
102 Math::PlanePath, Math::PlanePath::PixelRings, Math::PlanePath::Hypot,
103 Math::PlanePath::MultipleRings
104
106 <http://user42.tuxfamily.org/math-planepath/index.html>
107
109 Copyright 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020 Kevin
110 Ryde
111 This file is part of Math-PlanePath.
113 Math-PlanePath is free software; you can redistribute it and/or modify
115 it under the terms of the GNU General Public License as published by
116 the Free Software Foundation; either version 3, or (at your option) any
117 later version.
118 Math-PlanePath is distributed in the hope that it will be useful, but
120 WITHOUT ANY WARRANTY; without even the implied warranty of
121 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
122 General Public License for more details.
123 You should have received a copy of the GNU General Public License along
125 with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
126perl v5.34.0 2021-07-22 Math::PlanePath::FilledRings(3)