1Math::PlanePath::PixelRUisnegrs(C3o)ntributed Perl DocumMeanttha:t:iPolnanePath::PixelRings(3)
2
6 Math::PlanePath::PixelRings -- pixellated concentric circles
7
9 use Math::PlanePath::PixelRings;
10 my $path = Math::PlanePath::PixelRings->new;
11 my ($x, $y) = $path->n_to_xy (123);
12
14 This path puts points on the pixels of concentric circles using the
15 midpoint ellipse drawing algorithm.
16 63--62--61--60--59 5
18 / \
19 64 . 40--39--38 . 58 4
20 / / \ \
21 65 . 41 23--22--21 37 . 57 3
22 / / / \ \ \
23 66 . 42 24 10-- 9-- 8 20 36 . 56 2
24 | / / / \ \ \ |
25 67 43 25 11 . 3 . 7 19 35 55 1
26 | | | | / \ | | | |
27 67 44 26 12 4 1 2 6 18 34 54 Y=0
28 | | | | \ /
29 68 45 27 13 . 5 . 17 33 53 80 -1
30 | \ \ \ / / / |
31 69 . 46 28 14--15--16 32 52 . 79 -2
32 \ \ \ / / /
33 70 . 47 29--30--31 51 . 78 -3
34 \ \ / /
35 71 . 48--49--50 . 77 -4
36 \ /
37 72--73--74--75--76 -5
38 -5 -4 -3 -2 -1 X=0 1 2 3 4 5
40 The way the algorithm works means the rings don't overlap. Each is 4
42 or 8 pixels longer than the preceding. If the ring follows the
43 preceding tightly then it's 4 longer, for example N=18 to N=33. If it
44 goes wider then it's 8 longer, for example N=54 to N=80 ring. The
45 average extra is approximately 4*sqrt(2).
46 The rings can be thought of as part-way between the diagonals like
48 "DiamondSpiral" and the corners like "SquareSpiral".
49 * ** *****
51 * * *
52 * * *
53 * * *
54 * * *
55 diagonal ring corner
57 5 points 6 points 9 points
58 For example the N=54 to N=80 ring has a vertical part N=54,55,56 like a
60 corner then a diagonal part N=56,57,58,59. In bigger rings the
61 verticals are intermingled with the diagonals but the principle is the
62 same. The number of vertical steps determines where it crosses the
63 45-degree line, which is at R*sqrt(2) but rounded according to the
64 midpoint algorithm.
65
67 See "FUNCTIONS" in Math::PlanePath for behaviour common to all path
68 classes.
69 "$path = Math::PlanePath::PixelRings->new ()"
71 Create and return a new path object.
72 "($x,$y) = $path->n_to_xy ($n)"
74 For "$n < 1" the return is an empty list, it being considered there
75 are no negative points.
76 The behaviour for fractional $n is unspecified as yet.
78 "$n = $path->xy_to_n ($x,$y)"
80 Return an integer point number for coordinates "$x,$y". Each
81 integer N is considered the centre of a unit square and an "$x,$y"
82 within that square returns N.
83 Not every point of the plane is covered (like those marked by a "."
85 in the sample above). If "$x,$y" is not reached then the return is
86 "undef".
87
89 Math::PlanePath, Math::PlanePath::Hypot, Math::PlanePath::MultipleRings
90
92 <http://user42.tuxfamily.org/math-planepath/index.html>
93
95 Copyright 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
96 2020 Kevin Ryde
97 This file is part of Math-PlanePath.
99 Math-PlanePath is free software; you can redistribute it and/or modify
101 it under the terms of the GNU General Public License as published by
102 the Free Software Foundation; either version 3, or (at your option) any
103 later version.
104 Math-PlanePath is distributed in the hope that it will be useful, but
106 WITHOUT ANY WARRANTY; without even the implied warranty of
107 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
108 General Public License for more details.
109 You should have received a copy of the GNU General Public License along
111 with Math-PlanePath. If not, see <http://www.gnu.org/licenses/>.
112perl v5.34.0 2021-07-22 Math::PlanePath::PixelRings(3)