Math::PlanePath::FilledRings -- concentric filled lattice rings
use Math::PlanePath::FilledRings; my $path = Math::PlanePath::FilledRings->new; my ($x, $y) = $path->n_to_xy (123);
This path puts points on integer X,Y pixels of filled rings with radius 1 unit each ring.
110-109-108-107-106 6 / \ 112-111 79--78--77--76--75 105-104 5 | / \ | 114-113 80 48--47--46--45--44 74 103-102 4 | / | | \ | 115 81 50--49 27--26--25 43--42 73 101 3 / / | / \ | \ \ 116 82 52--51 28 14--13--12 24 41--40 72 100 2 | | | / / \ \ | | | 117 83 53 29 15 5-- 4-- 3 11 23 39 71 99 1 | | | | | | | | | | | | 118 84 54 30 16 6 1-- 2 10 22 38 70 98 <- Y=0 | | | | | | 119 85 55 31 17 7-- 8-- 9 21 37 69 97 137 -1 | | | \ \ / / | | | 120 86 56--57 32 18--19--20 36 67--68 96 136 -2 \ \ | \ / | / / 121 87 58--59 33--34--35 65--66 95 135 -3 | \ | | / | 122-123 88 60--61--62--63--64 94 133-134 -4 | \ / | 124-125 89--90--91--92--93 131-132 -5 \ / 126-127-128-129-130 ^ -6 -5 -4 -3 -2 -1 X=0 1 2 3 4 5 6
For example the ring N=22 to N=37 is all the points
2.5 < hypot(X,Y) < 3.5 where hypot(X,Y) = sqrt(X^2+Y^2)
See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.
$path = Math::PlanePath::FilledRings->new ()
Create and return a new path object.
($x,$y) = $path->n_to_xy ($n)
For $n < 1 the return is an empty list, it being considered there are no negative points.
$n < 1
The behaviour for fractional $n is unspecified as yet.
$n
Entries in Sloane's Online Encyclopedia of Integer Sequences related to this path include,
http://oeis.org/A036704 (etc) A036704 N-1 along X axis, being count of X,Y points norm <= n+1/2 A036705 first diffs of N on X axis, being count of X,Y points n-1/2 < norm <= n+1/2 A036706 1/4 of those diffs A036707 N/2+X-1 along X axis, being count norm <= n+1/2 in half plane Y>=0 A036708 (N(X,0)-N(X-1,0))/2+1, first diffs of the half plane count
Math::PlanePath, Math::PlanePath::PixelRings, Math::PlanePath::Hypot, Math::PlanePath::MultipleRings
http://user42.tuxfamily.org/math-planepath/index.html
Copyright 2012 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 <http://www.gnu.org/licenses/>.
To install Math::PlanePath, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Math::PlanePath
CPAN shell
perl -MCPAN -e shell install Math::PlanePath
For more information on module installation, please visit the detailed CPAN module installation guide.