Math::PlanePath::HexSpiralSkewed -- integer points in a diamond shape
use Math::PlanePath::HexSpiralSkewed; my $path = Math::PlanePath::HexSpiralSkewed->new; my ($x, $y) = $path->n_to_xy (123);
This path makes a hexagonal spiral with points skewed so as to fit a square grid and fully cover the plane.
13--12--11 ... 2 | \ \ 14 4---3 10 23 1 | | \ \ \ 15 5 1---2 9 22 <- y=0 \ \ | | 16 6---7---8 21 -1 \ | 17--18--19--20 -2 ^ ^ ^ ^ ^ ^ -2 -1 x=0 1 2 3 ...
The sequence is the same as for the plain HexSpiral, but this arrangement fits more points on a square grid. It's similar to the SquareSpiral but cuts two corners so each loop is 6 steps longer than the previous whereas for the SquareSpiral it's 8. See the DiamondSpiral for cutting all 4 corners.
$path = Math::PlanePath::HexSpiral->new ()
Create and return a new HexSpiral spiral object.
($x,$y) = $path->n_to_xy ($n)
Return the x,y coordinates of point number $n on the path.
$n
For $n < 1 the return is an empty list, it being considered the path starts at 1.
$n < 1
$n = $path->xy_to_n ($x,$y)
Return the point number for coordinates $x,$y. $x and $y are each rounded to the nearest integer, which has the effect of treating each point in the path as a square of side 1.
$x,$y
$x
$y
Math::PlanePath, Math::PlanePath::HexSpiral
http://user42.tuxfamily.org/math-planepath/index.html
Math-PlanePath is Copyright 2010 Kevin Ryde
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.