Math::PlanePath::PentSpiralSkewed -- integer points in a pentagonal shape
use Math::PlanePath::PentSpiralSkewed; my $path = Math::PlanePath::PentSpiralSkewed->new; my ($x, $y) = $path->n_to_xy (123);
This path makes a pentagonal (five-sided) spiral with points skewed so as to fit a square grid and fully cover the plane.
10 ... 2 / \ \ 11 3 9 20 1 / / \ \ \ 12 4 1--2 8 19 <- y=0 \ \ | | 13 5--6--7 18 -1 \ | 14-15-16-17 -2 ^ ^ ^ ^ ^ ^ -2 -1 x=0 1 2 3 ...
The pattern is similar to the SquareSpiral but cuts three corners which makes each cycle is faster. Each cycle is just 5 steps longer than the previous (where it's 8 for a SquareSpiral).
$path = Math::PlanePath::PentSpiral->new ()
Create and return a new PentSpiral spiral object.
($x,$y) = $path->n_to_xy ($n)
Return the x,y coordinates of point number
$non the path.
$n < 1the return is an empty list, it being considered the path starts at 1.
$n = $path->xy_to_n ($x,$y)
Return the point number for coordinates
$yare each rounded to the nearest integer, which has the effect of treating each point in the path as a square of side 1.
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/>.