NAME
Math::PlanePath::PentSpiralSkewed  integer points in a pentagonal shape
SYNOPSIS
use Math::PlanePath::PentSpiralSkewed;
my $path = Math::PlanePath::PentSpiralSkewed>new;
my ($x, $y) = $path>n_to_xy (123);
DESCRIPTION
This path makes a pentagonal (fivesided) 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 12 8 19 < y=0
\ \  
13 567 18 1
\ 
14151617 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).
FUNCTIONS
$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
$n
on the path.For
$n < 1
the 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
$x,$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.
SEE ALSO
Math::PlanePath, Math::PlanePath::SquareSpiral, Math::PlanePath::DiamondSpiral, Math::PlanePath::HexSpiralSkewed
HOME PAGE
http://user42.tuxfamily.org/mathplanepath/index.html
LICENSE
MathPlanePath is Copyright 2010 Kevin Ryde
MathPlanePath 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.
MathPlanePath 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 MathPlanePath. If not, see <http://www.gnu.org/licenses/>.