NAME
Math::PlanePath::PentSpiral  integer points in a pentagonal shape
SYNOPSIS
use Math::PlanePath::PentSpiral;
my $path = Math::PlanePath::PentSpiral>new;
my ($x, $y) = $path>n_to_xy (123);
DESCRIPTION
This path makes a pentagonal (fivesided) spiral with points spread out to fit on a square grid.
22 3
23 10 21 2
24 11 3 9 20 1
25 12 4 1 2 8 19 < y=0
26 13 5 6 7 18 ... 1
27 14 15 16 17 33 2
28 29 30 31 32 2
^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^
6 5 4 3 2 1 x=0 1 2 3 4 5 6 7
Each horizontal gap is 2, so for instance n=1 is at x=0,y=0 then n=2 is at x=2,y=0. The lower diagonals are 1 across and 1 down, so n=17 is at x=4,y=2 and n=18 is x=5,y=1. But the upper angles go 2 across and 1 up, so n=20 is x=4,y=1 then n=21 is x=2,y=2.
The effect is to make the sides equal length, except for a kink at the lower right corner. Only every second square in the plane is used. In the top half (y>=0) those squares line up, in the lower half (y<0) they're offset on alternate rows.
FUNCTIONS
See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.
$path = Math::PlanePath::PentSpiral>new ()

Create and return a new pentagon 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::PentSpiralSkewed, Math::PlanePath::HexSpiral
HOME PAGE
http://user42.tuxfamily.org/mathplanepath/index.html
LICENSE
Copyright 2010, 2011 Kevin Ryde
This file is part of MathPlanePath.
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/>.