NAME
Math::PlanePath::HexSpiral  integer points in a diamond shape
SYNOPSIS
use Math::PlanePath::HexSpiral;
my $path = Math::PlanePath::HexSpiral>new;
my ($x, $y) = $path>n_to_xy (123);
DESCRIPTION
This path makes a hexagonal spiral, with points spread out horizontally to fit on a square grid.
28  27  26  25 3
/ \
29 13  12  11 24 2
/ / \ \
30 14 4  3 10 23 1
/ / / \ \ \
31 15 5 1  2 9 22 < y=0
\ \ \ / /
32 16 6  7  8 21 1
\ \ /
33 17  18  19  20 2
\
34  35 ... 3
^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^
6 5 4 3 2 1 x=0 1 2 3 4 5 6
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 diagonals are just 1 across, so n=3 is at x=1,y=1. Each alternate row is offset from the one above or below. The resulting "triangles" between the points are flatter than they ought to be. Drawn on a square grid the angle up is 45 degrees making an isosceles right triangle instead of 60 for an equilateral triangle.
FUNCTIONS
$path = Math::PlanePath::HexSpiral>new ()

Create and return a new HexSpiral path 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$n
in the path as a square of side 1.Only every second square in the plane has an N. If
$x,$y
is a position without an N then the return isundef
.
SEE ALSO
Math::PlanePath, Math::PlanePath::HexSpiralSkewed, Math::PlanePath::TriangleSpiral
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/>.