Math::PlanePath::HexSpiral -- integer points in a diamond shape
use Math::PlanePath::HexSpiral; my $path = Math::PlanePath::HexSpiral->new; my ($x, $y) = $path->n_to_xy (123);
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.
$path = Math::PlanePath::HexSpiral->new ()
Create and return a new HexSpiral path object.
($x,$y) = $path->n_to_xy ($n)
Return the x,y coordinates of point number
$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
$nin the path as a square of side 1.
Only every second square in the plane has an N. If
$x,$yis a position without an N then the return is
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/>.