Math::PlanePath::HexSpiralSkewed -- integer points in a diamond shape
use Math::PlanePath::HexSpiralSkewed; my $path = Math::PlanePath::HexSpiralSkewed->new; my ($x, $y) = $path->n_to_xy (123);
This path makes a hexagonal spiral with points skewed so as to fit a square grid and fully cover the plane.
13--12--11 ... 2 | \ \ 14 4---3 10 23 1 | | \ \ \ 15 5 1---2 9 22 <- y=0 \ \ | | 16 6---7---8 21 -1 \ | 17--18--19--20 -2 ^ ^ ^ ^ ^ ^ -2 -1 x=0 1 2 3 ...
The sequence is the same as the plain HexSpiral, but this arrangement fits more points on a square grid. The skew pushes the top horizontal to the left, as illustrated by the following portion from the two. The bottom horizontal is similarly skewed but to the right.
HexSpiralSkewed HexSpiral 13--12--11 13--12--11 | \ / \ 14 10 14 10 | \ / \ 15 9 15 9
HexSpiralSkeweed is similar to the SquareSpiral but cuts off the top right and bottom left two corners so that each loop is 6 steps longer than the previous whereas for the SquareSpiral it's 8. See "Corners" in Math::PlanePath::SquareSpiral for other corner cutting.
$path = Math::PlanePath::HexSpiral->new ()
Create and return a new HexSpiral spiral object.
($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.
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