Math::PlanePath::HeptSpiralSkewed -- integer points around a skewed seven sided spiral
use Math::PlanePath::HeptSpiralSkewed; my $path = Math::PlanePath::HeptSpiralSkewed->new; my ($x, $y) = $path->n_to_xy (123);
This path makes a seven-sided spiral by cutting one corner of a square
34-33-32-31 3 | \ 35 14-13-12 30 2 | | \ \ 36 15 4--3 11 29 1 | | | \ \ \ 47 16 5 1--2 10 28 <- y=0 | | | | | 38 17 6--7--8- 9 27 -1 | | | 39 18-22-23-24-25-26 -2 | 40-41-42-43-44-... ^ -3 -2 -1 x=0 1 2 3
The path is as if around a heptagon, with the left and bottom here as two sides of the heptagon straightened out, and the flat top here skewed across to fit a square grid.
See "FUNCTIONS" in Math::PlanePath for behaviour common to all path classes.
$path = Math::PlanePath::HeptSpiralSkewed->new ()
Create and return a new path object.
($x,$y) = $path->n_to_xy ($n)
Return the X,Y coordinates of point number
$n on the path.
$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
$y are each rounded to the nearest integer, which has the effect of treating each N in the path as centred in a square of side 1, so the entire plane is covered.
Copyright 2010, 2011, 2012, 2013 Kevin Ryde
This file is part of Math-PlanePath.
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/>.