Math::PlanePath::Corner -- points shaped in a corner
use Math::PlanePath::Corner; my $path = Math::PlanePath::Corner->new; my ($x, $y) = $path->n_to_xy (123);
This path puts points in layers working outwards from the corner of the first quadrant.
... 5 | 26 ................ 4 | 17 18 19 20 21 . 3 | 10 11 12 13 22 . 2 | 5 6 7 14 23 . 1 | 2 3 8 15 24 . y=0 | 1 4 9 16 25 . ---------------------- x=0, 1 2 3 4 ...
The horizontal 1,4,9,16,etc at y=0 is the perfect squares. The diagonal 2,6,12,20,etc starting x=0,y=1 is the pronic numbers s*(s+1), half way between those squares.
Each stripe across then down is 2 longer than the previous and in that respect the corner is the same as the Pyramid and SacksSpiral paths. The Corner and the PyramidSides are the same thing, just with a stretch from a single quadrant to two.
$path = Math::PlanePath::Corner->new ()
Create and return a new path object.
($x,$y) = $path->n_to_xy ($n)
Return the x,y coordinates of point number
$non the path.
$n < 0.5the return is an empty list, it being considered there are no points before 1 in the corner.
$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 as a square of side 1, so the quadrant x>=-0.5 and y>=-0.5 is entirely covered.
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/>.