NAME
Math::PlanePath::Corner  points shaped in a corner
SYNOPSIS
use Math::PlanePath::Corner;
my $path = Math::PlanePath::Corner>new;
my ($x, $y) = $path>n_to_xy (123);
DESCRIPTION
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.
FUNCTIONS
$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
$n
on the path.For
$n < 0.5
the 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
$x,$y
.$x
and$y
are 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.
SEE ALSO
Math::PlanePath, Math::PlanePath::PyramidRows, Math::PlanePath::PyramidSides, Math::PlanePath::SacksSpiral
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/>.