NAME
Math::PlanePath::Diagonals  points in diagonal stripes
SYNOPSIS
use Math::PlanePath::Diagonals;
my $path = Math::PlanePath::Diagonals>new;
my ($x, $y) = $path>n_to_xy (123);
DESCRIPTION
This path follows successive diagonals going from the Y axis down to the X axis.
...
6  22
5  16 23
4  11 17 ...
3  7 12 18 ...
2  4 8 13 19 ...
1  2 5 9 14 20 ...
y=0  1 3 6 10 15 21 ...

x=0, 1 2 3 4 ...
The horizontal sequence 1,3,6,10,etc at y=0 is the triangular numbers s*(s+1)/2. If you plot them on a graph don't confuse that line with the axis or border!
FUNCTIONS
See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.
$path = Math::PlanePath::Diagonals>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 the path begins at 1. $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$n
as a square of side 1, so the quadrant x>=0.5, y>=0.5 is entirely covered.
FORMULAS
Rectangle to N Range
Within each row increasing X is increasing N, and in each column increasing Y is increasing N. On that basis in a rectangle the lower left corner is the minimum N and the upper right is the maximum N.
SEE ALSO
Math::PlanePath, Math::PlanePath::Corner, Math::PlanePath::Rows, Math::PlanePath::Columns
HOME PAGE
http://user42.tuxfamily.org/mathplanepath/index.html
LICENSE
Copyright 2010, 2011 Kevin Ryde
This file is part of MathPlanePath.
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/>.