Math::PlanePath::Diagonals -- points in diagonal stripes
use Math::PlanePath::Diagonals; my $path = Math::PlanePath::Diagonals->new; my ($x, $y) = $path->n_to_xy (123);
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 a border!)
$path = Math::PlanePath::Diagonals->new ()
Create and return a new path object.
($x,$y) = $path->n_to_xy ($n)
Return the X,Y coordinates of point number $n on the path.
$n
For $n < 0.5 the return is an empty list, it being considered the path begins at 1.
$n < 0.5
$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.
$x,$y
$x
$y
Within each row increasing X is increasing N, and each column increasing Y is increasing N. On that basis in a rectangle for rect_to_n_range the lower left corner is the minimum N and the upper right is the maximum N.
rect_to_n_range
Math::PlanePath, Math::PlanePath::Corner, Math::PlanePath::Rows, Math::PlanePath::Columns
http://user42.tuxfamily.org/math-planepath/index.html
Math-PlanePath is Copyright 2010, 2011 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/>.
To install Math::PlanePath, copy and paste the appropriate command in to your terminal.
cpanm
cpanm Math::PlanePath
CPAN shell
perl -MCPAN -e shell install Math::PlanePath
For more information on module installation, please visit the detailed CPAN module installation guide.