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 a border!)

FUNCTIONS

$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

N Range

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.

SEE ALSO

Math::PlanePath, Math::PlanePath::Corner, Math::PlanePath::Rows, Math::PlanePath::Columns

HOME PAGE

http://user42.tuxfamily.org/math-planepath/index.html

LICENSE

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/>.