++ed by:

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Kevin Ryde
and 1 contributors


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 border!


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.


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.


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




Copyright 2010, 2011 Kevin Ryde

This file is part of Math-PlanePath.

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/>.