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
$non the path.
$n < 0.5the 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
$yare each rounded to the nearest integer, which has the effect of treating each point
$nas a square of side 1, so the quadrant x>=-0.5, y>=-0.5 is entirely covered.
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.
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.
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