++ed by:

2 PAUSE users

Kevin Ryde
and 1 contributors


Math::PlanePath::Corner -- points shaped in a corner


 use Math::PlanePath::Corner;
 my $path = Math::PlanePath::Corner->new;
 my ($x, $y) = $path->n_to_xy (123);


This path puts points in layers working outwards from the corner of the first quadrant.

      5  |  26 ................
      4  |  17  18  19  20  21 .
      3  |  10  11  12  13  22 .
      2  |   5   6   7  14  23 .
      1  |   2   3   8  15  24 .
    y=0  |   1   4   9  16  25 .
           x=0,  1   2   3   4 ...

The horizontal 1,4,9,16,etc at y=0 is the perfect squares. The diagonal 2,6,12,20,etc starting x=0,y=1 is the pronic numbers s*(s+1), half way between those squares.

Each stripe across then down is 2 longer than the previous and in that respect the corner is the same as the Pyramid and SacksSpiral paths. The Corner and the PyramidSides are the same thing, just with a stretch from a single quadrant to two.


$path = Math::PlanePath::Corner->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 there are no points before 1 in the corner.

$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 as a square of side 1, so the quadrant x>=-0.5 and y>=-0.5 is entirely covered.


Math::PlanePath, Math::PlanePath::PyramidRows, Math::PlanePath::PyramidSides, Math::PlanePath::SacksSpiral




Math-PlanePath is Copyright 2010 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/>.