NAME

Math::PlanePath::PyramidSpiral -- integer points drawn around a pyramid

SYNOPSIS

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

DESCRIPTION

This path makes a pyramid shaped spiral,

                     31                            3
                  32 13 30                         2
               33 14  3 12 29                      1
            34 15  4  1  2 11 28              <- y=0
         35 16  5  6  7  8  9 10 27 ...           -1
      36 17 18 19 20 21 22 23 24 25 26 51         -2
   37 38 39 40 41 42 43 44 45 46 47 48 49 50      -3

                      ^
   -5 -4 -3  -2  -1  x=0  1   2   3  4  5  6 

The perfect squares 1,4,9,16 fall one before the bottom left corner of each loop, and the pronic numbers 2,6,12,20,30,etc are the vertical upwards from x=1.

This spiral goes around at the same rate as the SquareSpiral, just reshaped a bit. The height is the same as the square but the top left and top right corners are cut off (half way up) and the base extended left and right. Cutting the corners shortens the loop by 2 and extending the base lengthens it by 2, for the same rate.

FUNCTIONS

$path = Math::PlanePath::PyramidSpiral->new ()

Create and return a new pyramid spiral object.

($x,$y) = $path->n_to_xy ($n)

Return the x,y coordinates of point number $n on the path.

For $n < 1 the return is an empty list, it being considered the path starts 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 N in the path as centred in a square of side 1, so the entire plane is covered.

SEE ALSO

Math::PlanePath, Math::PlanePath::SquareSpiral, Math::PlanePath::PyramidRows

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/>.