Math::PlanePath::PyramidSpiral -- integer points drawn around a pyramid
use Math::PlanePath::PyramidSpiral; my $path = Math::PlanePath::PyramidSpiral->new; my ($x, $y) = $path->n_to_xy (123);
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 52 -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 7
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.
See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.
$path = Math::PlanePath::PyramidSpiral->new ()
Create and return a new pyramid spiral object.
($x,$y) = $path->n_to_xy ($n)
Return the X,Y coordinates of point number
$non the path.
$n < 1the 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
$yare 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.
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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