NAME

Math::PlanePath::PythagoreanUAD -- primitive pythagorean triples by U,A,D

SYNOPSIS

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

DESCRIPTION

Old ...

This path is the x,y coordinates of primitive Pythagorean triples taken as a breadth-first traversal of Barning's U/A/D generators.

As a method of visiting all triples near the origin this isn't very practical, since the UAD tree goes out to very distant points while some quite close to the origin remain.

In general at tree depth k, which means visiting N=1 through N=(3^k-1)/2, the smallest x visited is 2*k*(k+1). So going up to say x=364 requires some 800,000 points, the vast majority of which are out at higher x.

FUNCTIONS

$path = Math::PlanePath::PythagoreanUAD->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. Points begin at 0 and if $n < 0 then the return is an empty list.

Fractional positions give an X,Y position along a straight line between the integer positions. Integer positions are always just 1 apart either horizontally or vertically, so the effect is that the fraction part appears either added to or subtracted from X or Y.

SEE ALSO

Math::PlanePath

HOME PAGE

http://user42.tuxfamily.org/math-planepath/index.html

LICENSE

Copyright 2010, 2011, 2012 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/>.