/ 
math-image-47
River stage zero No dependents
/ Math::PlanePath::MathImageHypot

NAME

Math::PlanePath::MathImageHypot -- points by hypotenuse distance

SYNOPSIS

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

DESCRIPTION

In progresss ... the current implementation is very slack.

This path takes integer points X<0,Y<0 in order of their distance from the origin 0,0, that distance being the hypotenuse sqrt(X^2+Y^2).

 9      73  75  79  83  85
 8      58  62  64  67  71  81  ...
 7      45  48  52  54  61  69  78  86
 6      35  37  39  43  50  56  65  77  88
 5      26  28  30  33  41  47  55  68  80
 4      17  19  22  25  31  40  49  60  70  84
 3      11  13  15  20  24  32  42  53  66  82
 2       6   8   9  14  21  29  38  51  63  76
 1       3   4   7  12  18  27  36  46  59  74
Y=0      1   2   5  10  16  23  34  44  57  72

        X=0  1   2   3   4   5   6   7   8   9  ...

For example N=37 is at X=1,Y=6 which is sqrt(1*1+6*6) = sqrt(37) from the origin. The next closest to the origin is X=6,Y=2 at sqrt(40). In general it's the sums of two squares X^2+Y^2 taken in order from smallest to biggest.

Points X,Y and swapped Y,X are the same distance from the origin. The one with bigger X is taken first, then the swapped Y,X (as long as X!=Y). For example N=21 is X=4,Y=2 and N=22 is X=2,Y=4.

FUNCTIONS

$path = Math::PlanePath::MathImageHypot->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 < 1 the return is an empty list, it being considered the first point at X=0,Y=0 is N=1.

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

Return an integer point number for coordinates $x,$y. Each integer N is considered the centre of a unit square and an $x,$y within that square returns N.

SEE ALSO

Math::PlanePath, Math::PlanePath::PixelRings

HOME PAGE

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

LICENSE

Math-Image is Copyright 2011 Kevin Ryde

Math-Image 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-Image 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-Image. If not, see <http://www.gnu.org/licenses/>.