/ 
Math-PlanePath-50
River stage one • 3 direct dependents • 4 total dependents
/ Math::PlanePath::AztecDiamondRings

NAME

Math::PlanePath::AztecDiamondRings -- rings around an Aztec diamond shape

SYNOPSIS

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

DESCRIPTION

This path makes rings around an Aztec diamond shape,

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

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

This is very similar to the DiamondSpiral, but has all four corners flattened to 2 vertical or horizontal, instead of just one in the DiamondSpiral. This is only a small change to the alignment of numbers in the sides, but is more symmetric.

The hexagonal numbers 1,6,15,28,45,66,etc, k*(2k-1), are the vertical at X=0 going upwards. The hexagonal numbers of the "second kind" 3,10,21,36,55,78, etc k*(2k+1), are the vertical at X=-1 going downwards. Combining those two is the triangular numbers 3,6,10,15,21,etc, k*(k+1)/2, alternately on one line and the other.

FUNCTIONS

See "FUNCTIONS" in Math::PlanePath for the behaviour common to all path classes.

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

Create and return a new Aztec diamond 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 point in the path as a square of side 1, so the entire plane is covered.

SEE ALSO

Math::PlanePath, Math::PlanePath::DiamondSpiral

HOME PAGE

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

LICENSE

Copyright 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.

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/>.