NAME

Math::PlanePath::DragonArms -- four dragon curves

SYNOPSIS

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

DESCRIPTION

This is four arms of the dragon or paper folding curve by Heighway, Harter and others.

                   60/76 --64/191
                     |         
                   56/88 --52/187   183/40 --36/107
                               |      |        |
33/108    29/96    17/92    13/48 -- 44/28 -- 32/95
                                        |    
37/184    25/41     6/21 ---  2/9     5/24 -- 20/91    55/87
                     |                         |
49/188    14/45 --- 10/3        0     1/12 -- 16/47   51/186
           |                    |      |
 53/85    18/89 --- 22/7     11/4 --- 8/23    27/43   39/182
                    |               
          30/93 -- 26/42 -- 15/46    19/90    31/94   35/106
           |          |       |     
         34/105 --38/181   185/50 -- 54/86
                                      |
                           62/189 -- 58/74

 
   ^        ^        ^       ^         ^        ^       ^
  -3       -2       -1      X=0        1        2       3

The curve visits each X,Y point twice (except the origin 0,0). Each edge between X,Y points is traversed just once and each arm doesn't cross itself or other arms so it's just the vertexes which touch.

FUNCTIONS

$path = Math::PlanePath::DragonArms->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.

$n = $path->n_start()

Return 0, the first N in the path.

SEE ALSO

Math::PlanePath, Math::PlanePath::KochCurve