NAME

Math::PlanePath::MathImageQuintetCentres -- "plus" shape centres

SYNOPSIS

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

DESCRIPTION

This a self-similar curve tracing out a "+" shape like the QuintetCurve but taking the centre of each square visited by that curve.

                                     92                        12
                                   /  |
        124-...                  93  91--90      88            11
          |                        \       \   /   \
    122-123 120     102              94  82  89  86--87        10
       \   /  |    /  |            /   /  |       |
        121 119 103 101-100      95  81  83--84--85             9
               \   \       \       \   \
    114-115-116 118 104  32  99--98  96  80  78                 8
      |       |/   /   /  |       |/      |/   \
112-113 110 117 105  31  33--34  97  36  79  76--77             7
   \   /   \       \   \       \   /   \      |
    111     109-108 106  30  42  35  38--37  75                 6
                  |/   /   /  |       |    /
                107  29  43  41--40--39  74                     5
                       \   \              |
             24--25--26  28  44  46  72--73  70      68         4
              |       |/      |/   \   \   /   \   /   \
         22--23  20  27  18  45  48--47  71  56  69  66--67     3
           \   /   \   /   \      |        /   \      |
             21   6  19  16--17  49  54--55  58--57  65         2
               /   \      |       |    \      |    /
          4-- 5   8-- 7  15      50--51  53  59  64             1
           \      |    /              |/      |    \
      0-- 1   3   9  14              52      60--61  63     <- Y=0
          |/      |    \                          |/
          2      10--11  13                      62            -1
                      |/
                     12                                        -2

      ^
 -1  X=0  1   2   3   4   5   6   7   8   9  10  11  12  13

The base figure is "+" shape of the initial N=0 to N=4,

    .....
    .   .
    . 4 .
    .  \.
........\....
.   |   .\  .
. 0---1 . 3 .
.   | | ./  .
......|./....
    . |/.
    . 2 .
    .   .
    .....

FUNCTIONS

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

$path = Math::PlanePath::MathImageQuintetCentres->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::Flowsnake