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Math::Curve::Hilbert.3pm

NAME

Math::Curve::Hilbert - Perl Implementation of Hilberts space filling Curve

SYNOPSIS

   use Math::Curve::Hilbert;
 
   # get object representing 8x8 curve with a step of 10 (i.e. draw 80x80 pixels)
   my $hilbert = Math::Curve::Hilbert->new( direction=>'up', max=>3, clockwise=>1, step=>10);
 
   # get a point from coordinates
   my $point = $hilbert->PointFromCoordinates(20,60);
 
   # get coordinates from a point
   my ($x,$y) = $hilbert->CoordinatesFromPoint($point);
 
 
   # get range(s) from box
   my @ranges = $hilbert->RangeFromCoordinates($x1,$y1,$x2,$y2);
 
   #
   # draw image representing curve
 
   use GD;
   # create a new image
   my $im = new GD::Image(300,300);
   my $black = $im->colorAllocate(0,0,0);
   my $blue = $im->colorAllocate(0,0,255);
 
   my $count = 0;
   my ($x1,$y1) = $hilbert->CoordinatesFromPoint($count++);
   while ( ($hilbert->CoordinatesFromPoint($count))[0] ) {
       my ($x2,$y2) = $hilbert->CoordinatesFromPoint($count++);
       $im->line($x1,$y1,$x2,$y2,$black);
       ($x1,$y1) = ($x2,$y2);
   }
 
 

DESCRIPTION

The Hilbert Curve module provides some useful functions using Hilberts Space-filling Curve. This is handy for things like Dithering, Flattening n-dimensional data, fractals - all kind of things really.

``A Space Filling Curve is a special fractal curve which has the following basic characteristics:
 A it covers completely an area, a volume or a hyper-volume in a 2-d, 3-d or N-d space respectively,
 A each point is visited once and only once (the curve does not cross itself), and
 A neighbor points in the native space are likely to be neighbors in the space filling curve.'' definition from Multiple Range Query Optimization in Spatial Databases, Apostolos N. Papadopoulos and Yannis Manolopoulos

Other space filling curves include The Peano and Morton or Z-order curves. There is also the Hilbert II curve which has an 'S' shape rather than a 'U' shape. The Hilbert curve can also be applied to 3 dimensions, but this module only supports 2 dimensions.

Like most space filling curves, the area must be divided into 2 to the power of N parts, such as 8, 16, 32, etc

EXPORT

None by default.

METHODS

new

   # get object representing 8x8 curve with a step of 10 (i.e. draw 80x80 pixels)
   my $hilbert = Math::Curve::Hilbert->new( direction=>'up', max=>3, clockwise=>1, step=>10);
 
   direction specifies which direction the curve follows :
 
   up (clockwise) : up, right, down
   down (clockwise ) : down, right, up
   left (clockwise) : left, up, right
   right (clockwise) : right, down, left
 
   clockwise specifies if the curve moves clockwise or anti-clockwise, the default is clockwise
 
   max specifies the size of the grid to plot in powers of 2 - max=>2 would be a 4x4 grid, max=>4 would be 16 x 16 grid
 
   step specifies how large a step should be (used in drawing the curve), the default is 1
 
   X and Y allow you to specify a starting X and Y coordinate by passing a reference to a the value
 
 

PointFromCoordinates

   my $point = $hilbert->PointFromCoordinates(20,60);
 
 

CoordinatesFromPoint

   my ($x1,$y1) = $hilbert->CoordinatesFromPoint($point);
 
 

RangeFromCoordinates

   # get range(s) from box
   my @ranges = $hilbert->RangeFromCoordinates($x1,$y1,$x2,$y2);
 
 

AUTHOR

A. J. Trevena, <teejay@droogs.org>

SEE ALSO

perl.

<http://mathworld.wolfram.com/HilbertCurve.html>