Hilbert(3) User Contributed Perl Documentation Hilbert(3)NAMEMath::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>
perl v5.14.0 2004-02-06 Hilbert(3)
