NAME

Random::PoissonDisc - distribute points aesthetically in R^n

SYNOPSIS

    my $points = Random::PoissonDisc->points(
        dimensions => [100,100],
        r => $r,
    );
    print join( ",", @$_),"\n"
        for @$points;

This module allows relatively fast (linear in the number of points generated) generation of random points in n-dimensional space with a distance of at least r between each other. This distribution results in aesthetic so called "blue noise".

The algorithm was adapted from a sketch by Robert Bridson in https://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph07-poissondisk.pdf.

DATA REPRESENTATION

All vectors (or points) are represented as anonymous arrays of numbers. All have the same dimension as the cardinality of the dimensions array passed in the ->points method.

USER INTERFACE

Random::PoissonDisc->points( %options )

Returns a reference to an array of points.

Acceptable options are:

• r - minimum distance between points.

  Default is 10 units.

• dimensions - number of dimensions and respective value range as an arrayref.

  Default is

      [ 100, 100 ]

  meaning all points will be in R^2 , with each coordinate in the range [0, 100).

• candidates - Number of candidates to inspect before deciding that no new neighbours can be placed around a point.

  Default is 30.

  This number may or may not need to be tweaked if you go further up in dimensionality beyond 3 dimensions. The more candidates you inspect the longer the algorithm will run for generating a number of points.

  In the algorithm description, this constant is named k.

• avoid_edge - The distance from the edge of the plot.

  Default is 0

  If greater than zero, this will not plot points within that distance from the edge.

• center - Start adding points at the center of the plot.

  Default is 0

  If this is set to the default, the initial point will be added at a random position in the plot.

INTERNAL SUBROUTINES

These subroutines are used for the algorithm. If you want to port this module to PDL or any other vector library, you will likely have to rewrite these.

rnd( $low, $high )

    print rnd( 0, 1 );

Returns a uniform distributed random number in [ $low, $high ).

grid_coords( $grid_size, $point )

Returns the string representing the coordinates of the grid cell in which $point falls.

norm( @vector )

    print norm( 1,1 ); # 1.4142

Returns the Euclidean length of the vector, passed in as array.

vdist( $l, $r )

    print vdist( [1,0], [0,1] ); # 1.4142

Returns the Euclidean distance between two points (or vectors)

neighbour_points( $size, $point, $grid )

    my @neighbours = neighbour_points( $size, $p, \%grid )

Returns the points from the grid that have a distance between 0 and 2r around $point. These points are the candidates to check when trying to insert a new random point into the space.

random_unit_vector( $dimensions )

    print join ",", @{ random_unit_vector( 2 ) };

Returns a vector of unit length pointing in a random uniform distributed n-dimensional direction angle and returns a unit vector pointing in that direction

The algorithm used is outlined in Knuth, _The Art of Computer Programming_, vol. 2, 3rd. ed., section 3.4.1.E.6. but has not been verified formally or mathematically by the module author.

TODO

The module does not use PDL or any other vector library.

REPOSITORY

The public repository of this module is https://github.com/Corion/random-poissondisc.

SUPPORT

The public support forum of this module is https://perlmonks.org/.

BUG TRACKER

Please report bugs in this module via the RT CPAN bug queue at https://rt.cpan.org/Public/Dist/Display.html?Name=Random-PoissonDisc or via mail to random-poissondisc@rt.cpan.org.

AUTHOR

Max Maischein corion@cpan.org

COPYRIGHT (c)

Copyright 2011-2023 by Max Maischein corion@cpan.org.

LICENSE

This module is released under the same terms as Perl itself.

cpanm Random::PoissonDisc

perl -MCPAN -e shell
install Random::PoissonDisc