Mitchell's Best Candidate Algorithm
Another very simple, easy to implement, algorithm to generate a Poisson-disk/blue noise point distribution is the following one [ 1 ]: 


Decide a radius r, and therefore the expected number N of samples per area (use the formula for maximum packing density of k disks distributed on a toroidal domain see [ 2 ]) 
Generate 10~20 x N samples in your area using a plain unbiased montecarlo sampling
Until all samples respect poisson disk condition:


randomly choose a sample p 
remove all the samples at distance lower than r from p



Eventually step 3 can be furtherly iterated a small number of times choosing the sample with minimal number of surviving samples within distance r.

You can find an implementation of this algorithm in MeshLab.

References

[ 1 ] Efficient and Flexible Sampling with Blue Noise Properties of Triangular Meshes
Massimiliano Corsini, Paolo Cignoni, Roberto Scopigno
IEEE Transaction on Visualization and Computer Graphics, Volume 18, Number 6, page 914--924 - 2012

[ 2 ] A comparison of methods for generating Poisson disk distributions
 Ares Lagae, Philip Dutré,
Computer Graphics Forum vol:27 issue:1 , 2008