Bridson Poisson DisK Sampling with Variable Radius

This package contains a Python 3 implementation of the Poisson Disk Sampling algorithm of Bridson (2007). It has been adapted to be able to generate the sampling with a spatially variable sampling radius, i.e. the density of the sampling points is determined according to a given density distribution.

Usage

The usage of the package is illustrated in the included example.py file and the generated Poisson Disk Samplings for a set of input density distributions are displayed below and in the subdirectory exampleVisualisations.

The only required input of the routine is a 2D array specifying the sampling radii at each spatial position of the sampling grid. For instance, a uniform density distribution with a sampling radius of 5 and a sampling box of size 40x40 can be generated with

rad = np.zeros((40,40)) + 5

Note that the routine assumes the minimum chosen sampling radius to be 1.

Subsequently, the Poisson Disk Sampling can be generated via

from poissonDiskSampling import bridsonVariableRadius
nParticle, particleCoordinates = bridsonVariableRadius.poissonDiskSampling(rad, k=30, radiusType='default')

with the output nParticle containing the number of generated particles of the sampling and the 2D array particleCoordinates specifying the coordinates of these sampling particles.

The optional argument k states the number of attempts to create a new particle in the annulus between r and 2r around an existing particle. Following Bridson (2007), the default number is set to k=30 but higher values might be necessary some situations.

The other optional argument radiusType can be used to exploit a variation of the original Bridson (2007) algorithm. The default value of the parameter is default in which case it implements the original approach: potential new particles are created in an annulus between radius r and 2r around an already existing particle. If radiusType ='normDist' is set instead, the radii of new particles are drawn from a normal distribution centered around 1.5r with a standard deviation of 0.2r.

Limitations

Input density distributions with sharp steps in density or continuous density gradients along the x or y-axis of the grid sometimes result in an incomplete sampling. Often these issues can be avoided by increasing the number of iterations k used to spawn new particles in an annulus around an existing particle from the default value of k=30 to, for instance, k=100.

Examples

The figures below illustrate the generated Poisson Disk Samplings for a number of exemplary input density distributions.

License

This package is released under the MIT license.