poissonDiskSampling 1.0.0
Poisson Disk Sampling Algorithm with Variable Sampling Radius
License: MIT
Requires Python: >=3.6

Bridson Poisson DisK Sampling with Variable Radius
==================================================
This package contains a Python 3 implementation of the Poisson Disk Sampling algorithm of 
[Bridson (2007)](https://dl.acm.org/doi/10.1145/1278780.1278807). 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. 

![](https://gitlab.com/abittner/poissonDiskSampling/-/raw/master/exampleVisualisations/uniformDensity.png)
![](https://gitlab.com/abittner/poissonDiskSampling/-/raw/master/exampleVisualisations/sphericalDensity.png)

![](https://gitlab.com/abittner/poissonDiskSampling/-/raw/master/exampleVisualisations/quartersOfConstantDensity.png)
![](https://gitlab.com/abittner/poissonDiskSampling/-/raw/master/exampleVisualisations/chessboardPattern.png)


License
--------------------
This package is released under the MIT license.