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https://github.com/hosuaby/jq-voronoi

Implementation of Voronoi with jq
https://github.com/hosuaby/jq-voronoi

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Implementation of Voronoi with jq

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README 

        
# jq-voronoi

Implementation of Fortune's algorithm to calculate Voronoi diagram on

[jq](https://stedolan.github.io/jq/)





    




## Try it

Clone this repository. To run the following `jq` must be installed and availbale on PATH.



```bash

$ ./gensites | ./voronoi.sh | ./2svg --argjson box '[600, 600]' > /tmp/voronoi.svg

```



Check generated file */tmp/voronoi.svg*.



## Usage



Algorithm takes as input list of sites (points of two-dimentional plane) and returns as output a

list of voronoi cells (polygons delimiting zone of influence of sites). Script `voronoi/voronoi.jq`

(or wrapper `voronoi.sh`) takes as input array of points in cartesian coordinates.  

Consider the following example:





    




as JSON:



```javascript

[[0, 0], [100, 100], [20, 15], [60, 10], [90, 20], [45, 40], [25, 65], [65, 80]]

```



First two points are coordinates of respectively top-left & bottom-right corners of

bounding box. The rest are coordinates of sites that must imperatively be within bounding box.  

Script outputs an array of cells. Cell is an JSON array where the first element is a site, and the

rest are counter-clockwise ordered points forming polygon of voronoi cell of this site.



```javascript

[

  [

    /* Coordinates of site */

    [20, 15],

    

    /* Counter-clockwise ordered points forming polygon of voronoi cell of the site */

    [40.833333333333336, 19.166666666666668],

    [38.43749999999999, 0],

    [0, 0],

    [0, 42.25000000000001],

    [19.72222222222222, 40.27777777777778]

  ],

  ...   // other sites  

]

``` 



## Visualization:



### Render to SVG



Tool `2svg` can render calculated voronoi diagram into SVG file.



Usage:

```bash

$ echo '[[0, 0], [100, 100], ... ]' | ./voronoi.sh | ./2svg --argjson box '[100, 100]' > output.svg

```



`2svg` takes a single JSON argument `box`, defining bounding box. `box` can have 2 or 4 elements.



**Two elements** *(Example: [600, 600])*  

Box starts at [0, 0]



1. box width *= 600*

2. box height *= 600*



**Four elements** *(Example: [50, 50, 150, 150])*



1. top-left corner x *= 50*

2. top-left corner y *= 50*

3. bottom-right corner x *= 150*

4. bottom-right corner y *= 150*



Examples:



```bash

$ ./2svg --argjson box '[600, 600]'             # bounding box [0, 0] -> [600, 600]

$ ./2svg --argjson box '[50, 50, 150, 150]'     # bounding box [50, 50] -> [150, 150]

```



Voronoi diagram for

`[[0, 0], [100, 100], [20, 15], [60, 10], [90, 20], [45, 40], [25, 65], [65, 80]]`:





    



    

### Visualization sketch



Voronoi diagram can also be displayed by sketch.  

To run visualization sketch [Processing 3+](https://processing.org/) must be installed and

`processing-java` executable must be on the PATH.  

Redirect output of `voronoi.sh` (`voronoi/voronoi.jq`) to `display`. Script accepts two or four

parameters, defining bounding box.  

If user supplies two arguments, they are respectively `width` & `height` of the bounding box

starting at *[0, 0]*.  

If user provides four arguments, the two first arguments are x & y coordinates of top-left corner,

and last two are x & y coordinates of bottom-right corner of bounding box.



Examples:



```bash

$ display 600 600             # bounding box [0, 0] -> [600, 600]

$ display 50 50 150 150       # bounding box [50, 50] -> [150, 150]

```



To test visualisation:



```bash

$ ./gensites | ./voronoi.sh | ./display 600 600

```





    




## Voronoi on sphere



Computation of Voronoi diagram on spherical surface is based on paper ["Voronoi diagrams on the sphere" by Hyeon-Suk Na, Chung-Nim Lee & Otfried Cheong](https://www.sciencedirect.com/science/article/pii/S0925772102000779?via%3Dihub). Spherical Voronoi diagram is obtained in time O(_n_ log _n_) from two planar Voronoi diagrams and a little bit of glueing.



In order to compute Voronoi on sphere we must supply sites expressed in spherical coordinates on [unit sphere](https://en.wikipedia.org/wiki/Unit_sphere) _[φ, θ]_, where  


    0 ≤ φ ≤ 2π (azimuth)

    0 ≤ θ ≤ π  (zenith)




Coordinate _[0, 0]_ defines a north pole.



Example:



```bash

$ echo '[[1, 1.5], [1, 1], [1, 2.2]]' | ./voronoi.sh --sphere

```



Visualisation is done by Processing sketch:



```bash

$ ./gensites-sphere | ./voronoi.sh -s | ./display-sphere

```