Circle Packing

Reproducing the simplest version of the circle packing algorithm proposed in this article by Collins and Stephenson.</br></br> The /src folder contains the implementation of the algorithm written in C++ (the correspondent executables are located in /bin).</br></br> In order to have a circle packing, we need to start with a complex K. In cpack_test.cc the structure of such complex is hard-coded in the program.</br> With the help of cpack.py we can visualize an animation showing the creation of the circle packing as the algorithm progresses.<br> The program should be run like this:

./bin/cpack_test | python ./src/cpack.py

<p align="center"> <img src="https://github.com/amanitta/circlePacking/blob/master/cpack_01.gif"/> </p> It is possible to choose between fixed (default) and random boundary conditions using the options -f and -r in the executable.</br></br>

The other python script (pointsForComplex.py) provides instead with a way to create a complex with a certain number of boundary and interior points. The geometrical form of the complex is not important at all: the only thing which is relevant is knowing the neighbouring nodes to which each interior vertex is connected. The script thus places the boundary points equally spaced on a circle, while the interior points are chosen at random inside the circle itself. A Delaunay triangulation is exploited to link the vertices inside the circle. The output of the script consists of the list of neighbours for each internal vertex, sorted in clockwise order.</br> The program should be run like this

python pointsForComplex.py BOUNDARY INTERIOR [SEED]

<p align="center"> <img src="https://github.com/amanitta/circlePacking/blob/master/complex.jpg"> </p>

The output of the python script just mentioned can then be fed to cpack_final, which reads the structure of the complex created and runs the circle packing algorithm.</br> cpack_debug.py is extremely useful for debugging the program and understanding how the animation is created. It can also be used to show the final result of the run, as shown below.

 python ./src/pointsForComplex.py 9 8 30 | ./bin/cpack_final | python ./src/cpack_debug.py 

<p align="center"> <img src="https://github.com/amanitta/circlePacking/blob/master/cpack_debug.jpg"> </p>

Just as before, we can then produce an animation showing the action of the packing algorithm, now with an input (the complex) that has not to be hard-coded anywhere.

python ./src/pointsForComplex.py 20 25 987 | ./bin/cpack_final | python ./src/cpack.py 

Complex | Circle Packing :-------------------------:|:-------------------------: <img src="https://github.com/amanitta/circlePacking/blob/master/complex_final.jpg"/> | <img src="https://github.com/amanitta/circlePacking/blob/master/cpack_final.gif"/>