Apollonian gaskets

Function to compute and display the apollonian gasket of any 3D triangle or 3D regular polygon

This function requires you to install the four following ones to work (see how to install a function from the Matlab file exchange or simply download them all in the same directory as this one) :

triangle_incircle

regular_3D_polygon_incircle

line_plane_intersection

point_to_line_distance

Then first check the examples tab (.mlx file) here on the right for a complete description.

Once downloaded, typewrite 'help lines_intersection' or 'doc lines_intersection' in Matlab console for support.

[To benefit from the file documentation attached, be sure to download the file, not to just copy and paste it.]

For 2D in (Oxy) plane, just padd your input data with some 0 in Z dimension.

Main parameter recommended values :

0 <= nb_it <= 4 (the number of circles increases very rapidly in function of this parameter)

6 <= nb_samples <= 64 (for a quick display, depending on the power of your graphic card)

From the output data (circle centre coordinates vector and circle radius vector), you can retrieve the circle coordinates by rotating the usual 2D circles in the polygon plane (if this one is in 3D). To do so you may find useful the function :

rotate_3D

I also added apollonian_spherical_pseudo_gaskets function to compute and display pseudo spherical gaskets from one platonic solid face (regular polygon). Why 'pseudo' ? Since except the largest ones all the others are not actual circles for this function / example. See example below. To run this one for solids #4 and 5 (icosahedron and dodecahedron) you will also need to have the function :

platonic_solids

Please don't forget to rate this code if it helped you. Thanks ;-)

Other links I found useful to write this code :

Baderne d'Apollonius

Empilements apolloniens