This software generates a dense packing of regular tetrahedra @ Arash Nemati Hayati Dec 15, 2017 Email: [email protected]
The scheme used for optimization is a tight bipyramid propagation algorithm.
- Sketch the base triangle for a regular tetrahedron.
- Find possible vertex which make regular tetrahedra
- Initialize packing with one of the generated tetrahedra
- Find faces of the tetrahedra in the pack
- Find possible vertex as done in 2
- Consier each possible tetrahedron
- Check for collision between the new candidates vs the pack tetrahedra
- If checks passed, add tetrahedron to the pack
- Continue searching for new candidates as described in 4-6
Notes for furture improvements: -- Further optmization can be achieved by evaluating the packing density for different face selections different propgation directions and keep those tetrahedra which provides higher density.
-- Another dimension to the shceme complexity can be addded by rotating/translation of the base bipyramid
-- In this version, there is a limitation in the packing configuration. To get optimum packing, not all combinations of N_tet (number of tetrahedra in the pack) and len (length of tetrahedra) are possible. The threshold packing sizes at different length for this version are: N_tet = 25, len = 1 N_tet = 70, len = 0.01
For other packing configuations, sizes should be relaxed by reducing N_tet and/or len.
(This is suggested in the software if the input case cannot be efficiency optimized.)
Notes for execution on a Linux machine:
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Download the package from github at: [email protected]:arashnh11/Tetrahedra_pack.git
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Extract the files and then open a terminal: cd Tetrahedra_pack cd Build make