Abstract
A new constructive ellipse packing algorithm is presented. It allows to respect the imposed area, shape and spatial orientation distribution (i.e. the inertia tensor) and achieve high packing densities. The packing density decreases with increasing particles aspect ratio what is in agreement with results reported in the literature. The generated packings with complex imposed area, shape and spatial orientation distributions with densities in the range of 0.74 and 0.8 are presented. The efficiency of the algorithm is demonstrated by comparison with the Optimized Dropping and Rolling method for disk packing. Moreover, the proposed packing strategy enables to generate very easily non-equiaxed polygonal structures by using Laguerre-Voronoi tessellation of the generated disk-based ellipse packing.
Highlights
A new constructive ellipse packing algorithm is presented
In the context of space-filling problem, the sphere packing can be obtained by the dynamic methods, in which particles usually change their position and/or their size during the filling process to improve the local and global densities, or by the constructive methods, generating particles sequentially and calculating their positions thanks to geometrical rules
The dynamic methods were widely used for the ellipsoid packing and high densities were reported in published works [15,16,17,18]
Summary
A new constructive ellipse packing algorithm is presented. It allows to respect the imposed area, shape and spatial orientation distribution (i.e. the inertia tensor) and achieve high packing densities. To reach high packing densities, each new particle is placed at the lowest possible position by testing pairs of ellipses from the “Height list”. Densities and computation time provided by the proposed algorithm are compared with the Optimized Dropping and Rolling Method (ODRM) [9] in particular case of disk packing.
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