Methods and Algorithms

To generate a close packing of spheres with disperse sizes a well-known "drop and roll" algorithm is used.

The described algorithm is a square-law of the general number of packed spheres. To convert it to a nearly-linear algorithm, the special technique of grid hashing was used.

This technique is outlined in the following. Let us consider a cubic grid with cell size comparable with sizes of spheres. For each cell, let us build the list of packed spheres which centers lie in this cell. Then analysis of spheres disposed in several grid cells around the trajectory allows to find all intersections of the trajectory segment and the packed spheres. So, when parameters of the grid are customized well, the algorithm becomes almost linear with a multiplier depending from parameters of the whole packing of spheres (such as dispersion of spheres' radii, etc.)

S3D SpheroPack™ includes original algorithms of building skeletal and polyhedron structures over the given set of spheres.

S3D SpheroPack™ skeletal polyhedral model relies on the 3D Voronoi diagram built on the given set of spheres, skeletal triangulation model relies on the 3D Delaunay triangulation corresponding to this Voronoi diagram. The duality of the triangulation and polyhedral skeletal models is convenient for describing grains by means of radical polyhedra and pores using tetrahedrons of the triangulation.

Parameters, measured with S3D SpheroPack™

Integral parameters of the particles packing Average relative density of the packing Average relative porosity of the packing Average particle size Coordination number of the packing Differential parameters of the particles packing Relative density distribution within the packing Relative porosity distribution within the packing Cumulative distribution of relative density within the packing Cumulative distribution of relative porosity within the packing Distribution of particles by size Distribution of particles by areas Distribution of particles by volumes Integral parameters of polyhedral structures Average size of a polyhedron Average coordination number of a polyhedron Summary area of polyhedra surfaces Summary length of polyhedra ribs Summary number of polyhedra vertices Length of the pore channels Differential parameters of polyhedral structures Distribution of polyhedra by size Distribution of polyhedra by area Distribution of polyhedra by volume Distribution of polyhedra by the number of facets Distribution by particle volume to the volume of the circumscribed polyhedron ratio Distribution of polyhedra by size of the polyhedra section by the secant plane drawn at the given depth The specified characteristics can be determined both for selected particle classes and for all particles within the packing