Abstract
Covering spheroids (ellipsoids of revolution) by different spheres is studied. The research is motivated by packing non-spherical particles arising in natural sciences, e.g., in powder technologies. The concept of an ε -cover is introduced as an outer multi-spherical approximation of the spheroid with the proximity ε . A fast heuristic algorithm is proposed to construct an optimized ε -cover giving a reasonable balance between the value of the proximity parameter ε and the number of spheres used. Computational results are provided to demonstrate the efficiency of the approach.
Highlights
Covering a certain region by simple shapes has various applications
Our interest in covering problems is motivated by packing particles arising in science and engineering applications
Packing problems are widely used in modeling liquid and glass structures [1,2], representing granular materials [3], packing beds, and cermet [4], as well as in many other applications
Summary
Covering a certain region by simple shapes has various applications. Our interest in covering problems is motivated by packing particles arising in science and engineering applications. The second approach is based on tessellating the container/particles shapes with a grid and approximating them by corresponding collections of grid nodes (see, e.g., [15,24] and the references therein). This way, detecting the overlap is reduced to verify if two shapes share the same node. Among the different shapes used to represent the microstructure of non-spherical particles, the spheroid (ellipsoid of revolution) is one of the most frequently used (see, e.g., [5,6,7,8,10]).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
