Algorithm with hybrid method based for sphere packing in two-dimensional region

A new hybrid method was proposed for sphere packing in two-dimensional region, which combined the traditional dynamic method with the traditional constructive method. The algorithm calculated the particles' moving directions with two different methods according to the two different touching objectives during the process of falling. When the touching objective was particle, the moving direction was calculated with the purely geometric-based method in which the new direction was downward along the tangential direction of the two-contact particles' touching point. The moving direction of the particle approximated the physical law of the dynamic method. When the touching objective was the boundary of the container, the new direction was calculated with the elastic collision theory, which consisted with the physical law of the dynamic method. The touch detections between particles were based on the advancing-front elements of the constructive method. The time to create the granular particles set was linear with the particle number, and this process was completed in a comparatively short time with high density particles set.