NEW METHOD TO FIND COLLISIONS BETWEEN MOVING OBJECTS, APPLICATION: ROCKFALL SIMULATION

Every year many deaths and injuries and economical losses caused by rock and boulder falls cause harm to people who live in and pass through mountainous regions and routes. Rockfalls can be triggered even by small earthquakes. Realistic simulation of rock falls, along with defining their most vulnerable fall trajectories, can result in providing mitigation measures in the right places with the least costs. One of the keys to the successful simulation of a rockfall is considering real shape for falling objects which do not have simple geometrical outlines. When dealing with more realistic rock shapes rather than circular ones in the two dimensional space, the calculations become enormously long and expensive; hence, the simulation becomes impractical for most civil engineering projects. This leads to rough study of rockfall hazard of prone areas, which leads to overdesigning the measuring structures, and/or passing over the probable hazards; both of which end in economical losses and fatalities. The bottleneck in the rockfall simulation calculations is the phase in which collision between moving objects is checked. This paper is formulated to address the problem by presenting a novel method to complete this phase faster by means of a coordinate mapping to reduce the size of the simulation domain, using posets to form an adjacency matrix between objects, and use of an automatic-elimination pr ocess to avoid unnecessary collision calculations. This paper concentrates on solving the problem in a rectangular, two-dimensional region with randomly distributed objects of pentagonal shape. The results are then compared with the computationallyintensive naive approach, which sweeps the whole domain for checking collision between the moving objects, and its performance is shown.