In this paper, as the first part of the third step of our study on developing data analysis procedures for using 3-dimensional information offered by directional direct Dark Matter detection experiments in the future, we present our double-Monte Carlo scattering-by-scattering simulation of the 3-dimensional elastic WIMP-nucleus scattering process, which can provide 3-D velocity information (the magnitude, the direction, and the incoming/scattering time) of each incident halo WIMP as well as the recoil direction and the recoil energy of the scattered target nucleus in different celestial coordinate systems. For readers reference, (animated) simulation plots with different WIMP masses and several frequently used target nuclei for all functionable underground laboratories can be found and downloaded on our online (interactive) demonstration webpage (http://www.tir.tw/phys/hep/dm/amidas-2d/).
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