  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/).
