In the present paper, we investigate the optimal quadrature to retrieve the full-direction scattering behavior of a realistic arbitrarily-shaped ice particle, from a limited number of pre-calculated incident directions. Our motivation is to enable accurate recovery of single scattering properties of realistic hydrometeors at any incident direction, or equivalently particle orientation, from scattering databases that have been built with our 3D full-wave model MIDAS, at a reasonable computational cost, both in terms of calculation time and storage. Finding the optimal trade between accuracy and compute-storage cost will confirm the comprehensive superiority of MIDAS over existing DDA-bases codes, and make it a compelling method for solving the EM scattering problem involving complexly-shaped realistic hydrometeors.