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After the spheres have been parked into the system, 1000 points throughout the entire system are chosen along a regular cubic grid. The distance from an individual point on the grid to the nearest sphere surface is calculated; if the point lies within that sphere, the shortest distance to the surface is made negative. These 1000 distances are then sorted, from smallest to largest. The relative rank of these distances, as a function of this distance, is an estimate of the cumulative distribution function for all the paste-void spacings in the entire system.
Since the negative distances in this CDF correspond to points lying within an air void, the 50 th and 95 th percentiles of the paste-void proximity spacings for the paste fraction alone are calculated from the positive values in the list of distances.