Algorithm 2 Compactness algorithm

fork in [0, Kmax−1]   for j in [0, Jmax−1]     for i in [0, Imax−1]       xboundary = max (x|x is the x coordinate of points on the particles at M [i−1,j,k])       yboundary = max (y|y is the y coordinate of points on the particles at M [i,jn,k],            where jn in [j−nneighbor, j+nneighbor])       zboundary = max (z|z is the z coordinate of points on the particles at M [i,jn,kn],            where jn in [j−nneighbor, j+nneighbor] and kn in [k−nneighbor, k+nneighbor]    Assume:      Plane Px parallel to the yz-plane intersects the x-axis at xboundary.      Plane Py parallel to the xz-plane intersects the y-axis at yboundary.      Plane Pz parallel to the xy-plane intersects the z-axis at zboundary.        dx = distance between M [i,j,k] and Px        dy = distance between M [i,j,k] and Py        dz = distance between M [i,j,k] and Pz         while max (dx, dy, dz) ⩾ $\rho$           if dx = max (dx, dy, dz)             subtract dx/3 from the x coordinate of M [i,j,k]           else if dy = max (dx, dy, dz)             subtract dy/3 from the y coordinate of M [i,j,k]           else dz = max (dx, dy, dz)             subtract dz/3 from the z coordinate of M [i,j,k]           Recalculate dx,dy,dz           if loop has executed more than 1000 times:           Report exception and quit