RZS

RZV

This routine is used to ratio zone the region of space spanned by the input number n_iof copies of the input vector v_ij away from the initial point v_0j using the desired coordinate system. No attempt is made to insure that the 3 vectors are independent.
For ratio_method = component (default), the j-th component of the i-th vector v_ij is reduced by r_ijafter the k_i -th
step in the i-th direction away from the initial point. For this ratio_method the ratio flags f_iare not used. In this case an initial step of 1 for the j-th component of the i-th direction would become, for r_ij= 1/2, a step of the j-th component of the i-th direction of 1/2 at k_i= 1, 1/4 at k_i= 2, 1/8 at k_i= 3, 1/16 at k_i= 4,etc.
For ratio_method = vector and fj =1 (the default), the j-th vecor is reduced by r_ijafter the k_i -th step in the i-th direction. In this case an initial step of 1 in the j-th direction would become, for r_ij= 1/2, a setp in the j-th direction of 1/2 at k_i= 1, 1/4 at k_i= 2, 1/8 at k_i= 3, 1/16 at k_i= 4,etc.
For ratio_method = vector and fj =0, the j-th vecor is reduced by [1 - (1-r_ij)*2/(k_i + 1)] after the k_i -th step in the i-th direction. In this case an initial step of 1 in the j-th direction would become, for r_ij= 1/2, a step in the j-th direction of 1/2 at k_i= 1, 1/3 at k_i= 2, 1/4 at k_i= 3, 1/5 at k_i= 4,etc.
FORMAT:

rzv/xyz|rtz|rtp /
                [ n1,n2,n3
                 /v11,v12,v13/v21,v22,v23/v31,v32,v33
                  /v01,v02,v03
                 /r11,r12,r13/r21,r22,r23/r31,r32,r33
                 /component|vector
                 /f1,f2,f3]
default = xyz
default = 0:      n_i, v_i, v_0j
default = 1:      r_ij
default = component EXAMPLES: spiral of points rzv/rtz/n1,0,0/.1,10.,1/ , , / , , / , , /1.1,1,.9/ sc (simple cubic) point distribution rzv/xyz/n1,n2,n3/1,0,0/0,1,0/0,0,1/         same as
        rz/xyz/n1+1,n2+1,n3+1/0,0,0/n1,n2,n3/1,1,1
bcc (body centered cubic) point distribution rzv/xyz/n1,n2,n3/.5,.5,.5/.5,.5,-.5/.5,-.5,-.5/
compare the two command sequence (different bounding box) rz/xyz/n1+1,n2+1,n3+1/0,0,0/n1,n2,n3/1,1,1
rz/xyz/n1 ,n2 ,n3 /0,0,0/n1,n2,n3/0,0,0 fcc (face centered cubic) point distribution rzv/xyz/n1,n2,n3/.5,.5,0/0,.5,.5/.5,0,.5/
compare the four command sequence (different bounding box) rz/xyz/n1+1,n2+1,n3+1/0,0,0/n1,n2,n3/1,1,1
rz/xyz/n1 ,n2 ,n3+1/0,0,0/n1,n2,n3/0,0,1
rz/xyz/n1 ,n2+1,n3 /0,0,0/n1,n2,n3/0,1,0
rz/xyz/n1+1,n2 ,n3 /0,0,0/n1,n2,n3/1,0,0 hexagonal lattice of points in x,y plane, repeated in z direction rzv/xyz/n1,n2,n3/1,0,0/.5,0.866,0/0,0,1/ diamond point distribution (two command sequence) rzv/xyz/n1,n2,n3/.5,.5,0/0,.5,.5/.5,0,.5/           rzv/xyz/n1,n2,n3/.5,.5,0/0,.5,.5/.5,0,.5/.25,.25,.25 compare the eight command sequence (different bounding box) rz/xyz/n1+1,n2+1,n3+1/0,0,0/n1,n2,n3/1,1,1           rz/xyz/n1 ,n2 ,n3+1/0,0,0/n1,n2,n3/0,0,1
          rz/xyz/n1 ,n2+1,n3 /0,0,0/n1,n2,n3/0,1,0
          rz/xyz/n1+1,n2 ,n3 /0,0,0/n1,n2,n3/1,0,0 rz/xyz/n1+1,n2+1,n3+1/0.25,0.25,0.25/n1+.25,n2+.25,n3+.25/1,1,1
rz/xyz/n1 ,n2 ,n3+1/0.25,0.25,0.25/n1+.25,n2+.25,n3+.25/0,0,1
rz/xyz/n1 ,n2+1,n3 /0.25,0.25,0.25/n1+.25,n2+.25,n3+.25/0,1,0
rz/xyz/n1+1,n2 ,n3 /0.25,0.25,0.25/n1+.25,n2+.25,n3+.25/1,0,0 hcp (hexagonal close pack) point distribution (two command sequence) rzv/xyz/n1,n2,n3/1,0,0/.5,0.866,0/0,0,1/
rzv/xyz/n1,n2,n3/1,0,0/.5,0.866,0/0,0,1/.5,0.289,.5/ nice 2-d distribution of points in a circle of radius 1 rzv/xyz/10,60,0/0.1,0,0/0,60,0/0,0,1/0,0,0/1,0.5,1/1,1,1/1,1,1/vector/0,0,0

   CAVEATS -
      * filter should be used afterwards to remove possibly duplicate points
      * this can create some really bizzare point distributions
      * mistyped input after "rzv/[cgeom]" always returns successful point addition,
      but may be very different than desired
      * ratio_flag might better be a scalar or a matix, and its use might want to be extended to ratio_method=component.