# RZV

This command is deprecrated, see CREATEPTS.

This routine is used to ratio zone the region of space spanned by the input number n(i) of copies of the input vector v(ij) away from the initial point v(0j) using the desired coordinate system. The j-th component of the i-th vector V(ij) is reduced by r(ij) at each step in the i-th direction away from the initial point. No attempt is made to insure that the 3 vectors are independent.

## SYNTAX

```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 or vector &
/ [f1,f2,f3]
```

For `ratio_method` = component (default), the j-th component of the i-th vector vij is reduced by  rij after the ki-th step in the i-th direction away from the initial point.  For this ratio_method the ratio flags `f1,f2,f3` are not used.  In this case an initial step of 1 for the j-th component of the i-th direction would become, for rij  =  1/2, a step of the j-th component of the i-th direction of 1/2 at ki =  1, 1/4 at  ki =  2, 1/8 at  ki =  3, 1/16 at ki =  4,etc.

For `ratio_method` = vector and `fj` =1 (the default), the j-th vecor is reduced by rij  after the ki -th step in the i-th direction.  In this case an initial step of 1 in the j-th direction would become, for  rij  =  1/2, a setp in the j-th direction of 1/2 at ki =  1, 1/4 at  ki =  2, 1/8 at  ki =  3, 1/16 at ki =  4,etc.

For `ratio_method` = vector and `fj` =0, the j-th vecor is reduced by [1 - (1-rij  ) *2/(ki +  1)] after the ki -th step in the i-th direction.  In this case an initial step of 1 in the j-th direction would become, for  rij  =  1/2, a step in the j-th direction of 1/2 at ki =  1, 1/3 at  ki =  2, 1/4 at  ki =  3, 1/5 at ki =  4,etc.

default = xyz

default = 0:      ni, vi, v0j

default = 1:      rij

default = component

## EXAMPLES

``````rzv/rtz/n1,0,0/.1,10.,1/ , , / , , / , , /1.1,1,.9
``````

spiral of points

``````rzv/xyz/n1,n2,n3/1,0,0/0,1,0/0,0,1

rz/xyz/n1+1,n2+1,n3+1/0,0,0/n1,n2,n3/1,1,1
``````

simple cubic point distribution, both lines have the same result

``````rzv/xyz/n1,n2,n3/.5,.5,.5/.5,.5,-.5/.5,-.5,-.5/

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
``````

body centered cubic point distribution, compare with the rz two command sequence with different bounding box.

``````rzv/xyz/n1,n2,n3/.5,.5,0/0,.5,.5/.5,0,.5/

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
``````

face centered cubic point distribution compare with the four rz command sequence (different bounding box).

``````rzv/xyz/n1,n2,n3/1,0,0/.5,0.866,0/0,0,1
``````

hexagonal lattice of points in x,y plane, repeated in z direction

``````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

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
``````

diamond point distribution (two command sequence) compare the eight rz command sequence (different bounding box).

``````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/.5,0.2,.5
``````

hexagonal close pack point distribution?| (two command sequence)

``````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
``````

nice 2-d distribution of points in a circle of radius 1

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.