.. _rzv:

&nbsp_place_holder;

> **_RZV_**

> > This routine is used to ratio zone the region of space spanned by the
input number ni of copies of the input vector vij away from the initial point
v0j 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
vij is reduced by&nbsp_place_holder; rij&nbsp_place_holder; after the ki -th

step in the i-th direction away from the initial point.&nbsp_place_holder; For
this ratio_method the ratio flags fi are not used.&nbsp_place_holder; In this
case an initial step of 1 for the j-th component of the i-th direction would
become, for rij&nbsp_place_holder; =&nbsp_place_holder; 1/2, a step of the
j-th component of the i-th direction of 1/2 at ki =&nbsp_place_holder; 1, 1/4
at&nbsp_place_holder; ki =&nbsp_place_holder; 2, 1/8 at&nbsp_place_holder; ki
=&nbsp_place_holder; 3, 1/16 at ki =&nbsp_place_holder; 4,etc.

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

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

>

> FORMAT:

**rzv/xyz**|**rtz**|**rtp** /   
&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbs
p_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_
place_holder;&nbsp_place_holder;&nbsp_place_holder; [ n1,n2,n3

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbs
p_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_
place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;
/v11,v12,v13/v21,v22,v23/v31,v32,v33

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbs
p_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_
place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_pl
ace_holder; /v01,v02,v03

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbs
p_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_
place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;
/r11,r12,r13/r21,r22,r23/r31,r32,r33

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbs
p_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_
place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;
/**component**|**vector**

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbs
p_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_
place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;
/f1,f2,f3]

default = **xyz**

default = 0:&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_pla
ce_holder;&nbsp_place_holder; ni, vi, v0j

default = 1:&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_pla
ce_holder;&nbsp_place_holder; rij

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/ &nbsp_place_holder;
&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder;&nbsp_place_holder; same as

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;
**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&nbsp_place_holder; ,n2&nbsp_place_holder; ,n3&nbsp_place_holder; /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&nbsp_place_holder; ,n2&nbsp_place_holder; ,n3+1/0,0,0/n1,n2,n3/0,0,1   
**rz/xyz/n**1&nbsp_place_holder; ,n2+1,n3&nbsp_place_holder; /0,0,0/n1,n2,n3/0,1,0   
**rz/xyz**/n1+1,n2&nbsp_place_holder; ,n3&nbsp_place_holder; /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/ &nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder; **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 &nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;** rz/xyz/**n1&nbsp_place_holder; ,n2&nbsp_place_holder; ,n3+1/0,0,0/n1,n2,n3/0,0,1   
&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbs
p_place_holder; **rz/xyz**/n1&nbsp_place_holder; ,n2+1,n3&nbsp_place_holder;
/0,0,0/n1,n2,n3/0,1,0

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbs
p_place_holder; **rz/xyz**/n1+1,n2&nbsp_place_holder; ,n3&nbsp_place_holder;
/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&nbsp_place_holder; ,n2&nbsp_place_holder; ,n3+1/0.25,0.25,0.25/n1+.25,n2+.25,n3+.25/0,0,1   
**rz/xyz/**n1&nbsp_place_holder; ,n2+1,n3&nbsp_place_holder; /0.25,0.25,0.25/n1+.25,n2+.25,n3+.25/0,1,0   
**rz/xyz**/n1+1,n2&nbsp_place_holder; ,n3&nbsp_place_holder; /0.25,0.25,0.25/n1+.25,n2+.25,n3+.25/1,0,0 &nbsp_place_holder;hcp (hexagonal close pack) point distribution&nbsp_place_holder; (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

  
&nbsp_place_holder;&nbsp_place_holder; CAVEATS -

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder; * filter should be used afterwards to remove possibly
duplicate points

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder; * this can create some really bizzare point distributions

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder; * mistyped input after "rzv/[cgeom]" always returns
successful point addition,

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder; but may be very different than desired

&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&nbsp_place_holder;&n
bsp_place_holder; * ratio_flag might better be a scalar or a matix, and its
use might want to be extended to ratio_method=component.