CREATEPTS/VECTOR

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.

FORMAT:

reatepts/vector**/[ xyzrtzrtp /

[ n1,n2,n3

/v11,v12,v13/v21,v22,v23/v31,v32,v33

/v01,v02,v03

/r11,r12,r13/r21,r22,r23/r31,r32,r33 ]

default = 0:      n~i~, v~i~, v~0j~

default = 1:      r~ij~

EXAMPLES:

spiral of points

reatepts/vector/rtz**/n1,0,0/.1,10.,1/ , , / , , / , , /1.1,1,.9

sc (simple cubic) point distribution

reatepts/vector/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

reatepts/vector/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

reatepts/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

reatepts/xyz**/n1,n2,n3/1,0,0/.5,0.866,0/0,0,1

diamond point distribution (two command sequence)

reatepts/xyz**/n1,n2,n3/.5,.5,0/0,.5,.5/.5,0,.5

reatepts/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)

reatepts/xyz**/n1,n2,n3/1,0,0/.5,0.866,0/0,0,1/

reatepts/xyz**/n1,n2,n3/1,0,0/.5,0.866,0/0,0,1/.5,0.2,.5

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