RZRAN

This routine is used to add random points with a given target spacing to the region of space defined by the input minimum and maximum coordinate values using the specified geometry (xyz, rtz, or rtp), and the given local origin (specified in xyz coordinates). Within the bounding geometry, the points are distributed uniformly in space, with the average separation targeted at the input value of the spacing.  Near the boundaries of the geometry, the uniform distribution is modified slightly in order to create a well defined outer boundary.  Points are added separately on the corners, edges, and surfaces of the bounding geometry, uniformly randomly distributed with the same target spacing on each of these boundary objects. Points in the interior are offset by the sepcified edge protection distance from the exterior.  This separation helps LaGriT's connect algorithm avoid creating artificial "pits" in the interface surfaces.

FORMAT

rzran / cgeom / spacing / rmin1,rmin2,rmin3 / rmax1,rmax2,rmax3  & [/ xoff,yoff,zoff / edgedist / ranseed1,ranseed2 ]

while only rzran is required (will result in a single point at the origin), it is recommended that you use as the minimal command: rzran / cgeom / spacing /  rmin1,rmin2,rmin3 / rmax1,rmax2,rmax3

cgeom
   geometry label (same convention as for rz)
   allowed values: xyz|rtp|rtz
   default: xyz if not present, error return if not allowed

spacing
   target separation between the random points
   allowed values: spacing>0
   default: spacing=1

rmin1,rmin2,rmin3 / rmax1,rmax2,rmax3
   minimum and maximum coordinate values
   allowed values:
      all geometries: rmax.ge.rmin
      rtz: rmin1.ge.0, rmax2-rmin2.le.360
      rtp: rmin1.ge.0, rmin2.ge.0, rmax2.le.180, rmax3-rmin3.le.360
    defaults: rmin=0, rmax=rmin

xoff,yoff,zoff (specified in xyz coordinate system)
   local origin shift
   defaults: 0

edgedist
   edge protection distance aka interior-exterior offset
   default: spacing/2
   recommended value: spacing/2

ranseed1,ranseed2
   seeds for the random number generator
   defaults: -1 (do not re-seed, recommended)
      if either seed is .le. zero, the seeds are ignored
   recommended values if reseed:
      large-ish integers, ranseed1>ranseed2>0, ranseed2 odd.
   No initial seeds are needed, and repeating the command
   with the identical parameters and seeds should result
   in the identical point distribution. Repeating the
   command with no seeds specified should result in
   different point locations with the same distribution.
 

EXAMPLES

rzran / xyz / .1 / 0 0 0 / 1 1 1 /
   random points with target spacing 0.1 in a 1x1x1 box

rzran/ rtz / .1 /  0,0,0 / 1,180,360 / 2,3,4 / 0.2
   random points with target spacing 0.1 in a cylinder
   of radius 1 centered at xyz=(2,3,4) and with an
   edge protection distance of 0.2

rzran/ rtp / .5 /  5,0,0 / 5,180,360 /  , ,  /  / 98765 4321/
   random points with target spacing 0.5 on the surface
   of a sphere of radius 5 centered at the origin
   with new random seeds

CAVEATS

Filter should be used afterwards to remove possibly duplicate points. The algorithm to insure the points are uniformly distributed in space is not clever about handling values outside the allowed range for rtz and rtp geometries and so it simply truncates them to the allowed range if possible or aborts. Most importantly, angles are in degrees and theta for the rtp geometry runs from 0 to 180 degrees, with 0 degrees being the +z axis. It does know about the angular periodicity and there should be only the "corner" point artifacts of, eg, the +x axis being the origin of phi (rtp) or theta (rtz) if a full 360 degrees for these two variables in their respective coordinate systems is used.