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 specified edge protection distance from the exterior.
This separation helps LaGriT’s connect algorithm avoid creating artificial “pits” in the interface surfaces.
While only createpts/random is required (will result in a single point at the origin), it is recommended that you use as the minimal command, first line below.
createpts/random /geom/spacing/ rmin1,rmin2,rmin3 / rmax1,rmax2,rmax3
createpts/random /geom/spacing/rmin1,rmin2,rmin3 /rmax1,rmax2,rmax3 / &
[ xoff,yoff,zoff / edgedist / ranseed1,ranseed2 ]
geom:xyz specifies Cartesian coordinates (default).
rtz specifies cylindrical coordinates.
rtp specifies spherical coordinates.
spacing is the target separation between the random points, values must be > 0 (default is 1).
rmin1,rmin2,rmin3 / rmax1,rmax2,rmax3 are the minimum and maximum coordinate values (defaults: rmin=0, rmax=rmin).
For rtz rmax2-rmin2 must be <= 360. For rtp the values should be rmax2 <= 180, and rmax3-rmin3 <= 360.
All min values must be >= 0.
xoff,yoff,zoff is the local origin shift specified in xyz coordinate system (default is 0).
edgedist is the edge protection distance (default and recommended: spacing/2).
Note: if the spacing is larger with respect to the dimension of the geometry, the default setting may result in few or no interior
nodes. In this case decrease the value of edgedist.
ranseed1, ranseed2 are seeds for the random number generator, the default is -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.
createpts / random / xyz / .1 / 0 0 0 / 1 1 1 /
Random points with target spacing 0.1 in a 1x1x1 box.
createpts / random / rtz / .1 / 0,0,0 / 1,,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.
createpts / random / rtp / .5 / 5,0,0 / 5,,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.
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 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 degfrees for these two variables in their respective coordinate systems is used.