For 2D, uses input of a 2D planar polygon (convex or nonconvex) to create a set of uniform or variable spaced points using 2D Poisson Disk sampling. Optionally the vertices can be connected using Delaunay triangulation. For 3D, the command generates a point distribution within a 3D volume using a Poisson-Disk sampling algorithm. This ensures a minimum distance between points, resulting in a “blue noise” distribution that is ideal for high-quality tetrahedralization.
This poisson_disk command is available for LaGriT versions V3.3.3 or greater.
createpts /poisson_disk / [2d_polygon | 3d_box] / mo_out / mo_polygon / h_spacing_scalar / [connect | no_connect] / [user_resolution.mlgi] / [ poisson_seed integer ] [ number_of_samples integer ] [ resample_sweeps integer ]
2d_polygon character type indicating geometry for a 2D planar polygon, convex or nonconvex, in the XY plane. If the polygon you wish to distribute points in is not in XY plane, user must rotate it into XY plane.If the polygon is nonconvex, the algorithm may alter some small features depending on the details of the polygon and the user controlled input parameters. See examples below.
3d_box character type indicating geometry for 3D orthogonal box defined by (x,y,z) minimum and (x,y,z) maximum. (this is currently the only 3D geometry available)
mo_out name of output mesh object. This user defined mesh object will contain the vertex distribution or triangulation created by the poisson_disk algorithm.
For 2D, a second mesh object for mo_polygon name of input mesh object that contains a 2D planar polygon in the XY plane.
h_spacing_scalar of type real. In the case of uniform resolution, this user provided real number defines the target spacing between vertices created by the Poisson-Disk algorithm. If the mesh is connected, the triangle edges will be approximately equal to h_spacing_scalar. In the case of variable resolution, h_spacing_scalar is used as a multiplier in the function defined in user_resolution.mlgi.
connect will connect the vertices generated by Poisson disk algorithm connected. The output mesh object mo_out will be a Delaunay triangulation.
no_connect the output mesh object mo_out will contain the vertices generated by Poisson disk algorithm without triangle connectivity.
Default if this option is not used, the mesh will be uniform resolution defined by Argument 6 h_spacing_scalar.
user_resolution.mlgi is the name of a LaGriT control file for user defined resolution.
The control file defines a function h(x,y) that will be used to control vertex spacing in a variable resolution mesh. See examples below.
When the variable option is utilized, internal to the module a mesh object, ** mo_poi_h_field, with a real scalar attribute, **h_field_att, is created. By default for uniform resolution, h_field_att, is set to a constant value of h_spacing_scalar, however, when this option is exercised, the user must fill h_field_att with their own scalar field h(x,y). In addition, internal to the code the command:
define / POI_H_FACTOR / h_spacing_scalar
so one can access the value of h_spacing_scalar by using the variable POI_H_FACTOR in the LaGriT control file user_resolution.mlgi for setting variable resolution.
If a user script is provided as Argument 7, the sampling algorithm will query a local spacing value for every candidate point.
The algorithm looks for an attribute named h_field_att within a temporary mesh object named mo_poi_h_field. You can populate this attribute within your .mlgi script using several methods:
Before calling the command, the following global variables must be defined to establish the sampling domain and boundary behavior. Unlike 2D, where a polygon mesh is provided, 3D utilizes these global POI variables to define the volume.
Domain Limits: POI_XMIN, POI_YMIN, POI_ZMIN and POI_XMAX, POI_YMAX, POI_ZMAX define the corners of the 3D bounding box.
Boundary Buffer:
IF_POI_EDGE_BUFFER: Set to 1 to prevent points from being placed too close to the box faces. This is highly recommended when using connect to avoid poor quality elements (slivers) or negative coupling coefficients.
POI_EDGE_BUFFER: A multiplier for the buffer width (e.g., 1.0 equals a buffer of width $h$).
There are three optional parameters that are for advanced users only. They are keyword driven and can come in any order beginning as token 8 or 9. The user can specify none, one, two, or all three keyword driven parameters.
poisson_seed (integer default 1) is the seed for the random number generator. If once runs this module with the same input, by default each run will give the same result. However, if the user would like to produce multiple realizations with the same input (same input polygon, same resolution, etc.) but a different output mesh, then the user can change the value of poisson_seed for each realization.
number_of_samples (integer default:10) Number of new candidate points that are sampled around an accepted node. Lower values reduce overall sampling time, but can lead to holes in the final point distribution. Higher value lead to better density and converge but takes more time.
resample_sweeps (integer default:1) Number of additional sampling attempts in the domain. If there exists holes in the point distribution, increasing this value should fill in these holes.
It is suggested that the user should have the minimum value of h(x,y)= h_spacing_scalar, and then vary resolution by setting values greater than h_spacing_scalar. If one intends to have high resolution near objects and features and lower resolution away from the objects, then use of the compute/distance_field is a good way to define h(x,y).
createpts / poisson_disk / 2d_polygon / mo_poisson_pts / mo_polygon &
/ 0.01 / connect / user_h_field_att.mlgi &
poisson_seed 3 / resample_sweeps 4 / number_of_samples 20
createpts / poisson_disk / 2d_polygon / mo_poisson_pts / mo_polygon &
/ 0.01 / connect / user_h_field_att.mlgi &
poisson_seed 3
createpts / poisson_disk / 2d_polygon / mo_poisson_pts / mo_polygon &
/ 0.01 / connect / poisson_seed 3
Polygon input file: unit_square.poly
4 0 0 0 0
1 -0.5 -0.5 0
2 0.5 -0.5 0
3 0.5 0.5 0
4 -0.5 0.5 0
LaGriT control file
#
# Mesh a unit square with uniform and variable resolution tringles.
#
# Read polygon from a file.
#
read / avs / unit_square.poly / mo_polygon
#
# Uniform resolution, unit square polygon, vertex spacing 0.05:
#
createpts / poisson_disk / 2d_polygon / mo_poisson_pts / mo_polygon &
/ 0.05 / connect
dump / avs / output01_unit_square_uniform.inp / mo_poisson_pts
cmo / delete / mo_poisson_pts
#
# Variable resolution, unit square polygon, vertex spacing 0.01:
#
# WIDTH_FACTOR is used in user_h_field_att.mlgi
#
define / WIDTH_FACTOR / 10.0
createpts / poisson_disk / 2d_polygon / mo_poisson_pts / mo_polygon &
/ 0.01 / connect / user_h_field_att.mlgi
dump / avs / output02_unit_square_var.inp / mo_poisson_pts
cmo / delete / mo_poisson_pts
define / WIDTH_FACTOR / 20.0
createpts / poisson_disk / 2d_polygon / mo_poisson_pts / mo_polygon &
/ 0.01 / connect / user_h_field_att.mlgi
dump / avs / output03_unit_square_var.inp / mo_poisson_pts
cmo / delete / mo_poisson_pts
finish
Variable resolution defined in LaGriT control file: user_h_field_att.mlgi
Used in the example above, the resolution is set using the X coordinate (xic), the user defined POI_H_FACTOR = h_spacing_scalar = 0.01, and a floor function to ensure no values are below h_spacing_scalar.
#####################################################
# User defined h field function assignment
#####################################################
#
# h_field_att is already set to POI_H_FACTOR
#
define / MO_H_FIELD / mo_poi_h_field
#
# x**2
math / power / MO_H_FIELD / h_field_att / 1,0,0 / &
MO_H_FIELD / xic / 2.0
cmo/printatt/MO_H_FIELD/h_field_att/minmax
# sqrt(x**2)
math / power / MO_H_FIELD / h_field_att / 1,0,0 / &
MO_H_FIELD / h_field_att / 0.5
cmo / printatt/MO_H_FIELD/h_field_att/minmax
# POI_H_FACTOR*sqrt(x**2)
math/multiply/MO_H_FIELD/h_field_att/1,0,0/ &
MO_H_FIELD/h_field_att/ POI_H_FACTOR
math/multiply/MO_H_FIELD/h_field_att/1,0,0/ &
MO_H_FIELD/h_field_att/ WIDTH_FACTOR
cmo / printatt/MO_H_FIELD/h_field_att/minmax
math / floor / MO_H_FIELD/h_field_att/1,0,0/ &
MO_H_FIELD/h_field_att/POI_H_FACTOR
cmo/printatt/MO_H_FIELD/h_field_att/minmax
cmo / status / brief
#
# As a diagnostic one can output MO_H_FIELD and view
# the h(x,y) attribute that will be used to set resolution.
#
dump / avs / h_field_out.inp / MO_H_FIELD
#
finish