Example 9811: Generating a 3D Voronoi alveolar mesh within a unit cube

This example creates an alveolar mesh (19 alveoli around an alveolar duct) using a 3-D Voronoi meshing technique within a unit cube host mesh. The unit cube mesh is read in, boundary (B) and internal boundary (IB) nodes are generated at the cube surfaces and internal (I) nodes are generated uniformly within the unit cube. Delaunay triangulation of these points is formed and a Voronoi mesh is created from this. The resulting structural alveolar mesh consists of 2-D linear surface elements.

Created by Kelly Burrowes, 05/2003.

Delaunay nodes in cube	Delaunay triangulation	Initial Voronoi mesh
Remaining alveoli and duct cells	Duct cells shown with surfaces	Alveolar mesh

Voronoi elements along a central passage are allocated as duct cells, to allow air passage. All Voronoi cells adjacent to the central duct are then grouped as alveoli, these form the alveolar units. The duct cells are discarded to produce the alveolar mesh.

The comfile run by this example is as follows:

fem de param;r;alveoli;example;          #defines parameters
fem de coor 3,1;                         #defines coordinates
fem de reg;r;three;example;              #defines 3 regions
fem de base;r;alveoli;example;           #defines linear 1D, 2D, 3D and simplex 2D, 3D bases
fem de node;r;cube_host;example reg 1;   #defines 3D unit cube host
fem de elem;r;cube_host;example reg 1; 
fem export node;cube as cube reg 1;      #exports cube host for viewing
fem export elem;cube as cube reg 1;
fem de node;c delaunay reg 1 target 2 div 4 rad 0.01 internal; 

#creates delaunay seed points within host region 1 in target region 2, using 4 divisions of 
#cube volume, radius of 0.01 for internal boundary and boundary nodes and defines 
#regularly spaced internal seed points

fem de mesh;c delaunay basis 4 B boundary IB internal_boundary IN_nodes internal reg 2;

#specifies boundary, internal boundary, and internal node groups in region 2

fem update delaunay reg 2;
fem de mesh;c voronoi basis 3 B boundary IB internal_boundary IN_nodes internal convert reg 2 target 3 gen 3;

#calculates the Voronoi mesh based on the defined Delaunay nodes in region 2
#converts the Voronoi cells to nodes and 1-D elements into target region 3
#gen 3 specifies 3 generations (bifurcations) of alveolar ducts

fem export node;cell as cell reg 3;      #exports Voronoi nodes
fem export elem;alveoli as alveoli elem alveoli reg 3; #exports Voronoi 
fem export elem;duct as duct elem duct reg 3;
fem 


#NB/ Different results are obtained on linux than on the irix and aix operating 
#systems the small differences are generated in the delaunay triangulation 
#procedure and are most probably due to differences in rounding on the 2 
#platforms. Therefore different results are compared in ndiff on the different 
#platforms (16th June 2003).

Additional testing commands:

fem list voronoi total region 1

Files used by this example are:

Name              Modified     Size

example_9811.com  16-Jun-2003  1.8k
alveoli.exelem    26-Aug-2004  872k
alveoli.ipbase    16-Jan-2003  6.0k
alveoli.ippara    16-Jun-2003  5.9k
cell.exnode       26-Aug-2004   90k
cells.ipelem      20-Jan-2003  858k
cells.ipnode      20-Jan-2003  314k
cube.exelem       16-Jun-2003  3.6k
cube.exnode       16-Jun-2003  1.0k
cube_host.ipelem  16-Jan-2003  404 
cube_host.ipnode  16-Jan-2003  1.7k
draw.com          16-Jun-2003  799 
duct.exelem       26-Aug-2004  207k
test.com          10-Jul-2005  845 
test.ipbase       16-Jan-2003  6.0k
test_output.com   10-Jul-2005   32 
three.ipregi      16-Jun-2003   93 

Download the entire example:

Name                           Modified     Size

examples_9_98_981_9811.tar.gz  19-Aug-2006  343k

Testing status by version:

Testing status by file:

• cmiss_test.log
  

  i686-linux
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  mips-irix
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  Success	cm-debug-clear-malloc:	cmiss_test.log.retain.
  Success	cm-debug-clear-malloc7:	cmiss_test.log.retain.
  Success	cm64:	cmiss_test.log.retain.
  Success	cm64-debug:	cmiss_test.log.retain.
  Success	cm64-debug-clear-malloc:	cmiss_test.log.retain.
  rs6000-aix
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.
  Success	cm64:	cmiss_test.log.retain.
  Success	cm64-debug:	cmiss_test.log.retain.
  x86_64-linux
  Success	cm:	cmiss_test.log.retain.
  Success	cm-debug:	cmiss_test.log.retain.

  
  
• cmiss_test.out
  

  i686-linux
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  mips-irix
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  Success	cm-debug-clear-malloc:	ndiff test: no significant differences with generic answer.
  Success	cm-debug-clear-malloc7:	ndiff test: no significant differences with generic answer.
  Success	cm64:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug-clear-malloc:	ndiff test: no significant differences with irix answer.
  rs6000-aix
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.
  Success	cm64:	ndiff test: no significant differences with generic answer.
  Success	cm64-debug:	ndiff test: no significant differences with generic answer.
  x86_64-linux
  Success	cm:	ndiff test: no significant differences with generic answer.
  Success	cm-debug:	ndiff test: no significant differences with generic answer.

  
  

Html last generated: Sun Mar 6 05:50:35 2016

Input last modified: Sun Jul 10 02:09:49 2005