VC Prototype

Fri Mar 9 10:52:53 2018

Work Directory: /project/ep_cr/tam/meshing/VoroCrust/work/connect/proto_vor_tet/
LaGriT Mesh Output: simple2D.lgi.txt LaGriT command file
LaGriT Mesh Output: mesh2.out.txt report for just seeds
LaGriT Mesh Output: mesh.out.txt report for seeds plus corners

VoroCrust Cells (wire) and
Connected Tets (blue and red)

LaGriT Finite Element Mesh
Interior seeds (red)
Surface constraining seeds (blue)

LaGriT Finite Element Mesh
VoroCrust Voronoi Polygons
LaGriT Finite Element Mesh
VoroCrust Voronoi Polygons Clipped
LaGriT Finite Element Mesh

VoroCrust input is a triangulated surface representing the volume to fill.
VC will generate seed points (voronoi centers). These are interior (with voronoi cells full inside) and surface constraining (inside and outside the surface).
The result is a volume filled with voronoi polygons with variable number of faces.
Input models assume vornoi cells around each node point formed from tetrahedral.
So the number of faces for each voronoi cell is constant.
VC creates many surface seeds which makes it difficult to view and evaluate.


To better understand VC output we create a simplified 2D cube with possible seed locations.
Each corner has 4 seeds located inside and outside of the boundary surface.
The seed points into a Delaunay mesh and Voronoi volumes and areas are computed using LaGriT.

VC seeds connected into triangles

Proto input into VC is a box from 0,0 to 10,10
Simulated VC seeds are blue, added corner points are in red.
Simulated VC seeds for this surface are connected into triangles.
Write and view voronoi areas formed from these triangles.

Input Points for Box 0,0 to 10,10 and Connect with LaGriT
VC surface constraining seeds (blue), User added corners (red)
LaGriT Finite Element Mesh

VC seeds connected with recon 0

Voronoi Edges (red) and Input Box (black)
Nodes inside box (red), outside (blue)
LaGriT Finite Element Mesh
Triangle Edges (black)
and Voronoi Edges (red)

LaGriT Finite Element Mesh
Triangle Edges and Nodes (Voronoi volume)
Input Box shape (black)

LaGriT Finite Element Mesh
Total Voronoi  area =  116.5
Total Triangle area =  116.5

Outside Box
    1  2.06250E+00
    2  2.06250E+00
    5  2.06250E+00
    8  2.06250E+00
    9  2.06250E+00
   12  2.06250E+00
   15  2.06250E+00
   16  2.06250E+00

Inside Voronoi  area  =  100
Inside Triangle area  =  100

Inside Box
    3  1.25000E+01
    4  1.25000E+01
    6  1.25000E+01
    7  1.25000E+01
   10  1.25000E+01
   11  1.25000E+01
   13  1.25000E+01
   14  1.25000E+01

Matbldtri: total neg  10 mincoef=  -1.6666667E-01 maxcoef=  1.00000E+01
Negative coeff2d:   sort   edge     vor_coeff        row_node  col_node
Negative coeff2d:     1        41 -1.6666667E-01         8         2
Negative coeff2d:     2         4 -1.6666667E-01         1         5
Negative coeff2d:     3        22 -1.6666667E-01         5         1
Negative coeff2d:     4        10 -1.6666667E-01         2         8
Negative coeff2d:     5        87 -1.6666667E-01        16        12
Negative coeff2d:     6        69 -1.6666667E-01        12        16
Negative coeff2d:     7        51 -1.6666667E-01         9        15
Negative coeff2d:     8        82 -1.6666667E-01        15         9
Negative coeff2d:     9        15 -1.1102230E-16         3         5
Negative coeff2d:    10        23 -1.1102230E-16         5         3



VC seeds connected with recon 1 Delaunay

Voronoi Edges (red) and Input Box (black)
Nodes inside box (red), outside (blue)
LaGriT Finite Element Mesh
Triangle Edges (black)
and Voronoi Edges (red)

LaGriT Finite Element Mesh
Triangle Edges and Nodes (Voronoi volume)
Input Box shape (black)

LaGriT Finite Element Mesh
Total Voronoi  area =  116.5
Total Triangle area =  116.5

Outside Box
    1  2.06250E+00
    2  2.12500E+00
    5  2.12500E+00
    8  2.06250E+00
    9  2.12500E+00
   12  2.12500E+00
   15  2.06250E+00
   16  2.06250E+00

Inside Voronoi  area =  99.75 

Inside Box
    3  1.22500E+01
    6  1.23750E+01
   18  3.12500E-01
    4  1.23750E+01
    7  1.22500E+01
   19  3.12500E-01
   10  1.23750E+01
   13  1.22500E+01
   20  3.12500E-01
   11  1.23750E+01
   14  1.22500E+01
   17  3.12500E-01


Matbldtri: total neg 4 mincoef=  -7.8504623E-17 (zero) 






VC seeds plus Added Corner Points connected with recon 0

Voronoi Edges (red) and Input Box (black)
Nodes inside box (red), outside (blue)
LaGriT Finite Element Mesh
Triangle Edges (black)
and Voronoi Edges (red)

LaGriT Finite Element Mesh
Triangle Edges and Nodes (Voronoi volume)
Input Box shape (black)

LaGriT Finite Element Mesh
Total Voronoi  area  =  256
Total Triangle area  =  256

Outside Box
    1 -3.88163E+01
    2 -3.88163E+01
    3  3.89082E+01
    4  3.89082E+01
    7  3.89082E+01
   10  3.89082E+01
   11  3.89082E+01
   14  3.89082E+01
   17  3.89082E+01
   18  3.89082E+01
   19 -3.88163E+01
   20 -3.88163E+01

Inside Voronoi area =  100 

Inside Box
    5  1.25000E+01
    6  1.25000E+01
    8  1.25000E+01
    9  1.25000E+01
   12  1.25000E+01
   13  1.25000E+01
   15  1.25000E+01
   16  1.25000E+01


Matbldtri: total neg  14 mincoef=  -5.2187500E-01 maxcoef=   1.0000000E+01
Negative coeff2d:   sort   edge     vor_coeff        row_node  col_node
Negative coeff2d:     1      13   -5.2187500E-01         2        20
Negative coeff2d:     2     121   -5.2187500E-01        19        20
Negative coeff2d:     3     122   -5.2187500E-01        20         2
Negative coeff2d:     4     125   -5.2187500E-01        20        19
Negative coeff2d:     5     116   -5.2187500E-01        19         1
Negative coeff2d:     6       6   -5.2187500E-01         1        19
Negative coeff2d:     7       7   -5.2187500E-01         2         1
Negative coeff2d:     8       2   -5.2187500E-01         1         2
Negative coeff2d:     9      15   -8.8817842E-16         3         2
Negative coeff2d:    10       9   -8.8817842E-16         2         3
Negative coeff2d:    11      85   -1.1102230E-16        14         2
Negative coeff2d:    12      12   -1.1102230E-16         2        14
Negative coeff2d:    13      40   -1.1102230E-16         7         5
Negative coeff2d:    14      31   -1.1102230E-16         5         7



VC seeds plus Added Corner Points connected with recon 1 Delaunay

Voronoi Edges (red) and Input Box (black)
Nodes inside box (red), outside (blue)
LaGriT Finite Element Mesh
Triangle Edges (black)
and Voronoi Edges (red)

LaGriT Finite Element Mesh
Triangle Edges and Nodes (Voronoi volume)
Input Box shape (black)

LaGriT Finite Element Mesh
Total Voronoi  area  =  256
Total Triangle area  =  256

Outside Box
    1  3.78365E+00
    2  3.78365E+00
    3  1.01082E+01
    4  1.01082E+01
    7  1.01082E+01
   10  1.01082E+01
   11  1.01082E+01
   14  1.01082E+01
   17  1.01082E+01
   18  1.01082E+01
   19  3.78365E+00
   20  3.78365E+00
   21  7.50000E+00
   22  7.50000E+00
   23  7.50000E+00
   24  7.50000E+00
   25  7.50000E+00
   26  7.50000E+00
   27  7.50000E+00
   28  7.50000E+00
Inside Voronoi area =  100

    5  1.25000E+01
    6  1.25000E+01
    8  1.25000E+01
    9  1.25000E+01
   12  1.25000E+01
   13  1.25000E+01
   15  1.25000E+01
   16  1.25000E+01

Matbldtri: total neg 2 mincoef=  -1.1102230E-16 (zero)



Gallery of All Images with Image file names


tri0s are recon 0, just seeds
tri1s are recon 1, just seeds
tri0 are recon 0, seeds plus corners
tri1 are recon 1, seeds plus corners

    gallery.html