Image Gallery

VC Prototype

Fri Mar 9 10:52:53 2018

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)

VC seeds connected with recon 0

Voronoi Edges (red) and Input Box (black)
Nodes inside box (red), outside (blue)

Triangle Edges (black)
and Voronoi Edges (red)

Triangle Edges and Nodes (Voronoi volume)
Input Box shape (black)

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)

Triangle Edges (black)
and Voronoi Edges (red)

Triangle Edges and Nodes (Voronoi volume)
Input Box shape (black)

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)

Triangle Edges (black)
and Voronoi Edges (red)

Triangle Edges and Nodes (Voronoi volume)
Input Box shape (black)

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)

Triangle Edges (black)
and Voronoi Edges (red)

Triangle Edges and Nodes (Voronoi volume)
Input Box shape (black)

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