Wed Oct  8 09:07:07 2025

tetrahedron_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test tetrahedron().

tetrahedron_barycentric_test():
  tetrahedron_barycentric() converts XYZ to XSI.
  We are computing the XSI coordinates just to verify
  that the points are inside the tetrahedron.

  tetrahedron vertices
[[1. 4. 3.]
 [2. 4. 3.]
 [1. 6. 3.]
 [1. 4. 4.]]

  (X,Y,Z)   (XSI1,XSI2,XSI3,XSI4):

[1.25201034 4.34449885 3.05536873] [0.5203715  0.25201034 0.17224942 0.05536873]
[1.15071858 4.25443528 3.0623185 ] [0.65974528 0.15071858 0.12721764 0.0623185 ]
[1.28942363 4.24290637 3.13314891] [0.45597428 0.28942363 0.12145319 0.13314891]
[1.04325812 4.0114471  3.00759419] [0.94342413 0.04325812 0.00572355 0.00759419]
[1.0627002  4.02081266 3.01891444] [0.90797903 0.0627002  0.01040633 0.01891444]
[1.09728166 4.04938078 3.04246182] [0.83556613 0.09728166 0.02469039 0.04246182]
[1.03886696 4.00769227 3.00432088] [0.95296603 0.03886696 0.00384614 0.00432088]
[1.04666166 4.01745484 3.06871293] [0.87589799 0.04666166 0.00872742 0.06871293]
[1.02811943 4.01468613 3.03503473] [0.92950277 0.02811943 0.00734307 0.03503473]
[1.26735972 4.04902662 3.0205309 ] [0.68759607 0.26735972 0.02451331 0.0205309 ]

tetrahedron_centroid_test():
  tetrahedron_centroid() computes the centroid of a tetrahedron

  tetrahedron vertices
[[ 0.        0.942809 -0.333333]
 [-0.816496 -0.816496 -0.333333]
 [ 0.816496 -0.816496 -0.333333]
 [ 0.        0.        1.      ]]

  tetrahedron centroid():
[ 0.0000000e+00 -1.7254575e-01  2.5000000e-07]

tetrahedron_circumsphere_test():
  tetrahedron_circumsphere() computes the circumsphere
  of a tetrahedron.

  tetrahedron vertices:
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.        ]
 [ 0.          0.          0.81649658]]

  tetrahedron circumsphere center:
[1.11022302e-16 0.00000000e+00 2.04124145e-01]

  Circumsphere radius is  0.6123724356957946

tetrahedron_contains_point_test():
  tetrahedron_contains_point() finds if a point
  is inside a tetrahderon

  tetrahedron vertices:
[[ 0.        0.942809 -0.333333]
 [-0.816496 -0.816496 -0.333333]
 [ 0.816496 -0.816496 -0.333333]
 [ 0.        0.        1.      ]]

  P, Inside_Tetra?

[ 0.0816496 -0.2449488  0.6000001] True
[-1.4696928 -3.0219429 -0.1999997] False
[-0.8981456  0.6725976 -0.1999997] False

tetrahedron_dihedral_angles_test():
  tetrahedron_dihedral_angles() computes the dihedral angles
  of a tetrahedron.

  tetrahedron1 vertices:
[[ 0.        0.942809 -0.333333]
 [-0.816496 -0.816496 -0.333333]
 [ 0.816496 -0.816496 -0.333333]
 [ 0.        0.        1.      ]]

  Dihedral angles:
[1.28147531 1.28147531 1.03372905 1.02132929 1.37444431 1.37444431]

  tetrahedron2 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]

  Dihedral angles:
[1.57079633 1.57079633 1.57079633 0.95531662 0.95531662 0.95531662]

  tetrahedron3 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 2. 0.]
 [0. 0. 4.]]

  Dihedral angles:
[1.57079633 1.57079633 1.57079633 1.35080835 1.11916289 0.50973968]

  tetrahedron4 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [1. 1. 1.]]

  Dihedral angles:
[0.78539816 0.78539816 2.0943951  2.18627604 0.61547971 0.61547971]

tetrahedron_edge_length_test():
  tetrahedron_edge_length() computes the edge lengths.

  tetrahedron vertices
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.        ]
 [ 0.          0.          0.81649658]]

  tetrahedron edge lengths:
[1. 1. 1. 1. 1. 1.]

tetrahedron_edges_test():
  tetrahedron_edges() computes the edges.

  tetrahedron vertices
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.        ]
 [ 0.          0.          0.81649658]]

  tetrahedron edges:
  ab: [-0.8660254  0.5        0.       ]
  ac: [-0.8660254 -0.5        0.       ]
  ad: [-0.57735027  0.          0.81649658]
  bc: [ 0. -1.  0.]
  bd: [ 0.28867513 -0.5         0.81649658]
  cd: [0.28867513 0.5        0.81649658]

tetrahedron_face_angles_test():
  tetrahedron_face_angles() computes the 6 pairwise angles
  of the 4 faces of a tetrahedron.

  tetrahedron1 vertices:
[[ 0.        0.942809 -0.333333]
 [-0.816496 -0.816496 -0.333333]
 [ 0.816496 -0.816496 -0.333333]
 [ 0.        0.        1.      ]]

  Face angles:
[[0.86903723 1.13627771 1.13627771]
 [1.01960934 0.90870714 1.21327617]
 [1.01960934 0.90870714 1.21327617]
 [1.08952109 1.08952109 0.96255047]]

  tetrahedron2 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]

  Face angles:
[[1.57079633 0.78539816 0.78539816]
 [1.57079633 0.78539816 0.78539816]
 [1.57079633 0.78539816 0.78539816]
 [1.04719755 1.04719755 1.04719755]]

  tetrahedron3 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 2. 0.]
 [0. 0. 4.]]

  Face angles:
[[1.57079633 1.10714872 0.46364761]
 [1.57079633 1.32581766 0.24497866]
 [1.57079633 1.10714872 0.46364761]
 [1.46211729 1.15927948 0.52019589]]

  tetrahedron4 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [1. 1. 1.]]

  Face angles:
[[1.57079633 0.78539816 0.78539816]
 [0.95531662 1.57079633 0.61547971]
 [0.95531662 1.57079633 0.61547971]
 [1.04719755 1.04719755 1.04719755]]

tetrahedron_face_areas_test():
  tetrahedron_face_areas() computes the areas of the
  4 faces of a tetrahedron.

  tetrahedron1 vertices:
[[ 0.        0.942809 -0.333333]
 [-0.816496 -0.816496 -0.333333]
 [ 0.816496 -0.816496 -0.333333]
 [ 0.        0.        1.      ]]

  Face areas:
[1.4364655  1.34909859 1.34909859 1.27656809]

  tetrahedron2 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]

  Face areas:
[0.5       0.5       0.5       0.8660254]

  tetrahedron3 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 2. 0.]
 [0. 0. 4.]]

  Face areas:
[1.         2.         4.         4.58257569]

  tetrahedron4 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [1. 1. 1.]]

  Face areas:
[0.5        0.70710678 0.70710678 0.8660254 ]

tetrahedron_insphere_test():
  tetrahedron_insphere() computes the insphere
  of a tetrahedron.

  tetrahedron vertices:
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.        ]
 [ 0.          0.          0.81649658]]

  insphere center:
[-3.20493781e-17  0.00000000e+00  2.04124145e-01]

  Insphere radius is  0.20412414523193154

tetrahedron_lattice_layer_point_next_test():
  tetrahedron_lattice_layer_point_next() returns the next
  point in a tetrahedron lattice layer defined by:

    C(4) - 1 < X(1)/C(1) + X(2)/C(2) +X(3)/C(3) <= C(4).

  N =  3
  C =  [2. 3. 4. 0.]

  Layer 0

1 [0. 0. 0.]
  No more.

  Layer 1

1 [1. 0. 0.]
2 [2. 0. 0.]
3 [0. 1. 0.]
4 [1. 1. 0.]
5 [0. 2. 0.]
6 [0. 3. 0.]
7 [0. 0. 1.]
8 [1. 0. 1.]
9 [0. 1. 1.]
10 [0. 2. 1.]
11 [0. 0. 2.]
12 [1. 0. 2.]
13 [0. 1. 2.]
14 [0. 0. 3.]
15 [0. 0. 4.]
  No more.

  Layer 2

1 [3. 0. 0.]
2 [4. 0. 0.]
3 [2. 1. 0.]
4 [3. 1. 0.]
5 [1. 2. 0.]
6 [2. 2. 0.]
7 [1. 3. 0.]
8 [2. 3. 0.]
9 [0. 4. 0.]
10 [1. 4. 0.]
11 [0. 5. 0.]
12 [0. 6. 0.]
13 [2. 0. 1.]
14 [3. 0. 1.]
15 [1. 1. 1.]
16 [2. 1. 1.]
17 [1. 2. 1.]
18 [2. 2. 1.]
19 [0. 3. 1.]
20 [1. 3. 1.]
21 [0. 4. 1.]
22 [0. 5. 1.]
23 [2. 0. 2.]
24 [3. 0. 2.]
25 [1. 1. 2.]
26 [2. 1. 2.]
27 [0. 2. 2.]
28 [1. 2. 2.]
29 [0. 3. 2.]
30 [1. 3. 2.]
31 [0. 4. 2.]
32 [1. 0. 3.]
33 [2. 0. 3.]
34 [0. 1. 3.]
35 [1. 1. 3.]
36 [0. 2. 3.]
37 [1. 2. 3.]
38 [0. 3. 3.]
39 [1. 0. 4.]
40 [2. 0. 4.]
41 [0. 1. 4.]
42 [1. 1. 4.]
43 [0. 2. 4.]
44 [0. 3. 4.]
45 [0. 0. 5.]
46 [1. 0. 5.]
47 [0. 1. 5.]
48 [0. 2. 5.]
49 [0. 0. 6.]
50 [1. 0. 6.]
51 [0. 1. 6.]
52 [0. 0. 7.]
53 [0. 0. 8.]
  No more.

tetrahedron_lattice_point_next_test():
  tetrahedron_lattice_point_next() returns the next lattice
  point in a tetrahedron defined by:

    0 <= X[0]/C[0] + X[1]/C[1] + X[2]/C[2] <= C[3]

  N =  3
  C =  [4 3 2 1]

1 [0. 0. 0.]
2 [1. 0. 0.]
3 [2. 0. 0.]
4 [0. 1. 0.]
5 [1. 1. 0.]
  No more.

tetrahedron_quality1_test():
  tetrahedron_quality1() computes quality measure #1
  for a tetrahedron.

  tetrahedron1 vertices:
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.81649658]
 [ 0.          0.          0.81649658]]

  Tetrahedron quality is  0.5804677483825404

  tetrahedron2 vertices:
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.        ]
 [ 0.          0.          0.40824829]]

  Tetrahedron quality is  0.7320508075688775

tetrahedron_quality2_test():
  tetrahedron_quality2() computes quality measure #2
  for a tetrahedron.

  tetrahedron1 vertices:
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.81649658]
 [ 0.          0.          0.81649658]]

  Tetrahedron quality is  0.5657699767278936

  tetrahedron2 vertices:
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.        ]
 [ 0.          0.          0.40824829]]

  Tetrahedron quality is  0.7320508075688775

tetrahedron_quality3_test()
  tetrahedron_quality3() computes quality measure #3
  for a tetrahedron.

  tetrahedron1 vertices:
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.81649658]
 [ 0.          0.          0.81649658]]

  Tetrahedron quality is  0.6868285455319992

  tetrahedron2 vertices:
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.        ]
 [ 0.          0.          0.40824829]]

  Tetrahedron quality is  0.8399473665965823

tetrahedron_quality4_test():
  tetrahedron_quality4() computes quality measure #4
  for a tetrahedron.

  tetrahedron vertices:
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.81649658]
 [ 0.          0.          0.81649658]]

  Tetrahedron quality is  0.47664153118723623

  tetrahedron vertices:
[[ 0.57735027  0.          0.        ]
 [-0.28867513  0.5         0.        ]
 [-0.28867513 -0.5         0.        ]
 [ 0.          0.          0.40824829]]

  Tetrahedron quality is  0.6213203435596423

tetrahedron_rhombic_shape_test():
  tetrahedron_rhombic_size() returns dimension information
  tetrahedron_rhombic_shape() returns face and order info.

  We will use this information to compute the
  areas and centers of each face.

  Number of points =    10
  Number of edges =     6
  Number of faces =     4
  Maximum face order =  6

shape_print():
  Information about a polytope.

  The number of vertices is  10

  Vertices:

     Index          X               Y               Z

0 [-0.81649658  0.          0.        ]
1 [ 0.         -0.57735027  0.        ]
2 [0.         0.57735027 0.        ]
3 [0.         0.         0.81649658]
4 [-0.40824829 -0.28867513  0.        ]
5 [-0.40824829  0.28867513  0.        ]
6 [-0.40824829  0.          0.40824829]
7 [0. 0. 0.]
8 [ 0.         -0.28867513  0.40824829]
9 [0.         0.28867513 0.40824829]

  The number of faces is  4
  The maximum order of any face is  6

     Index     Order         Indices of Nodes in Face
                      
0 6 0 4 1 8 3 6 
1 6 1 7 2 9 3 8 
2 6 2 5 0 6 3 9 
3 6 0 5 2 7 1 4 

  Face  Order  Area

0 6 0.4714045207910318
1 6 0.4714045207910318
2 6 0.4714045207910318
3 6 0.4714045207910318

  Face  Center

0 [-0.27216553 -0.19245009  0.27216553]
1 [0.         0.         0.27216553]
2 [-0.27216553  0.19245009  0.27216553]
3 [-0.27216553  0.          0.        ]

tetrahedron_sample_test():
  tetrahedron_sample() samples a tetrahedron.
  We are computing the XSI coordinates just to verify
  that the points are inside the tetrahedron.

  tetrahedron vertices
[[1. 4. 3.]
 [2. 4. 3.]
 [1. 6. 3.]
 [1. 4. 4.]]

  (X,Y,Z)   (XSI1,XSI2,XSI3,XSI4):

[1.11798538 4.18037554 3.07019851] [0.72162834 0.11798538 0.09018777 0.07019851]
[1.2293246  4.01169454 3.00678057] [0.75804756 0.2293246  0.00584727 0.00678057]
[1.12910517 4.025645   3.01554706] [0.84252527 0.12910517 0.0128225  0.01554706]
[1.14502812 4.00055638 3.00093569] [8.53758001e-01 1.45028117e-01 2.78190527e-04 9.35691266e-04]
[1.1661302  4.01438412 3.00062387] [8.26053870e-01 1.66130202e-01 7.19206219e-03 6.23865851e-04]
[1.25742498 4.01845248 3.00480934] [0.72853944 0.25742498 0.00922624 0.00480934]
[1.3175936  4.46854809 3.01394438] [0.43418797 0.3175936  0.23427405 0.01394438]
[1.20174339 4.03268307 3.00623935] [0.77567572 0.20174339 0.01634154 0.00623935]
[1.05115443 4.00190597 3.00507326] [0.94281932 0.05115443 0.00095299 0.00507326]
[1.27476972 4.00093904 3.00504323] [7.19717523e-01 2.74769724e-01 4.69520715e-04 5.04323249e-03]

tetrahedron_shape_test():
  tetrahedron_size() returns dimension information
  tetrahedron_shape() returns face and order info.

  We will use this information to compute the
  areas and centers of each face.

  Number of points =    4
  Number of edges =     6
  Number of faces =     4
  Maximum face order =  3

shape_print():
  Information about a polytope.

  The number of vertices is  4

  Vertices:

     Index          X               Y               Z

0 [ 0.942809  0.       -0.333333]
1 [-0.471405  0.816497 -0.333333]
2 [-0.471405 -0.816497 -0.333333]
3 [0. 0. 1.]

  The number of faces is  4
  The maximum order of any face is  3

     Index     Order         Indices of Nodes in Face
                      
0 3 0 2 1 
1 3 0 1 3 
2 3 0 3 2 
3 3 1 2 3 

  Face  Order  Area

0 3 1.154701488358
1 3 1.1547007118869246
2 3 1.1547007118869248
3 3 1.1547010048610136

  Face  Center

0 [-3.33333333e-07  0.00000000e+00 -3.33333000e-01]
1 [0.15713467 0.27216567 0.11111133]
2 [ 0.15713467 -0.27216567  0.11111133]
3 [-0.31427     0.          0.11111133]

tetrahedron_solid_angles_test():
  tetrahedron_solid_angles() computes the solid angles
  associated with the vertices of a tetrahedron.

  tetrahedron1 vertices:
[[ 0.        0.942809 -0.333333]
 [-0.816496 -0.816496 -0.333333]
 [ 0.816496 -0.816496 -0.333333]
 [ 0.        0.        1.      ]]

  solid angles:
[0.45508702 0.53565626 0.53565626 0.64102502]

  tetrahedron2 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]

  solid angles:
[1.57079633 0.33983691 0.33983691 0.33983691]

  tetrahedron3 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 2. 0.]
 [0. 0. 4.]]

  solid angles:
[1.57079633 0.33983691 0.33983691 0.33983691]

  tetrahedron4 vertices:
[[0. 0. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [1. 1. 1.]]

  solid angles:
[0.52359878 0.44556125 0.44556125 0.18376187]

tetrahedron_volume_test():
  tetrahedron_volume() computes the volume of a tetrahedron

  tetrahedron vertices
[[ 0.        0.942809 -0.333333]
 [-0.816496 -0.816496 -0.333333]
 [ 0.816496 -0.816496 -0.333333]
 [ 0.        0.        1.      ]]

  Volume =  0.6384289494060559

tetrahedron01_lattice_point_num_test():
  tetrahedron01_lattice_point_num() counts
  lattice points inside the unit tetrahedron.

   0    1
   1    4
   2    10
   3    20
   4    35
   5    56
   6    84
   7    120
   8    165
   9    220
   10    286

tetrahedron01_sample_test()
  tetrahedron01_sample() samples the unit tetrahedron.

  Sample points in the unit tetrahedron:
[[0.06285074 0.00907099 0.33883319 0.00205012 0.07177621 0.24344238
  0.51599352 0.30651826 0.29782975 0.22365029]
 [0.754005   0.08748071 0.30614811 0.03304988 0.18296824 0.69649705
  0.17337048 0.41962116 0.34971387 0.40313015]
 [0.02853506 0.11932068 0.11825307 0.56406949 0.02399831 0.03767487
  0.02985716 0.16042637 0.07530167 0.1337789 ]]

tetrahedron01_volume_test():
  tetrahedron01_volume() returns the volume of the unit tetrahedron.

  tetrahedron01_volume() =  0.16666666666666666

triangle_angles_3d_test():
  triangle_angles_3d() computes the angles of a triangle in 3D.

  triangle vertices:
[[1.        2.        3.       ]
 [2.4142137 3.4142137 3.       ]
 [1.7071068 2.7071068 4.       ]]

      Radians      Degrees

0.7853981500943285 44.999999237787385
0.7853980793836574 44.99999518636436
1.570796424111807 90.00000557584825

triangle_area_3d_test():
  triangle_area_3d() computes the area of a triangle in 3D.

  triangle vertices:
[[1.        2.4142137 1.7071068]
 [2.        3.4142137 2.7071068]
 [3.        3.        4.       ]]

  Area =  1.1180340763927479

tetrahedron_test():
  Normal end of execution.
Wed Oct  8 09:07:07 2025