Spheres
We segment a sphere into coarse voxel meshes.
Segmentation
Using spheres.py,
"""This module creates a voxelized sphere and exports it as a .npy file.
Example
-------
source ~/autotwin/automesh/.venv/bin/activate
python spheres.py
"""
from pathlib import Path
from typing import Final
from matplotlib.colors import LightSource
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
def sphere(radius: int, dtype=np.uint8) -> np.ndarray:
"""Generate a 3D voxelized representation of a sphere.
Parameters
----------
radius: int
The radius of the sphere. Minimum value is 1.
dtype: data-type, optional
The data type of the output array. Default is np.uint8.
Returns
-------
np.ndarray
A 3D numpy array of shape (2*radius+1, 2*radius+1, 2*radius+1)
representing the voxelized sphere. Voxels within the sphere are
set to 1, and those outside are set to 0.
Raises
------
ValueError
If the radius is less than 1.
Example
-------
>>> sphere(radius=1) returns
array(
[
[[0, 0, 0], [0, 1, 0], [0, 0, 0]],
[[0, 1, 0], [1, 1, 1], [0, 1, 0]],
[[0, 0, 0], [0, 1, 0], [0, 0, 0]]
],
dtype=uint8
)
Reference
---------
Adapted from:
https://github.com/scikit-image/scikit-image/blob/v0.24.0/skimage/morphology/footprints.py#L763-L833
"""
if radius < 1:
raise ValueError("Radius must be >= 1")
n_voxels_per_side = 2 * radius + 1
vox_z, vox_y, vox_x = np.mgrid[
-radius:radius:n_voxels_per_side * 1j,
-radius:radius:n_voxels_per_side * 1j,
-radius:radius:n_voxels_per_side * 1j,
]
voxel_radius_squared = vox_x**2 + vox_y**2 + vox_z**2
result = np.array(voxel_radius_squared <= radius * radius, dtype=dtype)
return result
# User input begin
spheres = {
"radius_1": sphere(radius=1),
"radius_3": sphere(radius=3),
"radius_5": sphere(radius=5),
}
aa = Path(__file__)
bb = aa.with_suffix(".png")
# Visualize the elements.
# width, height = 8, 4
width, height = 6, 3
fig = plt.figure(figsize=(width, height))
# fig = plt.figure(figsize=(8, 8))
el, az, roll = 63, -110, 0
cmap = plt.get_cmap(name="tab10")
num_colors = len(spheres)
voxel_alpha: Final[float] = 0.9
colors = cmap(np.linspace(0, 1, num_colors))
lightsource = LightSource(azdeg=325, altdeg=45) # azimuth, elevation
# lightsource = LightSource(azdeg=325, altdeg=90) # azimuth, elevation
dpi: Final[int] = 300 # resolution, dots per inch
visualize: Final[bool] = False # turn to True to show the figure on screen
serialize: Final[bool] = False # turn to True to save .png and .npy files
# User input end
N_SUBPLOTS = len(spheres)
IDX = 1
for index, (key, value) in enumerate(spheres.items()):
ax = fig.add_subplot(1, N_SUBPLOTS, index+1, projection=Axes3D.name)
ax.voxels(
value,
facecolors=colors[index],
edgecolor=colors[index],
alpha=voxel_alpha,
lightsource=lightsource)
ax.set_title(key)
IDX += 1
# Set labels for the axes
ax.set_xlabel("x (voxels)")
ax.set_ylabel("y (voxels)")
ax.set_zlabel("z (voxels)")
# Set the camera view
ax.set_aspect("equal")
ax.view_init(elev=el, azim=az, roll=roll)
if serialize:
cc = aa.with_stem("spheres_" + key)
dd = cc.with_suffix(".npy")
# Save the data in .npy format
np.save(dd, value)
print(f"Saved: {dd}")
fig.tight_layout()
if visualize:
plt.show()
if serialize:
fig.savefig(bb, dpi=dpi)
print(f"Saved: {bb}")
create very coarse spheres of varying
resolution (radius=1, radius=3, and radius=5), as shown below:
Figure: Sphere segmentations at selected resolutions, shown in the voxel domain.
For the radius=1 case, the underyling data structure appears as:
spheres["radius_1"]
array([[[0, 0, 0],
[0, 1, 0],
[0, 0, 0]],
[[0, 1, 0],
[1, 1, 1],
[0, 1, 0]],
[[0, 0, 0],
[0, 1, 0],
[0, 0, 0]]], dtype=uint8)
For the radius=3 case, the underyling data structure appears as:
spheres["sradius_3"]
array([[[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]],
[[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0]],
[[0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0]],
[[0, 0, 0, 1, 0, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[1, 1, 1, 1, 1, 1, 1],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 1, 0, 0, 0]],
[[0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0]],
[[0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 1, 1, 1, 1, 1, 0],
[0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0]],
[[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0]]], dtype=uint8)
Because of its large size, the data structure for sphere_5 is not shown here.
These segmentations are saved to
Autotwin
Autotwin is used to convert the .npy segmentations into .inp meshes.
automesh -i spheres_radius_1.npy -o spheres_radius_1.inp -x 3 -y 3 -z 3
automesh -i spheres_radius_3.npy -o spheres_radius_3.inp -x 7 -y 7 -z 7
automesh -i spheres_radius_5.npy -o spheres_radius_5_.inp -x 11 -y 11 -z 11
Mesh
The spheres_radius_1.inp file:
*HEADING
autotwin.automesh
version 0.1.6
autogenerated on 2024-09-23 20:42:20.599041 UTC
**
*NODE, NSET=ALLNODES
1, 1.000000e0, 1.000000e0, 0.000000e0
2, 2.000000e0, 1.000000e0, 0.000000e0
3, 1.000000e0, 2.000000e0, 0.000000e0
4, 2.000000e0, 2.000000e0, 0.000000e0
5, 1.000000e0, 0.000000e0, 1.000000e0
6, 2.000000e0, 0.000000e0, 1.000000e0
7, 0.000000e0, 1.000000e0, 1.000000e0
8, 1.000000e0, 1.000000e0, 1.000000e0
9, 2.000000e0, 1.000000e0, 1.000000e0
10, 3.000000e0, 1.000000e0, 1.000000e0
11, 0.000000e0, 2.000000e0, 1.000000e0
12, 1.000000e0, 2.000000e0, 1.000000e0
13, 2.000000e0, 2.000000e0, 1.000000e0
14, 3.000000e0, 2.000000e0, 1.000000e0
15, 1.000000e0, 3.000000e0, 1.000000e0
16, 2.000000e0, 3.000000e0, 1.000000e0
17, 1.000000e0, 0.000000e0, 2.000000e0
18, 2.000000e0, 0.000000e0, 2.000000e0
19, 0.000000e0, 1.000000e0, 2.000000e0
20, 1.000000e0, 1.000000e0, 2.000000e0
21, 2.000000e0, 1.000000e0, 2.000000e0
22, 3.000000e0, 1.000000e0, 2.000000e0
23, 0.000000e0, 2.000000e0, 2.000000e0
24, 1.000000e0, 2.000000e0, 2.000000e0
25, 2.000000e0, 2.000000e0, 2.000000e0
26, 3.000000e0, 2.000000e0, 2.000000e0
27, 1.000000e0, 3.000000e0, 2.000000e0
28, 2.000000e0, 3.000000e0, 2.000000e0
29, 1.000000e0, 1.000000e0, 3.000000e0
30, 2.000000e0, 1.000000e0, 3.000000e0
31, 1.000000e0, 2.000000e0, 3.000000e0
32, 2.000000e0, 2.000000e0, 3.000000e0
**
*ELEMENT, TYPE=C3D8R, ELSET=EB1
1, 1, 2, 4, 3, 8, 9, 13, 12
2, 5, 6, 9, 8, 17, 18, 21, 20
3, 7, 8, 12, 11, 19, 20, 24, 23
4, 8, 9, 13, 12, 20, 21, 25, 24
5, 9, 10, 14, 13, 21, 22, 26, 25
6, 12, 13, 16, 15, 24, 25, 28, 27
7, 20, 21, 25, 24, 29, 30, 32, 31
**
*SOLID SECTION, ELSET=EB1, MATERIAL=Default-Steel
The spheres_radius_3.inp file:
*HEADING
autotwin.automesh
version 0.1.6
autogenerated on 2024-09-23 20:44:01.593367 UTC
**
*NODE, NSET=ALLNODES
1, 3.000000e0, 3.000000e0, 0.000000e0
2, 4.000000e0, 3.000000e0, 0.000000e0
3, 3.000000e0, 4.000000e0, 0.000000e0
4, 4.000000e0, 4.000000e0, 0.000000e0
5, 2.000000e0, 1.000000e0, 1.000000e0
6, 3.000000e0, 1.000000e0, 1.000000e0
7, 4.000000e0, 1.000000e0, 1.000000e0
8, 5.000000e0, 1.000000e0, 1.000000e0
9, 1.000000e0, 2.000000e0, 1.000000e0
10, 2.000000e0, 2.000000e0, 1.000000e0
11, 3.000000e0, 2.000000e0, 1.000000e0
12, 4.000000e0, 2.000000e0, 1.000000e0
13, 5.000000e0, 2.000000e0, 1.000000e0
14, 6.000000e0, 2.000000e0, 1.000000e0
15, 1.000000e0, 3.000000e0, 1.000000e0
16, 2.000000e0, 3.000000e0, 1.000000e0
17, 3.000000e0, 3.000000e0, 1.000000e0
18, 4.000000e0, 3.000000e0, 1.000000e0
19, 5.000000e0, 3.000000e0, 1.000000e0
20, 6.000000e0, 3.000000e0, 1.000000e0
21, 1.000000e0, 4.000000e0, 1.000000e0
22, 2.000000e0, 4.000000e0, 1.000000e0
23, 3.000000e0, 4.000000e0, 1.000000e0
24, 4.000000e0, 4.000000e0, 1.000000e0
25, 5.000000e0, 4.000000e0, 1.000000e0
26, 6.000000e0, 4.000000e0, 1.000000e0
27, 1.000000e0, 5.000000e0, 1.000000e0
28, 2.000000e0, 5.000000e0, 1.000000e0
29, 3.000000e0, 5.000000e0, 1.000000e0
30, 4.000000e0, 5.000000e0, 1.000000e0
31, 5.000000e0, 5.000000e0, 1.000000e0
32, 6.000000e0, 5.000000e0, 1.000000e0
33, 2.000000e0, 6.000000e0, 1.000000e0
34, 3.000000e0, 6.000000e0, 1.000000e0
35, 4.000000e0, 6.000000e0, 1.000000e0
36, 5.000000e0, 6.000000e0, 1.000000e0
37, 1.000000e0, 1.000000e0, 2.000000e0
38, 2.000000e0, 1.000000e0, 2.000000e0
39, 3.000000e0, 1.000000e0, 2.000000e0
40, 4.000000e0, 1.000000e0, 2.000000e0
41, 5.000000e0, 1.000000e0, 2.000000e0
42, 6.000000e0, 1.000000e0, 2.000000e0
43, 1.000000e0, 2.000000e0, 2.000000e0
44, 2.000000e0, 2.000000e0, 2.000000e0
45, 3.000000e0, 2.000000e0, 2.000000e0
46, 4.000000e0, 2.000000e0, 2.000000e0
47, 5.000000e0, 2.000000e0, 2.000000e0
48, 6.000000e0, 2.000000e0, 2.000000e0
49, 1.000000e0, 3.000000e0, 2.000000e0
50, 2.000000e0, 3.000000e0, 2.000000e0
51, 3.000000e0, 3.000000e0, 2.000000e0
52, 4.000000e0, 3.000000e0, 2.000000e0
53, 5.000000e0, 3.000000e0, 2.000000e0
54, 6.000000e0, 3.000000e0, 2.000000e0
55, 1.000000e0, 4.000000e0, 2.000000e0
56, 2.000000e0, 4.000000e0, 2.000000e0
57, 3.000000e0, 4.000000e0, 2.000000e0
58, 4.000000e0, 4.000000e0, 2.000000e0
59, 5.000000e0, 4.000000e0, 2.000000e0
60, 6.000000e0, 4.000000e0, 2.000000e0
61, 1.000000e0, 5.000000e0, 2.000000e0
62, 2.000000e0, 5.000000e0, 2.000000e0
63, 3.000000e0, 5.000000e0, 2.000000e0
64, 4.000000e0, 5.000000e0, 2.000000e0
65, 5.000000e0, 5.000000e0, 2.000000e0
66, 6.000000e0, 5.000000e0, 2.000000e0
67, 1.000000e0, 6.000000e0, 2.000000e0
68, 2.000000e0, 6.000000e0, 2.000000e0
69, 3.000000e0, 6.000000e0, 2.000000e0
70, 4.000000e0, 6.000000e0, 2.000000e0
71, 5.000000e0, 6.000000e0, 2.000000e0
72, 6.000000e0, 6.000000e0, 2.000000e0
73, 3.000000e0, 0.000000e0, 3.000000e0
74, 4.000000e0, 0.000000e0, 3.000000e0
75, 1.000000e0, 1.000000e0, 3.000000e0
76, 2.000000e0, 1.000000e0, 3.000000e0
77, 3.000000e0, 1.000000e0, 3.000000e0
78, 4.000000e0, 1.000000e0, 3.000000e0
79, 5.000000e0, 1.000000e0, 3.000000e0
80, 6.000000e0, 1.000000e0, 3.000000e0
81, 1.000000e0, 2.000000e0, 3.000000e0
82, 2.000000e0, 2.000000e0, 3.000000e0
83, 3.000000e0, 2.000000e0, 3.000000e0
84, 4.000000e0, 2.000000e0, 3.000000e0
85, 5.000000e0, 2.000000e0, 3.000000e0
86, 6.000000e0, 2.000000e0, 3.000000e0
87, 0.000000e0, 3.000000e0, 3.000000e0
88, 1.000000e0, 3.000000e0, 3.000000e0
89, 2.000000e0, 3.000000e0, 3.000000e0
90, 3.000000e0, 3.000000e0, 3.000000e0
91, 4.000000e0, 3.000000e0, 3.000000e0
92, 5.000000e0, 3.000000e0, 3.000000e0
93, 6.000000e0, 3.000000e0, 3.000000e0
94, 7.000000e0, 3.000000e0, 3.000000e0
95, 0.000000e0, 4.000000e0, 3.000000e0
96, 1.000000e0, 4.000000e0, 3.000000e0
97, 2.000000e0, 4.000000e0, 3.000000e0
98, 3.000000e0, 4.000000e0, 3.000000e0
99, 4.000000e0, 4.000000e0, 3.000000e0
100, 5.000000e0, 4.000000e0, 3.000000e0
101, 6.000000e0, 4.000000e0, 3.000000e0
102, 7.000000e0, 4.000000e0, 3.000000e0
103, 1.000000e0, 5.000000e0, 3.000000e0
104, 2.000000e0, 5.000000e0, 3.000000e0
105, 3.000000e0, 5.000000e0, 3.000000e0
106, 4.000000e0, 5.000000e0, 3.000000e0
107, 5.000000e0, 5.000000e0, 3.000000e0
108, 6.000000e0, 5.000000e0, 3.000000e0
109, 1.000000e0, 6.000000e0, 3.000000e0
110, 2.000000e0, 6.000000e0, 3.000000e0
111, 3.000000e0, 6.000000e0, 3.000000e0
112, 4.000000e0, 6.000000e0, 3.000000e0
113, 5.000000e0, 6.000000e0, 3.000000e0
114, 6.000000e0, 6.000000e0, 3.000000e0
115, 3.000000e0, 7.000000e0, 3.000000e0
116, 4.000000e0, 7.000000e0, 3.000000e0
117, 3.000000e0, 0.000000e0, 4.000000e0
118, 4.000000e0, 0.000000e0, 4.000000e0
119, 1.000000e0, 1.000000e0, 4.000000e0
120, 2.000000e0, 1.000000e0, 4.000000e0
121, 3.000000e0, 1.000000e0, 4.000000e0
122, 4.000000e0, 1.000000e0, 4.000000e0
123, 5.000000e0, 1.000000e0, 4.000000e0
124, 6.000000e0, 1.000000e0, 4.000000e0
125, 1.000000e0, 2.000000e0, 4.000000e0
126, 2.000000e0, 2.000000e0, 4.000000e0
127, 3.000000e0, 2.000000e0, 4.000000e0
128, 4.000000e0, 2.000000e0, 4.000000e0
129, 5.000000e0, 2.000000e0, 4.000000e0
130, 6.000000e0, 2.000000e0, 4.000000e0
131, 0.000000e0, 3.000000e0, 4.000000e0
132, 1.000000e0, 3.000000e0, 4.000000e0
133, 2.000000e0, 3.000000e0, 4.000000e0
134, 3.000000e0, 3.000000e0, 4.000000e0
135, 4.000000e0, 3.000000e0, 4.000000e0
136, 5.000000e0, 3.000000e0, 4.000000e0
137, 6.000000e0, 3.000000e0, 4.000000e0
138, 7.000000e0, 3.000000e0, 4.000000e0
139, 0.000000e0, 4.000000e0, 4.000000e0
140, 1.000000e0, 4.000000e0, 4.000000e0
141, 2.000000e0, 4.000000e0, 4.000000e0
142, 3.000000e0, 4.000000e0, 4.000000e0
143, 4.000000e0, 4.000000e0, 4.000000e0
144, 5.000000e0, 4.000000e0, 4.000000e0
145, 6.000000e0, 4.000000e0, 4.000000e0
146, 7.000000e0, 4.000000e0, 4.000000e0
147, 1.000000e0, 5.000000e0, 4.000000e0
148, 2.000000e0, 5.000000e0, 4.000000e0
149, 3.000000e0, 5.000000e0, 4.000000e0
150, 4.000000e0, 5.000000e0, 4.000000e0
151, 5.000000e0, 5.000000e0, 4.000000e0
152, 6.000000e0, 5.000000e0, 4.000000e0
153, 1.000000e0, 6.000000e0, 4.000000e0
154, 2.000000e0, 6.000000e0, 4.000000e0
155, 3.000000e0, 6.000000e0, 4.000000e0
156, 4.000000e0, 6.000000e0, 4.000000e0
157, 5.000000e0, 6.000000e0, 4.000000e0
158, 6.000000e0, 6.000000e0, 4.000000e0
159, 3.000000e0, 7.000000e0, 4.000000e0
160, 4.000000e0, 7.000000e0, 4.000000e0
161, 1.000000e0, 1.000000e0, 5.000000e0
162, 2.000000e0, 1.000000e0, 5.000000e0
163, 3.000000e0, 1.000000e0, 5.000000e0
164, 4.000000e0, 1.000000e0, 5.000000e0
165, 5.000000e0, 1.000000e0, 5.000000e0
166, 6.000000e0, 1.000000e0, 5.000000e0
167, 1.000000e0, 2.000000e0, 5.000000e0
168, 2.000000e0, 2.000000e0, 5.000000e0
169, 3.000000e0, 2.000000e0, 5.000000e0
170, 4.000000e0, 2.000000e0, 5.000000e0
171, 5.000000e0, 2.000000e0, 5.000000e0
172, 6.000000e0, 2.000000e0, 5.000000e0
173, 1.000000e0, 3.000000e0, 5.000000e0
174, 2.000000e0, 3.000000e0, 5.000000e0
175, 3.000000e0, 3.000000e0, 5.000000e0
176, 4.000000e0, 3.000000e0, 5.000000e0
177, 5.000000e0, 3.000000e0, 5.000000e0
178, 6.000000e0, 3.000000e0, 5.000000e0
179, 1.000000e0, 4.000000e0, 5.000000e0
180, 2.000000e0, 4.000000e0, 5.000000e0
181, 3.000000e0, 4.000000e0, 5.000000e0
182, 4.000000e0, 4.000000e0, 5.000000e0
183, 5.000000e0, 4.000000e0, 5.000000e0
184, 6.000000e0, 4.000000e0, 5.000000e0
185, 1.000000e0, 5.000000e0, 5.000000e0
186, 2.000000e0, 5.000000e0, 5.000000e0
187, 3.000000e0, 5.000000e0, 5.000000e0
188, 4.000000e0, 5.000000e0, 5.000000e0
189, 5.000000e0, 5.000000e0, 5.000000e0
190, 6.000000e0, 5.000000e0, 5.000000e0
191, 1.000000e0, 6.000000e0, 5.000000e0
192, 2.000000e0, 6.000000e0, 5.000000e0
193, 3.000000e0, 6.000000e0, 5.000000e0
194, 4.000000e0, 6.000000e0, 5.000000e0
195, 5.000000e0, 6.000000e0, 5.000000e0
196, 6.000000e0, 6.000000e0, 5.000000e0
197, 2.000000e0, 1.000000e0, 6.000000e0
198, 3.000000e0, 1.000000e0, 6.000000e0
199, 4.000000e0, 1.000000e0, 6.000000e0
200, 5.000000e0, 1.000000e0, 6.000000e0
201, 1.000000e0, 2.000000e0, 6.000000e0
202, 2.000000e0, 2.000000e0, 6.000000e0
203, 3.000000e0, 2.000000e0, 6.000000e0
204, 4.000000e0, 2.000000e0, 6.000000e0
205, 5.000000e0, 2.000000e0, 6.000000e0
206, 6.000000e0, 2.000000e0, 6.000000e0
207, 1.000000e0, 3.000000e0, 6.000000e0
208, 2.000000e0, 3.000000e0, 6.000000e0
209, 3.000000e0, 3.000000e0, 6.000000e0
210, 4.000000e0, 3.000000e0, 6.000000e0
211, 5.000000e0, 3.000000e0, 6.000000e0
212, 6.000000e0, 3.000000e0, 6.000000e0
213, 1.000000e0, 4.000000e0, 6.000000e0
214, 2.000000e0, 4.000000e0, 6.000000e0
215, 3.000000e0, 4.000000e0, 6.000000e0
216, 4.000000e0, 4.000000e0, 6.000000e0
217, 5.000000e0, 4.000000e0, 6.000000e0
218, 6.000000e0, 4.000000e0, 6.000000e0
219, 1.000000e0, 5.000000e0, 6.000000e0
220, 2.000000e0, 5.000000e0, 6.000000e0
221, 3.000000e0, 5.000000e0, 6.000000e0
222, 4.000000e0, 5.000000e0, 6.000000e0
223, 5.000000e0, 5.000000e0, 6.000000e0
224, 6.000000e0, 5.000000e0, 6.000000e0
225, 2.000000e0, 6.000000e0, 6.000000e0
226, 3.000000e0, 6.000000e0, 6.000000e0
227, 4.000000e0, 6.000000e0, 6.000000e0
228, 5.000000e0, 6.000000e0, 6.000000e0
229, 3.000000e0, 3.000000e0, 7.000000e0
230, 4.000000e0, 3.000000e0, 7.000000e0
231, 3.000000e0, 4.000000e0, 7.000000e0
232, 4.000000e0, 4.000000e0, 7.000000e0
**
*ELEMENT, TYPE=C3D8R, ELSET=EB1
1, 1, 2, 4, 3, 17, 18, 24, 23
2, 5, 6, 11, 10, 38, 39, 45, 44
3, 6, 7, 12, 11, 39, 40, 46, 45
4, 7, 8, 13, 12, 40, 41, 47, 46
5, 9, 10, 16, 15, 43, 44, 50, 49
6, 10, 11, 17, 16, 44, 45, 51, 50
7, 11, 12, 18, 17, 45, 46, 52, 51
8, 12, 13, 19, 18, 46, 47, 53, 52
9, 13, 14, 20, 19, 47, 48, 54, 53
10, 15, 16, 22, 21, 49, 50, 56, 55
11, 16, 17, 23, 22, 50, 51, 57, 56
12, 17, 18, 24, 23, 51, 52, 58, 57
13, 18, 19, 25, 24, 52, 53, 59, 58
14, 19, 20, 26, 25, 53, 54, 60, 59
15, 21, 22, 28, 27, 55, 56, 62, 61
16, 22, 23, 29, 28, 56, 57, 63, 62
17, 23, 24, 30, 29, 57, 58, 64, 63
18, 24, 25, 31, 30, 58, 59, 65, 64
19, 25, 26, 32, 31, 59, 60, 66, 65
20, 28, 29, 34, 33, 62, 63, 69, 68
21, 29, 30, 35, 34, 63, 64, 70, 69
22, 30, 31, 36, 35, 64, 65, 71, 70
23, 37, 38, 44, 43, 75, 76, 82, 81
24, 38, 39, 45, 44, 76, 77, 83, 82
25, 39, 40, 46, 45, 77, 78, 84, 83
26, 40, 41, 47, 46, 78, 79, 85, 84
27, 41, 42, 48, 47, 79, 80, 86, 85
28, 43, 44, 50, 49, 81, 82, 89, 88
29, 44, 45, 51, 50, 82, 83, 90, 89
30, 45, 46, 52, 51, 83, 84, 91, 90
31, 46, 47, 53, 52, 84, 85, 92, 91
32, 47, 48, 54, 53, 85, 86, 93, 92
33, 49, 50, 56, 55, 88, 89, 97, 96
34, 50, 51, 57, 56, 89, 90, 98, 97
35, 51, 52, 58, 57, 90, 91, 99, 98
36, 52, 53, 59, 58, 91, 92, 100, 99
37, 53, 54, 60, 59, 92, 93, 101, 100
38, 55, 56, 62, 61, 96, 97, 104, 103
39, 56, 57, 63, 62, 97, 98, 105, 104
40, 57, 58, 64, 63, 98, 99, 106, 105
41, 58, 59, 65, 64, 99, 100, 107, 106
42, 59, 60, 66, 65, 100, 101, 108, 107
43, 61, 62, 68, 67, 103, 104, 110, 109
44, 62, 63, 69, 68, 104, 105, 111, 110
45, 63, 64, 70, 69, 105, 106, 112, 111
46, 64, 65, 71, 70, 106, 107, 113, 112
47, 65, 66, 72, 71, 107, 108, 114, 113
48, 73, 74, 78, 77, 117, 118, 122, 121
49, 75, 76, 82, 81, 119, 120, 126, 125
50, 76, 77, 83, 82, 120, 121, 127, 126
51, 77, 78, 84, 83, 121, 122, 128, 127
52, 78, 79, 85, 84, 122, 123, 129, 128
53, 79, 80, 86, 85, 123, 124, 130, 129
54, 81, 82, 89, 88, 125, 126, 133, 132
55, 82, 83, 90, 89, 126, 127, 134, 133
56, 83, 84, 91, 90, 127, 128, 135, 134
57, 84, 85, 92, 91, 128, 129, 136, 135
58, 85, 86, 93, 92, 129, 130, 137, 136
59, 87, 88, 96, 95, 131, 132, 140, 139
60, 88, 89, 97, 96, 132, 133, 141, 140
61, 89, 90, 98, 97, 133, 134, 142, 141
62, 90, 91, 99, 98, 134, 135, 143, 142
63, 91, 92, 100, 99, 135, 136, 144, 143
64, 92, 93, 101, 100, 136, 137, 145, 144
65, 93, 94, 102, 101, 137, 138, 146, 145
66, 96, 97, 104, 103, 140, 141, 148, 147
67, 97, 98, 105, 104, 141, 142, 149, 148
68, 98, 99, 106, 105, 142, 143, 150, 149
69, 99, 100, 107, 106, 143, 144, 151, 150
70, 100, 101, 108, 107, 144, 145, 152, 151
71, 103, 104, 110, 109, 147, 148, 154, 153
72, 104, 105, 111, 110, 148, 149, 155, 154
73, 105, 106, 112, 111, 149, 150, 156, 155
74, 106, 107, 113, 112, 150, 151, 157, 156
75, 107, 108, 114, 113, 151, 152, 158, 157
76, 111, 112, 116, 115, 155, 156, 160, 159
77, 119, 120, 126, 125, 161, 162, 168, 167
78, 120, 121, 127, 126, 162, 163, 169, 168
79, 121, 122, 128, 127, 163, 164, 170, 169
80, 122, 123, 129, 128, 164, 165, 171, 170
81, 123, 124, 130, 129, 165, 166, 172, 171
82, 125, 126, 133, 132, 167, 168, 174, 173
83, 126, 127, 134, 133, 168, 169, 175, 174
84, 127, 128, 135, 134, 169, 170, 176, 175
85, 128, 129, 136, 135, 170, 171, 177, 176
86, 129, 130, 137, 136, 171, 172, 178, 177
87, 132, 133, 141, 140, 173, 174, 180, 179
88, 133, 134, 142, 141, 174, 175, 181, 180
89, 134, 135, 143, 142, 175, 176, 182, 181
90, 135, 136, 144, 143, 176, 177, 183, 182
91, 136, 137, 145, 144, 177, 178, 184, 183
92, 140, 141, 148, 147, 179, 180, 186, 185
93, 141, 142, 149, 148, 180, 181, 187, 186
94, 142, 143, 150, 149, 181, 182, 188, 187
95, 143, 144, 151, 150, 182, 183, 189, 188
96, 144, 145, 152, 151, 183, 184, 190, 189
97, 147, 148, 154, 153, 185, 186, 192, 191
98, 148, 149, 155, 154, 186, 187, 193, 192
99, 149, 150, 156, 155, 187, 188, 194, 193
100, 150, 151, 157, 156, 188, 189, 195, 194
101, 151, 152, 158, 157, 189, 190, 196, 195
102, 162, 163, 169, 168, 197, 198, 203, 202
103, 163, 164, 170, 169, 198, 199, 204, 203
104, 164, 165, 171, 170, 199, 200, 205, 204
105, 167, 168, 174, 173, 201, 202, 208, 207
106, 168, 169, 175, 174, 202, 203, 209, 208
107, 169, 170, 176, 175, 203, 204, 210, 209
108, 170, 171, 177, 176, 204, 205, 211, 210
109, 171, 172, 178, 177, 205, 206, 212, 211
110, 173, 174, 180, 179, 207, 208, 214, 213
111, 174, 175, 181, 180, 208, 209, 215, 214
112, 175, 176, 182, 181, 209, 210, 216, 215
113, 176, 177, 183, 182, 210, 211, 217, 216
114, 177, 178, 184, 183, 211, 212, 218, 217
115, 179, 180, 186, 185, 213, 214, 220, 219
116, 180, 181, 187, 186, 214, 215, 221, 220
117, 181, 182, 188, 187, 215, 216, 222, 221
118, 182, 183, 189, 188, 216, 217, 223, 222
119, 183, 184, 190, 189, 217, 218, 224, 223
120, 186, 187, 193, 192, 220, 221, 226, 225
121, 187, 188, 194, 193, 221, 222, 227, 226
122, 188, 189, 195, 194, 222, 223, 228, 227
123, 209, 210, 216, 215, 229, 230, 232, 231
**
*SOLID SECTION, ELSET=EB1, MATERIAL=Default-Steel
Because of its large size, the mesh structure for sphere_5 is not shown here.