Some basic questions about orientation fibers #918

killuaLeo · 2024-10-09T17:26:31Z

killuaLeo
Oct 9, 2024

Hi All,

For the orientation fibers, there are two vectors defined, one is the crystal direction vector, another is the ideal fiber direction vector. I want to know if the textured case is the perfect fiber, how this rotation is made? I considered the rotation process should be rotating from crystal direction to the fiber direction at the first time. However, I have tried one case and the rotation angles I have got is not the same as what I have thought. Can anyone help me with this question?

Best,
Di

Answered by rquey

Oct 10, 2024

@killuaLeo, you said:

The rotation angles from (1,0,0) to (0.7071,0.7071,0) in Euler-Bunge convention should be 45, 0, 0. However the .tess file didn't show the same rotation angles.

and the orientations are:

*ori
euler-bunge:active
45.000000000000 37.197179036517 -60.000000000000
-135.000000000000 77.644451093533 120.000000000000
-135.000000000000 76.639503389212 120.000000000000
-135.000000000000 74.478996824115 120.000000000000
-135.000000000000 49.348717797102 120.000000000000
-135.000000000000 71.980488627940 120.000000000000
45.000000000000 88.126367666311 -60.000000000000
45.000000000000 46.119024590915 -60.000000000000
45.000000000000 19.202892350055 -60.000000000000
-135.000000…

View full answer

mkasemer · 2024-10-09T17:54:20Z

mkasemer
Oct 9, 2024
Maintainer

So we are on the same page: a crystallographic fiber is defined by:

A crystal direction
A sample direction

In other words, it defines the set of orientations which have a specific crystal direction aligned with a specific sample direction.

However... without further description of what, exactly, you think is incorrect we cannot properly diagnose your issue. Please provide a MWE, as well as code version you are using.

5 replies

killuaLeo Oct 9, 2024
Author

Hi,

Thanks for your reply! I am trying to create a hcp polycrystal system with the crystal direction of (1, 0, 0) and the sample direction of (0.7071, 0.7071, 0). The input command shows as follows:
neper -T -n 10 -domain "cube(0.01,0.01,0.001)" -morpho "columnar(z),gg" -crysym hexagonal -ori "fiber(1,0,0,0.7071,0.7071,0)" -o inclined10texturedplate2 -format tess -ori descriptor euler-bunge:active
The rotation angles from (1,0,0) to (0.7071,0.7071,0) in Euler-Bunge convention should be 45, 0, 0. However the .tess file didn't show the same rotation angles. By the way, the version I'm using is 4.8.2-2.

The tesselation file output is shown below:
***tess
**format
3.4
**general
3 standard
**cell
10
*crysym
hexagonal
*seed
1 0.006573795799 0.004966463284 0.000500000000 0.002525151621
2 0.003748635307 0.002189794547 0.000500000000 0.003211142648
3 0.000837588783 0.009163960137 0.000500000000 0.000000000000
4 0.003690521437 0.008786240411 0.000500000000 0.001913349507
5 0.001296061509 0.006058105059 0.000500000000 0.000848029538
6 0.007502271456 0.003567489836 0.000500000000 0.000000142653
7 0.000503464383 0.001948616264 0.000500000000 0.002943262638
8 0.008738556418 0.009563674974 0.000500000000 0.005820341864
9 0.007888171659 0.004851784223 0.000500000000 0.001973236930
10 0.005189821980 0.005909055911 0.000500000000 0.002493279442
*ori
euler-bunge:active
45.000000000000 37.197179036517 -60.000000000000
-135.000000000000 77.644451093533 120.000000000000
-135.000000000000 76.639503389212 120.000000000000
-135.000000000000 74.478996824115 120.000000000000
-135.000000000000 49.348717797102 120.000000000000
-135.000000000000 71.980488627940 120.000000000000
45.000000000000 88.126367666311 -60.000000000000
45.000000000000 46.119024590915 -60.000000000000
45.000000000000 19.202892350055 -60.000000000000
-135.000000000000 69.114813460200 120.000000000000
**vertex
44
1 0.007974814530 0.002609749195 0.001000000000 0
2 0.007974814530 0.002609749195 -0.000000000000 0
3 0.005089661506 0.004359523842 -0.000000000000 0
4 0.007269483994 0.002141632925 -0.000000000000 0
5 0.007269483994 0.002141632925 0.001000000000 0
6 0.005089661506 0.004359523842 0.001000000000 0
7 0.008101725922 0.004064323974 0.001000000000 0
8 0.005668852724 0.005209928841 0.001000000000 0
9 0.005668852724 0.005209928841 -0.000000000000 0
10 0.008101725922 0.004064323974 -0.000000000000 0
11 0.002025816707 -0.000000000000 -0.000000000000 0
12 0.002025816707 -0.000000000000 0.001000000000 0
13 0.008055526507 -0.000000000000 -0.000000000000 0
14 0.008055526507 -0.000000000000 0.001000000000 0
15 0.002513082545 0.005357929411 0.001000000000 0
16 0.001667465181 0.004821793808 0.001000000000 0
17 0.001667465181 0.004821793808 -0.000000000000 0
18 0.002513082545 0.005357929411 -0.000000000000 0
19 0.000000000000 0.010000000000 0.000000000000 0
20 0.000000000000 0.010000000000 0.001000000000 0
21 0.001758144702 0.010000000000 0.001000000000 0
22 0.001758144702 0.010000000000 -0.000000000000 0
23 -0.000000000000 0.007569326472 -0.000000000000 0
24 -0.000000000000 0.007569326472 0.001000000000 0
25 0.001464961835 0.007785577722 0.001000000000 0
26 0.001464961835 0.007785577722 -0.000000000000 0
27 0.002568920602 0.006816643014 0.001000000000 0
28 0.002568920602 0.006816643014 -0.000000000000 0
29 0.003094680803 0.010000000000 -0.000000000000 0
30 0.003094680803 0.010000000000 0.001000000000 0
31 0.003509459913 0.007306757951 0.001000000000 0
32 0.003509459913 0.007306757951 -0.000000000000 0
33 -0.000000000000 0.005143397827 -0.000000000000 0
34 -0.000000000000 0.005143397827 0.001000000000 0
35 0.010000000000 0.000000000000 0.000000000000 0
36 0.010000000000 0.000000000000 0.001000000000 0
37 0.010000000000 0.002001228678 -0.000000000000 0
38 0.010000000000 0.002001228678 0.001000000000 0
39 0.000000000000 0.000000000000 0.000000000000 0
40 0.000000000000 0.000000000000 0.001000000000 0
41 0.010000000000 0.010000000000 0.000000000000 0
42 0.010000000000 0.010000000000 0.001000000000 0
43 0.010000000000 0.003721730431 0.001000000000 0
44 0.010000000000 0.003721730431 -0.000000000000 0
**edge
84
1 2 4 0
2 4 3 0
3 3 9 0
4 9 10 0
5 10 2 0
6 6 5 0
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8 1 7 0
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11 2 1 0
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51 27 28 0
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54 33 34 0
55 34 24 0
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57 17 33 0
58 34 16 0
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60 36 35 0
61 35 37 0
62 37 38 0
63 38 36 0
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65 13 35 0
66 2 37 0
67 38 1 0
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69 40 34 0
70 33 39 0
71 39 11 0
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74 42 43 0
75 43 44 0
76 44 41 0
77 41 29 0
78 30 42 0
79 44 10 0
80 9 32 0
81 7 43 0
82 31 8 0
83 37 44 0
84 43 38 0
**face
51
1 5 2 4 3 9 10
5 1 2 3 4 5
-0.000000000000 -0.000000000000 -0.000000000000 -1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
2 5 6 5 1 7 8
5 6 7 8 9 10
0.001000000000 0.000000000000 0.000000000000 1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
3 4 2 1 7 10
4 11 8 12 5
-0.007717794092 -0.996215328717 0.086919611308 -0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
4 4 3 6 8 9
4 13 -10 14 -3
-0.001752611629 -0.826512396759 0.562918518086 0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
5 4 1 2 4 5
4 -11 1 15 7
-0.002235467325 -0.552978262241 0.833195680191 -0.000000000000
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6 4 3 4 5 6
4 -2 15 -6 -13
-0.006685801725 -0.713201069624 -0.700959509734 0.000000000000
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7 4 7 8 9 10
4 9 14 4 -12
-0.007128530029 -0.426017251163 -0.904715038955 -0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
8 4 12 11 13 14
4 16 17 18 19
-0.000000000000 -0.000000000000 -1.000000000000 -0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
9 6 3 4 13 11 17 18
6 -2 20 -17 21 22 23
-0.000000000000 -0.000000000000 -0.000000000000 -1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
10 6 12 14 5 6 15 16
6 -19 24 -6 25 26 27
0.001000000000 0.000000000000 0.000000000000 1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
11 4 11 12 16 17
4 -16 -27 28 -21
-0.002020245146 -0.997249721186 -0.074114732640 0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
12 4 3 6 15 18
4 13 25 29 23
-0.005903982638 -0.361315159271 -0.932443754701 -0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
13 4 13 14 5 4
4 18 24 -15 20
-0.007562255761 -0.938766169309 -0.344554900358 -0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
14 4 15 16 17 18
4 26 28 22 -29
-0.003179417273 0.535463987428 -0.844558060862 -0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
15 4 20 19 23 24
4 30 31 32 33
-0.000000000000 -1.000000000000 -0.000000000000 -0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
16 4 19 20 21 22
4 -30 34 35 36
0.010000000000 0.000000000000 1.000000000000 0.000000000000
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4 -36 37 38 -31
-0.000000000000 -0.000000000000 -0.000000000000 -1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
18 4 21 20 24 25
4 -34 -33 39 40
0.001000000000 0.000000000000 0.000000000000 1.000000000000
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-0.000430418689 -0.991349083655 0.131251645081 -0.000000000000
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4 32 39 -41 38
0.007488181014 -0.146033136903 0.989279699037 -0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
21 4 22 21 30 29
4 -35 42 43 44
0.010000000000 0.000000000000 1.000000000000 0.000000000000
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5 45 -37 -44 46 47
-0.000000000000 -0.000000000000 -0.000000000000 -1.000000000000
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5 -40 48 49 50 -42
0.001000000000 0.000000000000 0.000000000000 1.000000000000
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0.006817795143 0.659649335909 0.751573518450 -0.000000000000
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4 -43 -50 -52 -46
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-0.000000000000 -1.000000000000 -0.000000000000 -0.000000000000
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6 -48 -39 -55 58 -26 59
0.001000000000 0.000000000000 0.000000000000 1.000000000000
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-0.002306297449 -0.999268164318 0.038250957905 -0.000000000000
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0.010000000000 1.000000000000 0.000000000000 0.000000000000
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5 -63 67 -7 -24 -64
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4 68 69 -54 70
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4 -68 71 -16 72
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0 0 0.000000000000 0.000000000000 0.000000000000
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4 -71 -70 -57 -21
-0.000000000000 -0.000000000000 -0.000000000000 -1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
40 4 40 12 16 34
4 -72 -27 -58 -69
0.001000000000 0.000000000000 0.000000000000 1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
41 4 41 42 43 44
4 73 74 75 76
0.010000000000 1.000000000000 0.000000000000 0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
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4 -73 77 -43 78
0.010000000000 0.000000000000 1.000000000000 0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
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6 -76 79 -4 80 -46 -77
-0.000000000000 -0.000000000000 -0.000000000000 -1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
44 6 8 7 43 42 30 31
6 -9 81 -74 -78 -50 82
0.001000000000 0.000000000000 0.000000000000 1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
45 4 43 44 10 7
4 75 79 -12 81
0.005438630738 0.177607027223 0.984101490641 -0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
46 4 8 9 32 31
4 14 80 52 82
0.007686859747 0.696637512576 0.717423289329 -0.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
47 4 38 37 44 43
4 -62 83 -75 84
0.010000000000 1.000000000000 0.000000000000 0.000000000000
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4 -66 -5 -79 -83
-0.000000000000 -0.000000000000 -0.000000000000 -1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
49 4 1 38 43 7
4 -67 -84 -81 -8
0.001000000000 0.000000000000 0.000000000000 1.000000000000
0 0 0.000000000000 0.000000000000 0.000000000000
50 5 3 18 28 32 9
5 -23 -56 -47 -80 -3
-0.000000000000 -0.000000000000 -0.000000000000 -1.000000000000
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51 5 27 15 6 8 31
5 -59 -25 -10 -82 -49
0.001000000000 0.000000000000 0.000000000000 1.000000000000
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**polyhedron
10
1 7 1 2 -3 4 -5 6 -7
2 8 8 9 10 11 -6 -12 -13 -14
3 6 15 16 17 18 -19 -20
4 7 21 22 23 19 24 -25 26
5 8 27 28 29 20 25 -30 -31 14
6 7 32 33 34 35 -36 5 13
7 6 37 38 39 40 -11 31
8 8 41 42 43 44 -45 7 -46 -26
9 6 47 48 49 3 36 45
10 7 50 51 -4 -24 30 12 46
**domain
*general
cube
*vertex
8
1 0.000000000000 0.000000000000 0.000000000000 x0y0z0
1 39
2 0.010000000000 0.000000000000 0.000000000000 x1y0z0
1 35
3 0.010000000000 0.010000000000 0.000000000000 x1y1z0
1 41
4 0.000000000000 0.010000000000 0.000000000000 x0y1z0
1 19
5 0.000000000000 0.000000000000 0.001000000000 x0y0z1
1 40
6 0.000000000000 0.010000000000 0.001000000000 x0y1z1
1 20
7 0.010000000000 0.010000000000 0.001000000000 x1y1z1
1 42
8 0.010000000000 0.000000000000 0.001000000000 x1y0z1
1 36
*edge
12
1 2 4 6
x0y1
1 30
2 2 6 5
x0z1
3 33 55 69
3 2 5 1
x0y0
1 68
4 2 1 4
x0z0
3 31 53 70
5 2 2 8
x1y0
1 60
6 2 8 7
x1z1
3 63 74 84
7 2 7 3
x1y1
1 73
8 2 3 2
x1z0
3 61 76 83
9 2 5 8
y0z1
3 19 64 72
10 2 2 1
y0z0
3 17 65 71
11 2 4 3
y1z0
3 36 44 77
12 2 7 6
y1z1
3 34 42 78
*face
6
1 4 4 6 5 1
4 1 2 3 4
plane
4 0.000000000000 1.000000000000 0.000000000000 0.000000000000
x0
3 15 27 37
2 4 2 8 7 3
4 5 6 7 8
plane
4 -0.010000000000 -1.000000000000 -0.000000000000 -0.000000000000
x1
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3 4 1 5 8 2
4 3 9 5 10
plane
4 0.000000000000 0.000000000000 1.000000000000 0.000000000000
y0
3 8 33 38
4 4 4 3 7 6
4 11 7 12 1
plane
4 -0.010000000000 -0.000000000000 -1.000000000000 -0.000000000000
y1
3 16 21 42
5 4 1 2 3 4
4 10 8 11 4
plane
4 0.000000000000 0.000000000000 0.000000000000 1.000000000000
z0
10 1 9 17 22 28 34 39 43 48 50
6 4 5 6 7 8
4 2 12 6 9
plane
4 -0.001000000000 -0.000000000000 -0.000000000000 -1.000000000000
z1
10 2 10 18 23 29 35 40 44 49 51
***end
__

mkasemer Oct 9, 2024
Maintainer

I would suggest taking some of those Euler-Bunge angles, converting to a rotation matrix, and transforming a 001 vector to the sample frame. This is the test to make sure those orientations yield something as-expected. Is this the case (my suspicion is yes, but I will let you do the verification).

killuaLeo Oct 9, 2024
Author

For the first angle set, the rotation matrix is

[0.8413   -0.1342   -0.5236
    0.3307    0.8940    0.3023
    0.4275   -0.4275    0.7966]

Using this to rotate 001 vector will get -0.5236, 0.3023, 0.7966 vector, also using this to rotate 100 vector will get 0.8413, 0.3307, 0.4275 vector.

For the second angle set, the rotation matrix is

[0.4846    0.2225    0.8460
    0.5367    0.6880   -0.4884
   -0.6907    0.6907    0.2140]

Using this to rotate 001 vector will get 0.8460, -0.4884, 0.2140 vector, also using this to rotate 100 vector will get 0.4846, 0.5367, -0.6907 vector.

rquey Oct 10, 2024
Maintainer

@killuaLeo, you said:

The rotation angles from (1,0,0) to (0.7071,0.7071,0) in Euler-Bunge convention should be 45, 0, 0. However the .tess file didn't show the same rotation angles.

and the orientations are:

*ori
euler-bunge:active
45.000000000000 37.197179036517 -60.000000000000
-135.000000000000 77.644451093533 120.000000000000
-135.000000000000 76.639503389212 120.000000000000
-135.000000000000 74.478996824115 120.000000000000
-135.000000000000 49.348717797102 120.000000000000
-135.000000000000 71.980488627940 120.000000000000
45.000000000000 88.126367666311 -60.000000000000
45.000000000000 46.119024590915 -60.000000000000
45.000000000000 19.202892350055 -60.000000000000
-135.000000000000 69.114813460200 120.000000000000

(1, 0, 0) | (0.707, 0.707, 0) is indeed obtained by a rotation of 45 degrees about Z, and this is why you get either 45 or (the equivalent -135) as first Euler angle. But a fiber is not just one orientation. It is all orientations obtained by rotation about the axis of the fiber, i.e. the 45°-tilted x. This is actually the second Euler angle. As for the third one, -60 and 120 is equivalent to 0 under hexagonal crystal symmetry.

In conclusion, the orientations do describe the specified orientation fiber.

PS. You should update to 4.10.1.

Answer selected by rquey

mkasemer Oct 11, 2024
Maintainer

@killuaLeo I was not aware that you were working with hexagonal symmetry, as I did not read closely enough. I also had a question on this, but @rquey is indeed correct.

Note that Neper will generate any orientation that lies along that fiber, and for any of the symmetrically equivalent crystallographic directions. For your case, you are interested in 1 0 0. A symmetrically equivalent crystallographic direction, would be (in MATLAB):

>> c = [sind(30) cosd(30) 0]';

When using the rotation matrix (which you have transposed, as @rquey said, please update Neper---EDIT: I may be incorrectly transposing, so please ignore that.):

>> R*c
ans =
    0.7071
    0.7071
    0.0000

Hope this helps clear up.

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Some basic questions about orientation fibers #918

killuaLeo Oct 9, 2024

Replies: 1 comment · 5 replies

mkasemer Oct 9, 2024 Maintainer

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