# Specifying Orientation Information for Tessellation Cells

Important

Read first: Generating and Meshing a Simple Tessellation and (optionally) Generating and Meshing a Fundamental Region of Orientation Space and Plotting a Pole Figure.

Orientations for the cells can be specified as input, using option `-ori`

. By default, “random orientations” are generated:

```
$ neper -T -n 1000 -crysym cubic
```

This generates a Tessellation File (.tess) named `n1000-id1.tess`

.

Note

In general, it is important to define the crystal symmetry, using

`-crysym`

.It is possible to generate only orientations (no actual tessellation) using

`-format`

`ori`

, which only produces an orientation file (technically a Data File) of extension`.ori`

.In the case where an actual tessellation is generated, the cell orientations are generated after (and fully independently of) the tessellation morphology.

The orientations can be visualized on a pole figure using the Visualization Module (-V) and `-space`

`pf`

:

```
$ neper -V n1000-id1.tess -imagesize 500:500 -space pf -print img1
```

We recognize a distribution of random orientations. The apparent higher density in the center is due to the use of the stereographic projection (see `-pfprojection`

), and an equal-area projection would effectively produce uniform density.

## Using an ODF

An ODF can be specified by providing a mesh of orientation space and intensity values at the mesh elements. A mesh of the fundamental region of Rodrigues space (for the considered crystal symmetry, here *cubic*) can be generated as follows (see tutorial “Generating and Meshing a Fundamental Region of Orientation Space”):

```
$ neper -T -n 1 -domain "rodrigues(cubic)" -o fr
$ neper -M fr.tess -cl 0.05
```

The elemental values of the ODF, which are defined externally, are written in an external file, `odf.txt`

. In the present case, it defines a generic rolling texture of an FCC material. The mesh of orientation space (generated as described above) also is provided by an external file, `fr.msh`

.

Cell orientations can be generated from the ODF as follows:

```
$ neper -T -n 1000 -ori "odf(mesh=file(fr.msh),val=file(odf.txt))" -crysym cubic
```

Important

The crystal symmetry must be specified using `-crysym`

and should be the same as the one of the orientation space (`fr.msh`

); otherwise, an error is generated.

The orientations can be visualized as before:

```
$ neper -V n1000-id1.tess -imagesize 500:500 -space pf -print img2
```

We recognize a typical rolling texture.

## Using Discrete Orientations and Orientation Fibers

An orientation distribution can be defined from “base”, discrete orientations and orientation fibers (see `-ori`

and Rotations and Orientations), optionally surrounded by distributions.

A simple case of a Cube-type orientation distribution can be obtained as follows:

```
$ neper -T -n 1000 -crysym cubic -ori "Cube:normal(8)"
```

Note

“`normal(8)`

” generates a distribution about the nominal orientation corresponding to a tri-variate normal distribution (in tangent space, \(r\,\theta\)) of a (1D) standard deviation equal to 8 degrees. When applied to an orientation fiber, the distribution becomes bi-variate (perpendicular to the fiber).

The orientations can be visualized as before:

```
$ neper -V n1000-id1.tess -imagesize 500:500 -space pf -print img3
```

A simple case of a \(\left<1 0 0\right> | X_i\) fiber surrounded by a distribution of a 1D standard deviation of 4 degrees can be obtained as follows:

```
$ neper -T -n 1000 -crysym cubic -ori "fiber(1,0,0,1,0,0):normal(4)"
```

The orientations can be visualized as before:

```
$ neper -V n1000-id1.tess -imagesize 500:500 -space pf -print img5
```

Several orientations (or orientation fibers) can be used to produce more complex distributions, each with its own weight and distribution. An example is as follows:

```
$ neper -T -n 1000 -crysym cubic -ori "2*Brass1:normal(3.9)+2*Brass2:normal(3.9)+S1:normal(4.7)+S2:normal(4.7)+S3:normal(4.7)+S4:normal(4.7)+0.8*Copper1:normal(5.6)+0.8*Copper2:normal(5.6)+Cube:normal(3.9)+2*Goss:normal(3.9)"
```

The orientations can be visualized as before:

```
$ neper -V n1000-id1.tess -imagesize 500:500 -space pf -print img4
```

Incidentally, it is similar to the one generated in Using an ODF.