Observe the effect of choosing the diameter to be Constant in the following example with only circular cross-section fibers. The generated structures are shown as 2D cross-section. To better observe the circular cross-section in 2D view, the fibers are all oriented perpendicular to the view direction.

When selecting Uniformly in interval, and entering a Minimum value and a Maximum value, the random diameters are distributed within the given interval and every feasible diameter has the same probability.

Taking the Gaussian distribution, the random diameter, length, or side length values follow a bell-shaped distribution. The values cluster around the entered Mean Value but may vary according to the entered Standard Deviation.

The value in Distribution Width corresponds to the interval on both sides of the mean value limiting the random diameter or angle values that are accepted.

As an example, a Distribution Width value of 10 means that the values may vary only -10 to +10  from the given Mean Value.

You can set the parameters so that negative values would be possible. Then, the negative values are ignored and only the range of possible values is generated. For example, a mean value of 20 and a distribution width of 25 would lead to values between 1 and 45.

For all distribution options (Gaussian, Probability Distribution and Log-Normal) on the right of the dialog the distribution is visualized in a 2D plot.

The red line shows the density distribution defined by Mean Value, Standard Deviation and Distribution Width. It displays how many objects of which diameter will be generated in percent. The blue curve shows the cumulative distribution.

The three dashed blue lines show the diameter values for 10% percentile, 50% percentile and 90% percentile of the distribution. For example, if the distribution is given for diameters as shown in the screenshot above, on average, 10% of the objects have a diameter smaller than 14µm (10% percentile), and 90% of the generated objects have a diameter smaller than 26µm (90% percentile). For further explanations, see the Wikipedia article.

Right-clicking into the plot opens a dialog to save the plot or to Edit the Axis Settings. Checking or unchecking the checkboxes next to the graph names decides which curves should be displayed.

More information about these options can be found in the Result Viewer User Guide.

If Cut-Off Distribution is checked, the distribution is truncated at the bounds. This means, that all values outside the bounds are dropped and not considered for generation. If this option is not checked, then all values that are outside of the bounds are set to be on the distribution bound. Not checking this option leads to an accumulation of values on the bounds.

In the following example, leaving Cut-Off Distribution unchecked leads to many objects with diameters of 40 or 60 µm.

In contrast, checking Cut-Off Distribution leads to more grains with diameter of 50 µm.

Further details on Gaussian distributions can be found e.g., on Wikipedia on Normal (or Gaussian) distributions.

The Probability Distribution table allows to enter user-defined probability distributions. The Number of Rows can be increased or decreased to enter as many value pairs as desired. The Value corresponds to the chosen property, e.g. diameter, length, or angle. The Count Probability of the values must lay between 0 and 1 and their sum must be equal to 1.

Especially for large tables, it is useful to observe the value of Probability Sum, i.e., the sum of the count probabilities. When the Probability Sum is not equal to 1, click the Normalize button to automatically round the Count Probability values.

The buttons Load and Save allow loading a previous probability distribution and saving the current one for later use.

The Log-Normal distribution describes the situation in which the logarithm of the diameter values follows a normal distribution.

The diameter values group around the entered Arithmetic Mean Value and scatter according to the entered Arithmetic Standard Deviation. The values in Lower Bound and Upper Bound restrict the possible values that the random diameters can take to the given interval.