Observe the effect of choosing the diameter to be constant in the following example with only infinite circular cross-section objects. The generated structures are shown as 3D Rendering and as 2D cross-section. To better observe the circular cross-section in 2D view, the Anisotropy in Plane is set to 100.

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 Bound corresponds to the interval on both sides of the mean value limiting the random diameter or angle values that are accepted. For diameters, a Distribution Bound value of 10 µm means that the diameter values may vary only -10 µm to +10 µm 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 diameters is generated. For example, a diameter mean value of 20 µm and a distribution bound of 25 µm and a voxel length of 1 µm would lead to values between 1 and 50 µm.

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 Diameter Percentage 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 diameter distribution.

The three dashed blue lines show the diameter values for 10% percentile, 50% percentile and 90% percentile of the distribution. On average, 10% of the objects have a diameter smaller than the 10% percentile value, and 90% of the generated objects have a diameter higher than that value. 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 Values correspond to the chosen property, e.g. diameter, length, or angle. Their Count Probability must lay between 0 and 1.

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.