The options in the Generation Mode panel control the distribution used for the stochastic field which is segmented to obtain the final structure. It is possible to choose Isotropic Squared-Exponential (Gaussian Kernel), Anisotropic Squared-Exponential (Gaussian Kernel), Isotropic Exponential (Laplacian Kernel), Anisotropic Exponential (Laplacian Kernel), Isotropic Linear Decay, Anisotropic Linear Decay, or a Custom random field.
An Isotropic Squared-Exponential (Gaussian Kernel) random field is used to create the structure. Enter the Correlation Length to define the standard deviation of the used Gauss kernel. With higher values the features of the generated structure become larger.
For the Gaussian Kernel the following equation applies:
(22) Isotropic Gaussian Kernel
where is the correlation length.
In the following example observe how the feature size changes for two different correlation lengths, while all other parameters are kept the same.
A Gaussian random field is used to create the structure. Enter the Correlation Length for X-direction , Y-direction , and Z-direction . These values define the standard deviations in each main axis of the used Gaussian kernel. Higher values lead to larger pores. If the same value is entered for all three directions, it is the same as Isotropic Squared-Exponential.
For the Gaussian Kernel the following equation applies:
(23) Anisotropic Gaussian Kernel
where is the correlation length in the respective direction.
In the following example, the values 3, 10 and 20 are used for , , and , respectively. Observe the different feature shapes for the different view directions.
An Isotropic Exponential (Laplacian Kernel) random field is used to create the structure. Enter the Correlation Length to define the standard deviation of the used LaplacianKernel. With higher values the features of the generated structure become larger.
For a Laplacian Kernel the following equation applies:
(24) Isotropic Laplacian Kernel
where is the correlation length.
In the following example observe how the feature size changes for two different correlation lengths, while all other parameters are kept the same.
An Laplacian random field is used to create the structure. Enter the Correlation Length for X-direction , Y-direction , and Z-direction . These values define the standard deviations in each main axis of the used Laplacian kernel. Higher values lead to larger pores. If the same value is entered for all three directions, it is the same as Isotropic Exponential.
For a Laplacian Kernel the following equation applies:
(25) Anisotropic Laplacian Kernel
where is the correlation length in the respective direction.
In the following example, the values 3, 10 and 20 are used for , , and , respectively. Observe the different feature shapes for the different view directions.
If Isotropic Linear Decay is selected, a linear decreasing correlation function is used to create the stochastic field. It starts in 0 with the value 1. The correlation function reaches 0 in and stays 0 for larger values. Thus, the gradient is between 0 and sigma and 0 for larger values.
With higher values the features of the generated structure become larger. It can be necessary to post-process the results withProcessGeo Cleanse.
If Anisotropic LinearDecay is selected, different linear decreasing correlation functions are used for X-, Y-, and Z-direction to create the stochastic field. They are defined as described for the isotropic case above. Enter , , and to determine the corresponding gradients: , , and . Higher values lead to larger features. It can be necessary to post-process the results with ProcessGeo Cleanse.
In this example, observe the differences in the three view directions.
A Custom stochastic field is created and segmented to generate the structure.
If checked, the tab Custom Generation Options becomes available. Combine the different random field and gradient options in the Custom Generation Options tab. This tab can also be reached by clicking Go To Tab in the Generation Mode panel. In addition to linear and Gaussian random fields also linear gradient, sphere gradient and membrane gradient are available.
Isotropic Squared-Exponential (Gaussian Kernel)
