Procedures

Function that returns the theoretical acf PARAM%imp_acf.

Function that returns the acf of an array. $$\begin{align*} acf(i,j) &= (z \ast z)(i,j) = \sum_{k,l}^{n,n} z(k+1-i,l+1-j)z(k,l) \\ TF(acf) &= ACF = Z \cdot Z \\ acf &= TF^{-1}(ACF) = TF^{-1}(Z^2) \end{align*}$$

Function that returns the starting surface of random heights

Function that adds to the series mean the border integrals as explained in the docs

Function that allocates arrays in global variable PARAM

Function that returns an apodized array.
To prevent gaps from appearing after FFT (because of non periodic waves), the surface must be transformed, but not too much. Here a modified Tukey window is determined. The starting surface is not modified below the “correlation lengths”. Above the correlation lengths, a smooth decrease is forced with a cosine squared.

Function that apodize the acf to prevent spectral leakage

Function that apodize the reference surface for acf calculus purposes

Function that returns $\exp \left(\alpha \sqrt{\left(\frac{x}{\tau_1}\right)^2+ \left(\frac{y}{\tau_2}\right)^2} \right)$

Function that returns a set of heights that matches desired statistical moments.

Function that returns the autocorrelation function of a surface in PARAM%acf_surf

Function that returns …

Function that returns the theoretical autocorrelation function in an array.
The autocorrelation function is supposed to be obtained from a real surface which must be periodic or nearly periodic (because of the use of FFTs). In addition, the surface is supposed to be 0 mean and normalized ($\sigma = 1$), therefore acf is zero-mean and normalized so that its max value is 1.

Function that returns the vector PARAM%order that contains the heights order.

Function that returns crit_acf the mean absolute difference between theoretical and calculated acfs, above z (usually 0.2 as recommended by iso 25178)

Function that returns PARAM%surf, the surface made of heights with the required statistical moments, in the right order.

Function that returns the starting surface of random heights

Function to calculate the skewness and kurtosis of an exponential series.
The principle is the same as calculs_skku_tan, however it fits better some particular series quite binary (roughly two heights).

Function to calculate the skewness and kurtosis of a tangent series

Quantify de distance between desired moments and calculated moments

Geometrical characteristics of the numerical surface

Function that applies the digital filter to the random heights

The loop ends here

End of script

Generic cost function: difference between the imposed statistical moments and those obtained. The optimization problem must be turned into a maximization problem (as often in the optimization routines).

Function that reads a digital surf file and turns it into a mask

This subroutine initializes a real matrix tab of dimensions nx by ny with ones

Function that creates a periodic macro-texture: knowing the FFT of an analytical texture

Number of concurrent threads

This is a refactoring of the PIKAIA unconstrained optimization code from the High Altitude Observatory. The original code is public domain and was written by Paul Charbonneau & Barry Knapp.

Function that calculates the mean absolute difference between the desired Acf and the one obtained. However, the important zone where both should match is above the cut - where the correlation lengths are determined.

Main function…

Function that generates the heights when the function limits have been determined.

Function that reads a digital surf file and returns the surface in PARAM%surf

Function that reads a script file. Keywords are identified and corresponding actions are triggered.

Function that set parameters for image reproduction

Function that save an array tab as a digital surf file.

Function that applies a low-pass filter to the surface PARAM%surf

Returns the default surface spectrum

Starting the loop

Start the script reading

Required statistical moments

Define surface statistical moments as reference

Function that returns the best subsurface from the final surface.

The function analyses determinates ISO 25178 parameters of the current surface.

Profile function based on the tangent function