slippy.surface.HurstFractalSurface

class slippy.surface.HurstFractalSurface(sigma: float, hurst_exponent: float, roll_off_frequency: float = 0, generate: bool = False, grid_spacing: Optional[float] = None, extent: Optional[tuple] = None, shape: Optional[tuple] = None)

Hurst fractal surfaces

Parameters

• sigma (float) – The RSM roughness of the surface

• hurst_exponent (float) – The hurst exponent, must be between 0 and 1, related to the fractal dimension by D = 3-H

• roll_off_frequency (float, optional (0.0)) –

• generate (bool, optional (False)) – If true the surface profile is generated on instantiation, two of: grid_spacing, extent or shape must be set

• grid_spacing (float, optional (None)) – The grid spacing of the surface profile

• extent (tuple, optional (None)) – The overall surface dimensions in the x and y directions

• shape (tuple, optional (None)) – The number of grid points in the x and y directions, computation is faster for powers of 2

See also

ProbFreqSurface, RandomSurface, surface_like

Notes

generates a hurst fractal surface with frequency components from q0 to cut off frequency in even steps of q0.

amplitudes are given by:

q0 amplitude**2 *((h**2+k**2)/2)**(1-Hurst parameter)

where h,k = -N…N where N=cut off frequency/ q0 phases are randomly generated on construction of the surface object, repeated calls to the discretise function will discretise on the same surface but repeated calls to this class will generate different realisations

References

A new efficient numerical method for contact mechanics of rough surfaces C.Putignano L.Afferrante G.Carbone G.Demelio

Examples

>>> #create the surface object with the specified fractal parameters
>>> my_surface=HurstFractalSurface(1,0.2,1000, shape=(128, 128), grid_spacing=0.01)
>>> #descrtise the surface over a grid 1 unit by 1 unit with a grid_spacing of 0.01
>>> my_surface.discretise()
>>> my_surface.show()

__init__(sigma: float, hurst_exponent: float, roll_off_frequency: float = 0, generate: bool = False, grid_spacing: Optional[float] = None, extent: Optional[tuple] = None, shape: Optional[tuple] = None)

Methods

__init__(sigma, hurst_exponent[, ...])
convert_coordinates(y_coord, x_coord)
discretise([return_new])	Generate a new profile realisation, return a new surface if needed
fill_holes([hole_value, mk_copy, ...])	Replaces specified values with filler
find_summits([mask, four_nearest, ...])	Find summits after low pass filtering
get_acf([profile_in])	Find the auto correlation function of the surface
get_fft([profile_in])	Find the fourier transform of the surface
get_height_of_mat_vr(ratio[, void, mask, ...])	Find the height of a given material or void volume ratio
get_mat_vr(height[, void, mask, ratio])	Find the material or void volume ratio for a given height
get_points_from_extent([extent, ...])	Gets the grid points from the extent and the grid spacing
get_psd()	Find the power spectral density of the surface
get_summit_curvature([summits, mask, ...])	Get summit curvatures
interpolate(y_points, x_points[, mode, ...])	Easy memoized interpolation on surface objects
low_pass_filter(cut_off_freq[, return_copy])	Low pass FIR filter the surface profile
max_shape()
mesh(depth[, method, parameters])	Returns a Mesh object for the surface
read_al3d(file_name[, return_data])	Reads an alicona al3d file and sets the profile and grid_spacing property of the surface
read_csv(file_name[, delimiter, ...])	Read a profile from a csv or txt file, header lines are automatically skipped
read_mat(path[, profile_name, grid_spacing_name])	Reads .mat files as surfaces
resample([new_grid_spacing, return_profile, ...])	Resample or crop the profile by interpolation
rotate(radians)
roughness(parameter_name[, mask, ...])	Find areal roughness parameters
shift([shift])
show([property_to_plot, plot_type, ax, ...])	Plot surface properties
subtract_polynomial(order[, mask])	Flatten the surface by subtracting a polynomial
wear(name, x_pts, y_pts, depth)	Add wear / geometry changes to the surface profile

Attributes

acf	The auto correlation function of the surface profile
dimensions	The number of spatial dimensions that
extent	The overall dimensions of the surface in the same units as grid spacing
fft	The fast fourier transform of the surface
grid_spacing	The distance between grid points in the x and y directions
is_analytic
is_discrete	A bool flag, True if there is a profile present
mask	A mask used to exclude some values from analysis, a single float or an array of bool the same size as profile Either a boolean array of size self.size or a float of the value to be excluded
material	A material object describing the properties of the surface
moving_surface
profile	The height data for the surface profile
psd	The power spectral density of the surface
shape	The shape of the surface profile array, the number of points in each direction
size	The total number of points in the surface
surface_type	A description of the surface type
unworn_profile
wear_volumes