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Generate a random, self-affine surface topography map
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# Copyright (c) 2015 Lars Pastewka | |
# | |
# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files | |
# (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, | |
# publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do | |
# so, subject to the following conditions: | |
# | |
# The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. | |
# | |
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF | |
# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE | |
# FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN | |
# CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. | |
# | |
# This code uses a Fourier-filtering algorithm to create the rough surfaces. | |
# The algorithm is briefly described in sections 3 of the following papers: | |
# T. D. B. Jacobs, T. Junge, and L. Pastewka, Surf. Topogr. Metrol. Prop. 5, 13001 (2017). | |
# S. B. Ramisetti, C. Campañá, G. Anciaux, J.-F. Molinari, M. H. Müser, and M. O. Robbins, J. Phys. Condens. Matter 23, 215004 (2011). | |
# | |
from __future__ import division, print_function | |
import sys | |
from argparse import ArgumentParser, ArgumentTypeError | |
import numpy as np | |
### | |
def progressbar(x, maxx, len=60): | |
xx = x/maxx | |
return '|'+int(xx*len)*'#'+((len-int(xx*len))*'-')+'| {:>3}% ' \ | |
'({}/{})'.format(int(xx*100), x, maxx) | |
### | |
def irfft2(karr, rarr): | |
nrows, ncolumns = karr.shape | |
for i in range(ncolumns): | |
sys.stdout.write('{}\r'.format(progressbar(i, ncolumns+nrows-1))) | |
sys.stdout.flush() | |
karr[:, i] = np.fft.ifft(karr[:, i]) | |
for i in range(nrows): | |
sys.stdout.write('{}\r'.format(progressbar(i+ncolumns, ncolumns+nrows-1))) | |
sys.stdout.flush() | |
rarr[i, :] = np.fft.irfft(karr[i, :]) | |
### | |
def self_affine_prefactor(nx, ny, sx, sy, Hurst, rms_height=None, | |
rms_slope=None, short_cutoff=None, long_cutoff=None): | |
if short_cutoff is not None: | |
q_max = 2*np.pi/short_cutoff | |
else: | |
q_max = np.pi*min(nx/sx, ny/sy) | |
if long_cutoff is not None: | |
q_min = 2*np.pi/long_cutoff | |
else: | |
q_min = 2*np.pi*max(1/sx, 1/sy) | |
area = sx*sy | |
if rms_height is not None: | |
fac = 2*rms_height/np.sqrt(q_min**(-2*Hurst)- | |
q_max**(-2*Hurst))*np.sqrt(Hurst*np.pi) | |
elif rms_slope is not None: | |
fac = 2*rms_slope/np.sqrt(q_max**(2-2*Hurst)- | |
q_min**(2-2*Hurst))*np.sqrt((1-Hurst)*np.pi) | |
else: | |
raise ValueError('Neither rms height nor rms slope is defined!') | |
return fac * nx*ny/np.sqrt(area) | |
def Fourier_synthesis(nx, ny, sx, sy, Hurst, rms_height=None, rms_slope=None, | |
short_cutoff=None, long_cutoff=None, rolloff=1.0, | |
rfn='rarr.numpy', kfn='karr.numpy'): | |
if short_cutoff is not None: | |
q_max = 2*np.pi/short_cutoff | |
else: | |
q_max = np.pi*min(nx/sx, ny/sy) | |
if long_cutoff is not None: | |
q_min = 2*np.pi/long_cutoff | |
else: | |
q_min = None | |
fac = self_affine_prefactor(nx, ny, sx, sy, Hurst, rms_height=rms_height, | |
rms_slope=rms_slope, short_cutoff=short_cutoff, | |
long_cutoff=long_cutoff) | |
kny = ny//2+1 | |
# Memory mapped arrays | |
rarr = np.memmap(rfn, np.float64, 'w+', shape=(nx, ny)) | |
karr = np.memmap(kfn, np.complex128, 'w+', shape=(nx, kny)) | |
print('Creating Fourier representation:') | |
qy = 2*np.pi*np.arange(kny)/sy | |
for x in range(nx): | |
sys.stdout.write('{}\r'.format(progressbar(x, nx-1))) | |
sys.stdout.flush() | |
if x > nx//2: | |
qx = 2*np.pi*(nx-x)/sx | |
else: | |
qx = 2*np.pi*x/sx | |
q_sq = qx**2 + qy**2 | |
if x == 0: | |
q_sq[0] = 1. | |
phase = np.exp(2*np.pi*np.random.rand(kny)*1j) | |
ran = fac * phase*np.random.normal(size=kny) | |
karr[x, :] = ran * q_sq**(-(1+Hurst)/2) | |
karr[x, q_sq > q_max**2] = 0. | |
if q_min is not None: | |
mask = q_sq < q_min**2 | |
karr[x, mask] = rolloff * ran[mask] * q_min**(-(1+Hurst)) | |
if nx % 2 == 0: | |
karr[0, 0] = np.real(karr[0, 0]) | |
karr[1:nx//2, 0] = karr[-1:nx//2:-1, 0].conj() | |
else: | |
karr[0, 0] = np.real(karr[0, 0]) | |
karr[nx//2, 0] = np.real(karr[nx//2, 0]) | |
karr[1:nx//2, 0] = karr[-1:nx//2+1:-1, 0].conj() | |
#rarr = np.fft.irfft2(karr) | |
print('\nInverse FFT:') | |
irfft2(karr, rarr) | |
print() | |
return rarr, karr | |
### | |
def tuple2(s, type=float): | |
try: | |
x, y = (type(x) for x in s.split(',')) | |
return x, y | |
except: | |
raise ArgumentTypeError('Size must be sx,sy') | |
### | |
if __name__ == '__main__': | |
commandline = ' '.join(sys.argv[:]) | |
parser = ArgumentParser(description='Create a self-affine, randomly rough' | |
'surface using a Fourier-filtering ' | |
'algorithm.') | |
parser.add_argument('filename', metavar='FILENAME', | |
help='name of topography output file') | |
parser.add_argument('--rms-height', dest='rms_height', | |
type=float, | |
help='create surface with root mean square height HEIGHT', | |
metavar='HEIGHT') | |
parser.add_argument('--rms-slope', dest='rms_slope', | |
type=float, | |
help='create surface with root mean square slope SLOPE', | |
metavar='SLOPE') | |
parser.add_argument('--Hurst', dest='Hurst', type=float, default=0.8, | |
help='self-affine scaling with Hurst exponent HURST', | |
metavar='HURST') | |
parser.add_argument('--short-cutoff', dest='short_cutoff', type=float, | |
help='use short wavelength cutoff SHORTCUTOFF', | |
metavar='SHORTCUTOFF') | |
parser.add_argument('--long-cutoff', dest='long_cutoff', type=float, | |
help='use long wavelength cutoff LONGCUTOFF', | |
metavar='LONGCUTOFF') | |
parser.add_argument('--rolloff', dest='rolloff', type=float, default=1.0, | |
help='rolloff to ROLLOFF * power at LONGCUTOFF', | |
metavar='ROLLOFF') | |
parser.add_argument('--resolution', dest='shape', | |
type=lambda x: tuple2(x, int), default=(128, 128), | |
help='output topography map has resolution RESOLUTION', | |
metavar='RESOLUTION') | |
parser.add_argument('--size', dest='size', | |
type=tuple2, default=(1., 1.), | |
help='size of surface is SIZE', | |
metavar='SIZE') | |
parser.add_argument('--unit', dest='unit', | |
type=str, default='m', | |
help='length unit is UNIT (this information is simply ' | |
'dumped to the output file)', | |
metavar='UNIT') | |
arguments = parser.parse_args() | |
print('filename = {}'.format(arguments.filename)) | |
print('rms-height = {}'.format(arguments.rms_height)) | |
print('rms-slope = {}'.format(arguments.rms_slope)) | |
print('Hurst = {}'.format(arguments.Hurst)) | |
print('short-cutoff = {}'.format(arguments.short_cutoff)) | |
print('long-cutoff = {}'.format(arguments.long_cutoff)) | |
print('rolloff = {}'.format(arguments.rolloff)) | |
print('resolution = {}'.format(arguments.shape)) | |
print('size = {}'.format(arguments.size)) | |
print('unit = {}'.format(arguments.unit)) | |
nx, ny = arguments.shape | |
sx, sy = arguments.size | |
surface, surfaceq = Fourier_synthesis(nx, ny, sx, sy, arguments.Hurst, | |
rms_height=arguments.rms_height, | |
rms_slope=arguments.rms_slope, | |
short_cutoff=arguments.short_cutoff, | |
long_cutoff=arguments.long_cutoff, | |
rolloff=arguments.rolloff) | |
print('Saving outfile topography...') | |
np.savetxt(arguments.filename, surface, header='{}\nWidth: {} {}\n' | |
'Height: {} {}\nValue units: {}'.format(commandline, | |
sx, arguments.unit, | |
sy, arguments.unit, | |
arguments.unit)) | |
print('...done') |
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