/usr/lib/python2.7/dist-packages/pyFAI/spline.py is in pyfai 0.3.5-1.
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# -*- coding: UTF8 -*-
###########################################################################
# Written 2009-12-22 by Jérôme Kieffer
# Copyright (C) 2009 European Synchrotron Radiation Facility
# Grenoble, France
#
# Principal authors: Jérôme Kieffer (jerome.kieffer@esrf.fr)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
########################################################################################
""" This is piece of software aims to manipulate spline files for
geometric corrections of the 2D detectors using cubic-spline"""
__author__ = "Jérôme Kieffer"
__contact__ = "Jerome.Kieffer@esrf.eu"
__license__ = "GPLv3+"
__copyright__ = "European Synchrotron Radiation Facility, Grenoble, France"
import os, time, sys
import numpy, scipy, Image, fabio
import scipy.optimize
import scipy.interpolate
import scipy.interpolate.fitpack
class Spline:
"""This class is a python representation of the spline file
Those file represent cubic splines for 2D detector distortions and makes heavy use of
fitpack (dierckx in netlib) --- A Python-C wrapper to FITPACK (by P. Dierckx).
FITPACK is a collection of FORTRAN programs for curve and surface fitting with splines and tensor product splines.
See
http://www.cs.kuleuven.ac.be/cwis/research/nalag/research/topics/fitpack.html
or
http://www.netlib.org/dierckx/index.html
"""
def __init__(self, filename=None):
"""this is the constructor of the Spline class, for"""
self.splineOrder = 3 #This is the default, so cubic splines
self.lenStrFloat = 14 # by default one float is 14 char in ascii
self.xmin = None
self.ymin = None
self.xmax = None
self.ymax = None
self.xDispArray = None
self.yDispArray = None
self.xSplineKnotsX = []
self.xSplineKnotsY = []
self.xSplineCoeff = []
self.ySplineKnotsX = []
self.ySplineKnotsY = []
self.ySplineCoeff = []
self.pixelSize = None
self.grid = None
self.filename = None
if filename is not None:
self.read(filename)
def __repr__(self):
txt = "Array size: x= %s - %s\ty= %s - %s" % (self.xmin, self.xmax, self.ymin, self.ymax)
txt += "\nPixel size = %s microns, Grid spacing = %s" % (self.pixelSize, self.grid)
txt += "\nX-Displacement spline %i X_knots, %i Y_knots and %i coef: should be (X_knot-1-X_order)*(Y_knot-1-Y_order)" \
% (len(self.xSplineKnotsX), len(self.xSplineKnotsY), len(self.xSplineCoeff))
txt += "\nY-Displacement spline %i X_knots, %i Y_knots and %i coef: should be (X_knot-1-X_order)*(Y_knot-1-Y_order)" \
% (len(self.ySplineKnotsX), len(self.ySplineKnotsY), len(self.ySplineCoeff))
return txt
def zeros(self, xmin=0.0, ymin=0.0, xmax=2048.0, ymax=2048.0, pixSize=None):
"""defines a spline file with no ( zero ) displacement.
@type xmin: float
@type xmax: float
@type ymax: float
@type ymin: float
@param xmin: minimum coordinate in x, usually zero
@param xmax: maximum coordinate in x (+1) usually 2048
@param ymin: minimum coordinate in y, usually zero
@param ymax: maximum coordinate y (+1) usually 2048
"""
self.xmin = xmin
self.ymin = ymin
self.xmax = xmax
self.ymax = ymax
self.xDispArray = numpy.zeros((int(xmax - xmin + 1), int(ymax - ymin + 1)))
self.yDispArray = numpy.zeros((int(xmax - xmin + 1), int(ymax - ymin + 1)))
if pixSize:
self.pixelSize = pixSize
def zeros_like(self, other):
"""defines a spline file with no ( zero ) displacement with the same shape as the other one given.
@param other: another Spline
@type other: Spline
"""
self.zeros(self, other.xmin, other.ymin, other.xmax, other.ymax)
def read(self, filename):
"""read an ascii spline file from file
@param filename: name of the file containing the cubic spline distortion file
@type filename: string
"""
if not os.path.isfile(filename):
raise IOError("File does not exist %s" % filename)
self.filename = filename
stringSpline = [ i.rstrip() for i in open (filename).readlines() ]
indexLine = 0
for oneLine in stringSpline:
stripedLine = oneLine.strip().upper()
if stripedLine == "VALID REGION":
data = stringSpline[ indexLine + 1 ]
self.xmin = float(data[self.lenStrFloat * 0:self.lenStrFloat * 1])
self.ymin = float(data[self.lenStrFloat * 1:self.lenStrFloat * 2])
self.xmax = float(data[self.lenStrFloat * 2:self.lenStrFloat * 3])
self.ymax = float(data[self.lenStrFloat * 3:self.lenStrFloat * 4])
elif stripedLine == "GRID SPACING, X-PIXEL SIZE, Y-PIXEL SIZE":
data = stringSpline[ indexLine + 1 ]
self.grid = float(data[:self.lenStrFloat])
self.pixelSize = (float(data[self.lenStrFloat:self.lenStrFloat * 2]), float(data[self.lenStrFloat * 2:self.lenStrFloat * 3]))
elif stripedLine == "X-DISTORTION":
data = stringSpline[ indexLine + 1 ]
[splineKnotsXLen, splineKnotsYLen] = [ int(i) for i in data.split() ]
databloc = []
for line in stringSpline[ indexLine + 2 : ]:
if len(line) > 0 :
for i in range(len(line) / self.lenStrFloat):
databloc.append(float(line[i * self.lenStrFloat: (i + 1) * self.lenStrFloat ]))
else:
break
self.xSplineKnotsX = databloc[ : splineKnotsXLen ]
self.xSplineKnotsY = databloc[splineKnotsXLen: splineKnotsXLen + splineKnotsYLen]
self.xSplineCoeff = databloc[ splineKnotsXLen + splineKnotsYLen: ]
elif stripedLine == "Y-DISTORTION":
data = stringSpline[ indexLine + 1 ]
[splineKnotsXLen, splineKnotsYLen] = [ int(i) for i in data.split() ]
databloc = []
for line in stringSpline[ indexLine + 2 : ]:
if len(line) > 0 :
for i in range(len(line) / self.lenStrFloat):
databloc.append(float(line[i * self.lenStrFloat: (i + 1) * self.lenStrFloat ]))
else:
break
self.ySplineKnotsX = databloc[ : splineKnotsXLen ]
self.ySplineKnotsY = databloc[splineKnotsXLen: splineKnotsXLen + splineKnotsYLen]
self.ySplineCoeff = databloc[ splineKnotsXLen + splineKnotsYLen: ]
# Keep this at the end
indexLine += 1
def comparison(self, ref, verbose=False):
"""Compares the current spline distortion with a reference
@param ref: another spline file
@return: True or False depending if the splines are the same or not """
self.spline2array()
ref.spline2array()
deltax = (self.xDispArray - ref.xDispArray)
deltay = (self.yDispArray - ref.yDispArray)
histX = numpy.histogram(deltax.reshape(deltax.size), bins=100)
histY = numpy.histogram(deltay.reshape(deltay.size), bins=100)
histXdr = (histX[1][1:] + histX[1][:-1]) / 2.0
histYdr = (histY[1][1:] + histY[1][:-1]) / 2.0
histXmax = histXdr [histX[0].argmax()]
histYmax = histYdr [histY[0].argmax()]
maxErrX = abs(deltax).max()
maxErrY = abs(deltay).max()
curvX = scipy.interpolate.interp1d(histXdr, histX[0] - histX[0].max() / 2.0)
curvY = scipy.interpolate.interp1d(histYdr, histY[0] - histY[0].max() / 2.0)
fFWHM_X = scipy.optimize.bisect(curvX , histXmax, histXdr[-1]) - scipy.optimize.bisect(curvX , histXdr[0], histXmax)
fFWHM_Y = scipy.optimize.bisect(curvY , histYmax, histYdr[-1]) - scipy.optimize.bisect(curvY , histYdr[0], histYmax)
print ("Analysis of the difference between two splines")
print ("Maximum error in X= %.3f pixels,\t in Y= %.3f pixels." % (maxErrX, maxErrY))
print ("Maximum of histogram in X= %.3f pixels,\t in Y= %.3f pixels." % (histXmax, histYmax))
print ("Mean of histogram in X= %.3f pixels,\t in Y= %.3f pixels." % (deltax.mean(), deltay.mean()))
print ("FWHM in X= %.3f pixels,\t in Y= %.3f pixels." % (fFWHM_X, fFWHM_Y))
if verbose:
import pylab
pylab.plot(histXdr , histX[0], label="error in X")
pylab.plot(histYdr, histY[0], label="error in Y")
pylab.legend()
pylab.show()
return (fFWHM_X < 0.05) and (fFWHM_Y < 0.05) and (maxErrX < 0.5) and (maxErrY < 0.5) \
and (deltax.mean() < 0.01) and(deltay.mean() < 0.01) and (histXmax < 0.01) and (histYmax < 0.01)
def spline2array(self, timing=False):
"""calculates the displacement matrix using fitpack
bisplev(x, y, tck, dx = 0, dy = 0)
Evaluate a bivariate B-spline and its derivatives.
Return a rank-2 array of spline function values (or spline derivative
values) at points given by the cross-product of the rank-1 arrays x and y.
In special cases, return an array or just a float if either x or y or
both are floats.
"""
if (self.xDispArray == None) :
x_1d_array = numpy.arange(self.xmin, self.xmax + 1)
y_1d_array = numpy.arange(self.ymin, self.ymax + 1)
startTime = time.time()
self.xDispArray = scipy.interpolate.fitpack.bisplev(x_1d_array, y_1d_array, \
[self.xSplineKnotsX, self.xSplineKnotsY, self.xSplineCoeff, self.splineOrder, self.splineOrder ], \
dx=0, dy=0).transpose()
intermediateTime = time.time()
self.yDispArray = scipy.interpolate.fitpack.bisplev(x_1d_array, y_1d_array, \
[self.ySplineKnotsX, self.ySplineKnotsY, self.ySplineCoeff, self.splineOrder, self.splineOrder ], \
dx=0, dy=0).transpose()
if timing:
print "Timing for: X-Displacement spline evaluation: %.3f sec, Y-Displacement Spline evaluation: %.3f sec." % \
((intermediateTime - startTime), (time.time() - intermediateTime))
def splineFuncX(self, x, y):
""" calculates the displacement matrix using fitpack for the X direction
@param x: numpy array repesenting the points in the x direction
@param y: numpy array repesenting the points in the y direction
@return: displacement matrix for the X direction
@rtype: numpy arrays
"""
if x.ndim == 2:
if abs(x[1:, :] - x[:-1, :] - numpy.zeros((x.shape[0] - 1, x.shape[1]))).max() < 1e-6:
x = x[0]
y = y[:, 0]
elif abs(x[:, 1:] - x[:, :-1] - numpy.zeros((x.shape[0], x.shape[1] - 1))).max() < 1e-6:
x = x[:, 0]
y = y[0]
xDispArray = scipy.interpolate.fitpack.bisplev(x, y, \
[self.xSplineKnotsX, self.xSplineKnotsY, self.xSplineCoeff, self.splineOrder, self.splineOrder ], \
dx=0, dy=0).transpose()
return xDispArray
def splineFuncY(self, x, y):
""" calculates the displacement matrix using fitpack for the Y direction
@param x: numpy array repesenting the points in the x direction
@param y: numpy array repesenting the points in the y direction
@return: displacement matrix for the Y direction
@rtype: numpy array
"""
if x.ndim == 2:
if abs(x[1:, :] - x[:-1, :] - numpy.zeros((x.shape[0] - 1, x.shape[1]))).max() < 1e-6:
x = x[0]
y = y[:, 0]
elif abs(x[:, 1:] - x[:, :-1] - numpy.zeros((x.shape[0], x.shape[1] - 1))).max() < 1e-6:
x = x[:, 0]
y = y[0]
yDispArray = scipy.interpolate.fitpack.bisplev(x, y, \
[self.ySplineKnotsX, self.ySplineKnotsY, self.ySplineCoeff, self.splineOrder, self.splineOrder ], \
dx=0, dy=0).transpose()
return yDispArray
def array2spline(self, smoothing=1000, timing=False):
"""calculates the spline coefficents from the displacements matrix using fitpack
"""
self.xmin = 0.0
self.ymin = 0.0
self.xmax = float(self.xDispArray.shape[0] - 1)
self.ymax = float(self.yDispArray.shape[1] - 1)
if timing:
startTime = time.time()
xRectBivariateSpline = scipy.interpolate.fitpack2.RectBivariateSpline(numpy.arange(self.xmax + 1.0), numpy.arange(self.ymax + 1), self.xDispArray.transpose(), s=smoothing)
if timing:
intermediateTime = time.time()
yRectBivariateSpline = scipy.interpolate.fitpack2.RectBivariateSpline(numpy.arange(self.xmax + 1.0), numpy.arange(self.ymax + 1), self.yDispArray.transpose(), s=smoothing)
if timing:
print "X-Displ evaluation= %.3f sec, Y-Displ evaluation= %.3f sec." % (intermediateTime - startTime, time.time() - intermediateTime)
print len(xRectBivariateSpline.get_coeffs()), "x-coefs", xRectBivariateSpline.get_coeffs()
print len(yRectBivariateSpline.get_coeffs()), "y-coefs", yRectBivariateSpline.get_coeffs()
print len(xRectBivariateSpline.get_knots()[0]), len(xRectBivariateSpline.get_knots()[1]), "x-knots", xRectBivariateSpline.get_knots()
print len(yRectBivariateSpline.get_knots()[0]), len(yRectBivariateSpline.get_knots()[1]), "y-knots", yRectBivariateSpline.get_knots()
print "Residual x,y", xRectBivariateSpline.get_residual(), yRectBivariateSpline.get_residual()
self.xSplineKnotsX = xRectBivariateSpline.get_knots()[0]
self.xSplineKnotsY = xRectBivariateSpline.get_knots()[1]
self.xSplineCoeff = xRectBivariateSpline.get_coeffs()
self.ySplineKnotsX = yRectBivariateSpline.get_knots()[0]
self.ySplineKnotsY = yRectBivariateSpline.get_knots()[1]
self.ySplineCoeff = yRectBivariateSpline.get_coeffs()
def writeEDF(self, basename):
"""save the distortion matrices into a couple of files called basename-x.edf and basename-y.edf
"""
try:
from fabio.edfimage import edfimage
#from EdfFile import EdfFile as EDF
except ImportError:
print "You will need the Fabio library available from the Fable sourceforge"
return
self.spline2array()
edfDispX = edfimage(data=self.xDispArray.astype("float32"), header={})
edfDispY = edfimage(data=self.yDispArray.astype("float32"), header={})
edfDispX.write(basename + "-x.edf", force_type="float32")
edfDispY.write(basename + "-y.edf", force_type="float32")
def write(self, filename):
"""save the cubic spline in an ascii file usable with Fit2D or SPD
@param filename: name of the file containing the cubic spline distortion file
@type filename: string
"""
txt = "SPATIAL DISTORTION SPLINE INTERPOLATION COEFFICIENTS\n\n VALID REGION\n%14.7E%14.7E%14.7E%14.7E\n\n" % (self.xmin, self.ymin, self.xmax, self.ymax)
txt += " GRID SPACING, X-PIXEL SIZE, Y-PIXEL SIZE\n%14.7E%14.7E%14.7E\n\n" % (self.grid, self.pixelSize[0], self.pixelSize[1])
txt += " X-DISTORTION\n%6i%6i" % (len(self.xSplineKnotsX), len(self.xSplineKnotsY))
for i in range(len(self.xSplineKnotsX)):
if i % 5 == 0:
txt += "\n"
txt += "%14.7E" % self.xSplineKnotsX[i]
for i in range(len(self.xSplineKnotsY)):
if i % 5 == 0:
txt += "\n"
txt += "%14.7E" % self.xSplineKnotsY[i]
for i in range(len(self.xSplineCoeff)):
if i % 5 == 0:
txt += "\n"
txt += "%14.7E" % self.xSplineCoeff[i]
txt += "\n\n Y-DISTORTION\n%6i%6i" % (len(self.ySplineKnotsX), len(self.ySplineKnotsY))
for i in range(len(self.ySplineKnotsX)):
if i % 5 == 0:
txt += "\n"
txt += "%14.7E" % self.ySplineKnotsX[i]
for i in range(len(self.ySplineKnotsY)):
if i % 5 == 0:
txt += "\n"
txt += "%14.7E" % self.ySplineKnotsY[i]
for i in range(len(self.ySplineCoeff)):
if i % 5 == 0:
txt += "\n"
txt += "%14.7E" % self.ySplineCoeff[i]
txt += "\n"
open(filename, "w").write(txt)
def tilt(self, center=(0.0, 0.0), tiltAngle=0.0, tiltPlanRot=0.0, distanceSampleDetector=1.0, timing=False):
"""The tilt method apply a virtual tilt on the detector, the point of tilt is given by the center
@param center: position of the point of tilt, this point will not be moved.
@type center: 2tuple of floats
@param tiltAngle: the value of the tilt in degrees
@type tiltAngle: float in the range [-90:+90] degrees
@param tiltPlanRot: the rotation of the tilt plan with the Ox axis (0 deg for y axis invariant, 90 deg for x axis invariant)
@type tiltPlanRot: Float in the range [-180:180]
@type distanceSampleDetector: float
@param distanceSampleDetector: the distance from sample to detector in meter (along the beam, so distance from sample to center)
@return: tilted Spline instance
@rtype: Spline
"""
if self.xDispArray is None:
if self.filename is None:
self.zeros()
else:
self.read()
print("center=%s, tilt=%s, tiltPlanRot=%s, distanceSampleDetector=%sm, pixelSize=%sµm" % (center, tiltAngle, tiltPlanRot, distanceSampleDetector, self.pixelSize))
if timing:
startTime = time.time()
distance = 1.0e6 * distanceSampleDetector #from meters to microns
cosb = numpy.cos(numpy.radians(tiltPlanRot))
sinb = numpy.sin(numpy.radians(tiltPlanRot))
cosf = numpy.cos(numpy.radians(tiltAngle))
sinf = numpy.sin(numpy.radians(tiltAngle))
x = lambda i, j: j - center[0] - 0.5 #x and y are tilted in C/Fortran representation
y = lambda i, j: i - center[1] - 0.5
iPos = numpy.fromfunction(x, (int(self.ymax - self.ymin + 1), int(self.xmax - self.xmin + 1)))
jPos = numpy.fromfunction(y, (int(self.ymax - self.ymin + 1), int(self.xmax - self.xmin + 1)))
xPos = (iPos + self.xDispArray) * self.pixelSize[0]
yPos = (jPos + self.yDispArray) * self.pixelSize[1]
tiltArrayX = distance * (xPos * (cosf * cosb * cosb + sinb * sinb) + yPos * (cosf * cosb * sinb - cosb * sinb)) / \
(distance + xPos * sinf * cosb + yPos * sinf * sinb) / self.pixelSize[0] - iPos
tiltArrayY = distance * (xPos * (cosf * sinb * cosb - cosb * sinb) + yPos * (cosf * sinb * sinb + cosb * cosb)) / \
(distance + xPos * sinf * cosb + yPos * sinf * sinb) / self.pixelSize[1] - jPos
tiltedSpline = Spline()
tiltedSpline.pixelSize = self.pixelSize
tiltedSpline.grid = self.grid
tiltedSpline.xDispArray = tiltArrayX
tiltedSpline.yDispArray = tiltArrayY
#tiltedSpline.array2spline(smoothing=1e-6, timing=True)
if timing:
print("Time for the generation of the distorted spline: %.3f sec" % (time.time() - startTime))
return tiltedSpline
# def setPixelSize(self, pixelSize):
# """
# sets the size of the pixel from a 2-tuple of floats expressed in microns.
# """
# if len(pixelSize) == 2 :
# self.pixelSize = pixelSize
# def getPixelSize(self):
# """
# @return: the size of the pixel from a
# @rtype: 2-tuple of floats expressed in microns.
# """
# return self.pixelSize
#
def setPixelSize(self, pixelSize):
"""
sets the size of the pixel from a 2-tuple of floats expressed in meters.
@param: pixel size in meter
@type pixelSize: 2-tuple of float
"""
if len(pixelSize) == 2 :
self.pixelSize = (pixelSize[0] * 1.0e6, pixelSize[1] * 1.0e6)
def getPixelSize(self):
"""
@return: the size of the pixel from a 2D detector
@rtype: 2-tuple of floats expressed in meter.
"""
return (self.pixelSize[0] * 1.0e-6, self.pixelSize[1] * 1.0e-6)
# def horizontalFlip(self):
# """calculate the flipped spline file interverting xmin and xmax
# @return: another spline file"""
# other = Spline()
# other.xmin = self.xmin
# other.xmax = self.xmax
# other.ymin = self.ymin
# other.ymax = self.ymax
# other.pixelSize = self.pixelSize
# other.grid = self.grid
# other.xSplineKnotsX = [ self.xmax + self.xmin - x for x in self.xSplineKnotsX ]
# #other.xSplineKnotsX = self.xSplineKnotsX[:]
# other.xSplineKnotsY = self.xSplineKnotsY[:]
# other.xSplineCoeff = [ -i for i in self.xSplineCoeff]
# other.ySplineKnotsX = [ self.xmax + self.xmin - x for x in self.xSplineKnotsX ]
# #other.ySplineKnotsX = self.ySplineKnotsX[:]
# other.ySplineKnotsY = self.ySplineKnotsY[:]
# other.ySplineCoeff = self.ySplineCoeff[:]
# return other
#
#def xDispHorFlip(array):
# """make an horizontal flip of the given X displacement array"""
# return - numpy.fliplr(array)
#def yDispHorFlip(array):
# """make an horizontal flip of the given Y displacement array"""
# return numpy.fliplr(array)
#def xDispVerFlip(array):
# """make a vertical flip of the given X displacement array"""
# return numpy.flipud(array)
#def yDispVerFlip(array):
# """make a vertical flip of the given Y displacement array"""
# return - numpy.flipud(array)
if __name__ == '__main__':
# """this is the main program if somebody wants to use this as a library"""
#
#
#
#
## spline.write("test")
# new = Spline()
# new.pixelSize = spline.pixelSize
# new.grid = spline.grid
# new.xDispArray = xDispHorFlip(spline.xDispArray[:])
# new.yDispArray = yDispHorFlip(spline.yDispArray[:])
# new.array2spline(smoothing=10, timing=False)
# print "matrix flipped", new
# flipped = spline.horizontalFlip()
# print "Spline flipped", flipped
#
#
# print "---" * 50
#
#
# print new.comparison(flipped, verbose=True)
# new.write("new.spline")
# new.xDispArray = None
# new.yDispArray = None
# new.spline2array(timing=True)
# print new.comparison(spline, verbose=True)
# Size of the image in pixels:
##########################################################
# spline = Spline()
# spline.zeros(0, 0, 2000, 2000)
# spline.spline2array()
# spline.pixelSize = (100, 100)
# spline.grid = 1
CENTER = (1000, 1000)
TILT = 10 #deg
ROTATION_TILT = 0 #deg
DISTANCE = 100 #mm
SPLINE_FILE = "example.spline"
for keyword in sys.argv[1:]:
if os.path.isfile(keyword):
SPLINE_FILE = keyword
elif keyword.lower().find("center=") in [0, 1, 2]:
CENTER = map(float, keyword.split("=")[1].split("x"))
elif keyword.lower().find("dist=") in [0, 1, 2]:
DISTANCE = float(keyword.split("=")[1])
elif keyword.lower().find("tilt=") in [0, 1, 2]:
TILT = float(keyword.split("=")[1])
elif keyword.lower().find("rot=") in [0, 1, 2]:
ROTATION_TILT = float(keyword.split("=")[1])
spline = Spline()
spline.read(SPLINE_FILE)
print ("Original Spline: %s" % spline)
spline.spline2array(timing=True)
tilted = spline.tilt(CENTER, TILT, ROTATION_TILT, DISTANCE, timing=True)
#tilted.write("tilted-t%i-p%i-d%i.spline" % (TILT, ROTATION_TILT, DISTANCE))
tilted.writeEDF("%s-tilted-t%i-p%i-d%i" % (os.path.splitext(SPLINE_FILE)[0], TILT, ROTATION_TILT, DISTANCE))
# for i in range(0, 14, 2):
# tilted.array2spline(smoothing=(10.0 ** (-i)), timing=True)
# tilted.write("tilted-t%i-p%i-d%i-s%i.spline" % (TILT, ROTATION_TILT, DISTANCE, i))
# fromspline = Spline()
# fromspline.read("tilted-t%i-p%i-d%i-s%i.spline" % (TILT, ROTATION_TILT, DISTANCE, i))
# print fromspline.comparison(tilted, verbose=True)
# spline = Spline()
# spline.read("tilted-t%i-p%i-d%i.spline" % (TILT, ROTATION_TILT, DISTANCE))
# spline.spline2array(timing=True)
# print spline.comparison(tilted, verbose=True)
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