/usr/lib/python2.7/dist-packages/pyFAI/utils/ellipse.py is in python-pyfai 0.15.0+dfsg1-1.
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# -*- coding: utf-8 -*-
#
# Project: Azimuthal integration
# https://github.com/silx-kit/pyFAI
#
# Copyright (C) 2017-2018 European Synchrotron Radiation Facility, Grenoble, France
#
# Principal author: Jérôme Kieffer (Jerome.Kieffer@ESRF.eu)
#
# 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 modules contains a function to fit without refinement an ellipse
on a set of points ....
"""
from __future__ import division, print_function
__author__ = "Jerome Kieffer"
__contact__ = "Jerome.Kieffer@ESRF.eu"
__license__ = "MIT"
__copyright__ = "European Synchrotron Radiation Facility, Grenoble, France"
__date__ = "09/01/2018"
__status__ = "production"
__docformat__ = 'restructuredtext'
import numpy
from collections import namedtuple
Ellipse = namedtuple("Ellipse", ["center_1", "center_2", "angle", "half_long_axis", "half_short_axis"])
def fit_ellipse(pty, ptx):
"""Fit an ellipse
inspired from
http://nicky.vanforeest.com/misc/fitEllipse/fitEllipse.html
:param pty: point coordinates in the slow dimension (y)
:param ptx: point coordinates in the fast dimension (x)
"""
x = ptx[:, numpy.newaxis]
y = pty[:, numpy.newaxis]
D = numpy.hstack((x * x, x * y, y * y, x, y, numpy.ones_like(x)))
S = numpy.dot(D.T, D)
C = numpy.zeros([6, 6])
C[0, 2] = C[2, 0] = 2
C[1, 1] = -1
E, V = numpy.linalg.eig(numpy.dot(numpy.linalg.inv(S), C))
n = numpy.argmax(numpy.abs(E))
res = V[:, n]
b, c, d, f, g, a = res[1] / 2, res[2], res[3] / 2, res[4] / 2, res[5], res[0]
num = b * b - a * c
x0 = (c * d - b * f) / num
y0 = (a * f - b * d) / num
if b == 0:
if a > c:
angle = 0
else:
angle = numpy.pi / 2
else:
if a > c:
angle = numpy.arctan2(2 * b, (a - c)) / 2
else:
angle = numpy.pi / 2 + numpy.arctan2(2 * b, (a - c)) / 2
up = 2 * (a * f * f + c * d * d + g * b * b - 2 * b * d * f - a * c * g)
down1 = (b * b - a * c) * ((c - a) * numpy.sqrt(1 + 4 * b * b / ((a - c) * (a - c))) - (c + a))
down2 = (b * b - a * c) * ((a - c) * numpy.sqrt(1 + 4 * b * b / ((a - c) * (a - c))) - (c + a))
res1 = numpy.sqrt(up / down1)
res2 = numpy.sqrt(up / down2)
return Ellipse(y0, x0, angle, max(res1, res2), min(res1, res2))
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