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# !/usr/bin/env python
# -*- 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 ....
"""
__author__ = "Jérôme Kieffer"
__contact__ = "Jerome.Kieffer@ESRF.eu"
__license__ = "MIT"
__copyright__ = "European Synchrotron Radiation Facility, Grenoble, France"
__date__ = "21/01/2021"
__status__ = "production"
__docformat__ = 'restructuredtext'
import numpy
import logging
from math import sqrt, atan2, pi
from collections import namedtuple
_logger = logging.getLogger(__name__)
Ellipse = namedtuple("Ellipse", ["center_1", "center_2", "angle", "half_long_axis", "half_short_axis"])
def fit_ellipse(pty, ptx, _allow_delta=True):
"""Fit an ellipse
Math from
https://mathworld.wolfram.com/Ellipse.html #15
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)
:raise ValueError: If the ellipse can't be fitted
"""
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)
try:
inv = numpy.linalg.inv(S)
except numpy.linalg.LinAlgError:
if not _allow_delta:
raise ValueError("Ellipse can't be fitted: singular matrix")
# Try to do the same with a delta
delta = 100
ellipse = fit_ellipse(pty + delta, ptx + delta, _allow_delta=False)
y0, x0, angle, wlong, wshort = ellipse
return Ellipse(y0 - delta, x0 - delta, angle, wlong, wshort)
C = numpy.zeros([6, 6], dtype=numpy.float64)
C[0, 2] = C[2, 0] = 2.0
C[1, 1] = -1.0
E, V = numpy.linalg.eig(numpy.dot(inv, C))
# First of all, sieve out all infinite and complex eigenvalues and come back to the Real world
m = numpy.logical_and(numpy.isfinite(E), numpy.isreal(E))
E, V = E[m].real, V[:, m].real
# Ensures a>0, invert eigenvectors concerned
V[:, V[0] < 0] = -V[:, V[0] < 0]
# See https://mathworld.wolfram.com/Ellipse.html #15
# Eigenvector must meet constraint (ac - b^2)>0 to be valid.
A = V[0]
B = V[1] / 2.0
C = V[2]
D = V[3] / 2.0
F = V[4] / 2.0
G = V[5]
# Condition 1: Delta = det((a b d)(b c f)(d f g)) !=0
Delta = A * (C * G - F * F) - G * B * B + D * (2 * B * F - C * D)
# Condition 2: J>0
J = (A * C - B * B)
# Condition 3: Delta/(A+C)<0, replaces by Delta*(A+C)<0, less warnings
m = numpy.logical_and(J > 0, Delta != 0)
m = numpy.logical_and(m, Delta * (A + C) < 0)
n = numpy.where(m)[0]
if len(n) == 0:
raise ValueError("Ellipse can't be fitted: No Eigenvalue match all 3 criteria")
else:
n = n[0]
a = A[n]
b = B[n]
c = C[n]
d = D[n]
f = F[n]
g = G[n]
# Calculation of the center:
denom = b * b - a * c
x0 = (c * d - b * f) / denom
y0 = (a * f - b * d) / denom
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) * sqrt(1 + 4 * b * b / ((a - c) * (a - c))) - (c + a))
down2 = (b * b - a * c) * ((a - c) * sqrt(1 + 4 * b * b / ((a - c) * (a - c))) - (c + a))
a2 = up / down1
b2 = up / down2
if a2 <= 0 or b2 <= 0:
raise ValueError("Ellipse can't be fitted, negative sqrt")
res1 = sqrt(a2)
res2 = sqrt(b2)
if a == c:
angle = 0 # we have a circle
elif res2 > res1:
res1, res2 = res2, res1
angle = 0.5 * (pi + atan2(2 * b, (a - c)))
else:
angle = 0.5 * (pi + atan2(2 * b, (a - c)))
return Ellipse(y0, x0, angle, res1, res2)
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