There is actually a post very similar to this but asking a different question from about 5 years ago.
I have a set of points which are not elliptical, and I would like to fit an ellipse to them in the least squares sense. These are the functions I found to do the computation. I checked them over briefly but couldn't find any errors.
http://nicky.vanforeest.com/misc/fitEllipse/fitEllipse.html
import numpy as np
import numpy.linalg as linalg
import matplotlib.pyplot as plt
def fitEllipse(x,y):
x = x[:,np.newaxis]
y = y[:,np.newaxis]
D = np.hstack((x*x, x*y, y*y, x, y, np.ones_like(x)))
S = np.dot(D.T,D)
C = np.zeros([6,6])
C[0,2] = C[2,0] = 2; C[1,1] = -1
E, V = linalg.eig(np.dot(linalg.inv(S), C))
#print E
n = np.argmax(np.abs(E))
a = V[:,n]
return a
def ellipse_center(a):
b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0]
num = b*b-a*c
x0=(c*d-b*f)/num
y0=(a*f-b*d)/num
return np.array([x0,y0])
def ellipse_angle_of_rotation( a ):
b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0]
return 0.5*np.arctan(2*b/(a-c))
def ellipse_axis_length( a ):
b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0]
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)*np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a))
down2=(b*b-a*c)*( (a-c)*np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a))
res1=np.sqrt(up/down1)
res2=np.sqrt(up/down2)
return np.array([res1, res2])
My problem is this: I have sets of geospatial data to which I need to fit these ellipses. In order to compare ellipses at different latitudes I need to project them all to local tangent planes. This is easy. HOWEVER: With one such sample set of data, the functions work and give me a well-formed ellipse. When I do the projection, however, it gives me an ellipse whose major axis is somehow shorter than the the minor axis, which makes computing a non-imaginary eccentricity difficult :P ($e = \sqrt{1 - b/a}$).
Even if my projection were wrong (it isn't), these functions should still be able to take these points and produce a fit. I can't figure out why with some datasets it produces nonsense geometrical data. Any ideas?
If not, does anybody have any other way to fit an ellipse to data in python?
