Upload fit_ellipse.py

fit_ellipse.py

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+# Author: aqeelanwar 
+# Created: 4 May,2020, 1:30 AM
+# Email: aqeel.anwar@gatech.edu
+
+import numpy as np
+from numpy.linalg import eig, inv
+
+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 =  eig(np.dot(inv(S), C))
+    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])
+
+def ellipse_angle_of_rotation2( a ):
+    b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0]
+    if b == 0:
+        if a > c:
+            return 0
+        else:
+            return np.pi/2
+    else:
+        if a > c:
+            return np.arctan(2*b/(a-c))/2
+        else:
+            return np.pi/2 + np.arctan(2*b/(a-c))/2
+
+# a = fitEllipse(x,y)
+# center = ellipse_center(a)
+# #phi = ellipse_angle_of_rotation(a)
+# phi = ellipse_angle_of_rotation2(a)
+# axes = ellipse_axis_length(a)
+#
+# print("center = ",  center)
+# print("angle of rotation = ",  phi)
+# print("axes = ", axes)
+