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I have 2 sets of 4 coordinates on a xy plane with 4 Radii for each set. For the 1st set all the Radii are same forming it a perfect circle. where as for the second set the 4 Radii are little different forming a deformed circle. Can someone help me on how to plot these 2 shapes on a graph

Set1 : xy coordinates : [(0,1),(1,0),(0,-1),(-1,0)], Radii[1,1,1,1]

Set2 : xy coordinates : [(0,1),(1.2,0),(0,-0.9),(-1,0)], Radii[1,1.2,0.9,1]

I want the shape of set2 to look like a deformed circle. So, please help me with the math equation and the python implementation of the same.

Thanks for your time.

bigreddot
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Raghava kattamudi
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  • Maybe this can help you: https://stackoverflow.com/questions/47873759/how-to-fit-a-2d-ellipse-to-given-points – AMH Jun 11 '20 at 07:07
  • I don't understand what the coordinates represent. Do you just plot a circle with the given radius at the specified coordinates? If not, can you draw and attach a picture that shows what you want to get? – Eugene Pakhomov Jun 11 '20 at 07:11

1 Answers1

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Adapted from How to fit a 2D ellipse to given points.enter image description here

This should be a good start.

import numpy as np
import matplotlib.pyplot as plt

# circle = np.array([(0,1),(1,0),(0,-1),(-1,0)])
circle = np.array([(0,1),(1.2,0),(0,-0.9),(-1,0)]) 

# Extract x coords and y coords of the ellipse as column vectors
X = circle[:,0:1]
Y = circle[:,1:]

# Formulate and solve the least squares problem ||Ax - b ||^2
A = np.hstack([X**2, X * Y, Y**2, X, Y])
b = np.ones_like(X)
x = np.linalg.lstsq(A, b, rcond=-1)[0].squeeze()

# Print the equation of the ellipse in standard form
print('The ellipse is given by {0:.3}x^2 + {1:.3}xy +{2:.3}y^2 +{3:.3}x + {4:.3}y = 1'.format(*x))

# Plot the circle
plt.scatter(X, Y, label='Data Points')

# Plot the least squares ellipse
x_coord = np.linspace(-2,2,300)
y_coord = np.linspace(-2,2,300)
X_coord, Y_coord = np.meshgrid(x_coord, y_coord)
Z_coord = x[0] * X_coord ** 2 + x[1] * X_coord * Y_coord + x[2] * Y_coord**2 + x[3] * X_coord + x[4] * Y_coord
plt.contour(X_coord, Y_coord, Z_coord, levels=[1], colors=('r'), linewidths=2)

plt.legend()
plt.xlabel('X')
plt.ylabel('Y')
plt.show()
AMH
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