CODEWITHSUNDEEP
pythonmatlabcurve-fitting
kevin lee
kevin lee

Reputation: 123

How to use a smooth curve to link points approximately distributing in a circle?

I have a set of twelve points, which center at (0, 0) and distribute approximately in a circle, at the interval of 30 degrees, shown in the image. The twelve points

I want to use a smooth curve to link (go through) them like the image below (I draw the red line by hand). a hand-drawn curve in red

I want to make it in python or matlab. I have tried some interpolation methods for the upper half and lower half separately, and wanted to combine them as a complete curve. However, the results always overshoot.

Thank you for any suggestions!

Upvotes: 1

Views: 217

Answers (2)

kevin lee
kevin lee

Reputation: 123

Thank for suggestions from @flawr. According to the answer from @flawr, I implemented the periodic spline interpolation in python (still working on implementing fourier interpolation in python.). Here is the code:

import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import CubicSpline

# set up toy data
t = np.linspace(0, 2*np.pi, 10)
t = t[0:-1]
a = 0.08
b = 0.08
x = np.cos(t + a * np.random.normal(size=len(t))) + b * np.random.normal(size=len(t))
y = np.sin(t + a * np.random.normal(size=len(t))) + b * np.random.normal(size=len(t))
plt.scatter(x, y)

# periodic spline interpolation
z = []
for idx in range(len(x)):
    z.append(complex(x[idx], y[idx]))
z.append(complex(x[0], y[0]))
len_z = len(z)
t = [i for i in range(len_z)]
cs = CubicSpline(t, z, bc_type='periodic')

xs = np.linspace(0, len_z, 200)
y_new = cs(xs)

plt.plot(y_new.real, y_new.imag)
plt.show()

Upvotes: 0

flawr
flawr

Reputation: 11628

I think the key here is to note that you have to consider it as a parametrized curve in 2d, not just a 1d to 2d function. Furthermore since it should be something like a circle, you need an interpolation method that supports periodic boundaries. Here are two methods for which this applies:

% set up toy data
t = linspace(0, 2*pi, 10);
t = t(1:end-1);
a = 0.08;
b = 0.08;
x = cos(t+a*randn(size(t))) + b*randn(size(t));
y = sin(t+a*randn(size(t))) + b*randn(size(t));
plot(x, y, 'ok');

% fourier interpolation
z = x+1i*y;
y = interpft(z, 200);
hold on
plot(real(y), imag(y), '-.r')

% periodic spline interpolation
z = [z, z(1)];
n = numel(z);
t = 1:n;
pp = csape(t, z, 'periodic');
ts = linspace(1, n, 200);
y = ppval(pp, ts);;
plot(real(y), imag(y), ':b');

Upvotes: 2

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