Interpolating between curves using SciPy

Question

Here is my plot:

The existing curves are functions obtained using interp1d and I have the raw data as well.

How can I extrapolate to get a curve for 71.5 and interpolate to get a curve for 44.3 using SciPy?

Answer 1

You could interpolate between the two closest curves with weights depending on the value differences. The weights should sum to 1. For the extrapolation, the furthest away curve will have a negative weight.

The code supposes the same number of x and y values for each curve.

import matplotlib.pyplot as plt
import numpy as np

c30 = np.array([[29.58, 10992.90], [34.06, 10488.35], [36.53, 10166.76], [38.92, 9836.60], [41.99, 9298.52], [45.13, 8708.54], [47.68, 8153.57], [49.34, 7768.64], [50.30, 7546.69]])
c45 = np.array([[26.79, 10598.67], [28.89, 10282.69], [30.99, 9962.94], [33.09, 9622.18], [35.18, 9220.9], [37.28, 8773.75], [39.38, 8311.88], [41.48, 7836.1], [43.58, 7344.26]])
c60 = np.array([[24.44, 9518.93], [25.81, 9231.69], [27.17, 8919.78], [28.54, 8576.69], [29.9, 8213.69], [31.27, 7841.51], [32.64, 7437.91], [34., 7004.48], [35.37, 6569.1]])

plt.plot(c30[:, 0], c30[:, 1], color='dodgerblue', label='30')
plt.plot(c45[:, 0], c45[:, 1], color='limegreen', label='45')
plt.plot(c60[:, 0], c60[:, 1], color='crimson', label='60')

c44_3 = ((44.3 - 30) * c45 + (45 - 44.3) * c30) / (45 - 30)
c71_5 = ((71.5 - 45) * c60 + (60 - 71.5) * c45) / (60 - 45)

plt.plot(c44_3[:, 0], c44_3[:, 1], color='orange', label='44.3')
plt.plot(c71_5[:, 0], c71_5[:, 1], color='purple', label='71.5')
plt.legend()
plt.show()