How to generate equispaced interpolating values

Question

I have a list of (x,y) values that are not uniformly spaced. Here is the archive used in this question.

I am able to interpolate between the values but what I get ar

Answer 1

Convert your xy-data to a parametrized curve, i.e. calculate all all distances between the points and generate the coordinates on the curve by cumulative summing. Then interpolate the x- and y-coordinates independently with respect to the new coordinates.

import numpy as np
from matplotlib import pyplot as plt

data = '''0.615   5.349
    0.615   5.413
    0.617   6.674
    0.617   6.616
    0.63    7.418
    0.642   7.809
    0.648   8.04
    0.673   8.789
    0.695   9.45
    0.712   9.825
    0.734   10.265
    0.748   10.516
    0.764   10.782
    0.775   10.979
    0.783   11.1
    0.808   11.479
    0.849   11.951
    0.899   12.295
    0.951   12.537
    0.972   12.675
    1.038   12.937
    1.098   13.173
    1.162   13.464
    1.228   13.789
    1.294   14.126
    1.363   14.518
    1.441   14.969
    1.545   15.538
    1.64    16.071
    1.765   16.7
    1.904   17.484
    2.027   18.36
    2.123   19.235
    2.149   19.655
    2.172   20.096
    2.198   20.528
    2.221   20.945
    2.265   21.352
    2.312   21.76
    2.365   22.228
    2.401   22.836
    2.477   23.804'''

data = np.array([line.split() for line in data.split('\n')],dtype=float)

x,y = data.T
xd = np.diff(x)
yd = np.diff(y)
dist = np.sqrt(xd**2+yd**2)
u = np.cumsum(dist)
u = np.hstack([[0],u])

t = np.linspace(0,u.max(),10)
xn = np.interp(t, u, x)
yn = np.interp(t, u, y)

f = plt.figure()
ax = f.add_subplot(111)
ax.set_aspect('equal')
ax.plot(x,y,'o', alpha=0.3)
ax.plot(xn,yn,'ro', markersize=8)
ax.set_xlim(0,5)