The following call:

rbf = Rbf(points[0], points[1], values,epsilon=2)

results in an error:

LinAlgError: singular matrix

with the following values:

In [3]: points
Out[3]: 
(array([71, 50, 48, 84, 71, 74, 89, 76, 70, 77, 74, 79, 83, 71, 72, 78, 73,84, 75, 65, 73, 82, 48, 86, 74, 86, 66, 74, 68, 74, 81, 74, 88, 66,57, 50, 72, 86, 72, 92, 81, 67, 82, 78, 69, 70, 73, 71, 76, 72, 74,75]),array([32, 34,  4, 35,  1,  7, 47, 16, 37, 14, 65, 18, 32,  4,  3, 27, 25,34, 18, 25,  6, 25, 34, 41, 16, 35, 44,  2, 32,  2, 37, 60, 45, 32,33, 42, 54, 31, 18, 38, 24, 18, 45, 48,  9, 63, 56, 45,  9, 59,  5,12]))In [4]: values
Out[4]: 
array([ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.])

What can I do to avoid it and still solve the interpolation problem?

I think what you're trying to do is kernel density estimation. You can use scipy.stats.gaussian_kde for this:

import numpy as np
from scipy.stats import gaussian_kde
from matplotlib import pyplot as pp# kernel density estimate of the PDF
kde = gaussian_kde(points)# evaluate the estimated PDF on a grid
x,y = np.mgrid[40:101,-20:101]
z = kde((x.ravel(),y.ravel())).reshape(*x.shape)# plot
fig,ax = pp.subplots(1,1)
ax.hold(True)
pc = ax.pcolor(x,y,z)
cb = pp.colorbar(pc)
cb.ax.set_ylabel('Probability density')
ax.plot(points[0],points[1],'o',mfc='w',mec='k')pp.show()

The statsmodels module also has some more elaborate tools for kernel density estimation.