Question

Given a sequence of points in a 2D plane, [(x0,y0), (x1,y1), ...], I want to find a spline curve which passes through these points.

The classes in scipy.interpolate for 1D spline requires increasing x, since the list of these x-coordinates is not necessary increasing (i.e. the curve is not a function, f(x)=y, but rather a parametrised curve). Unfortunately, neither it is a function along y (otherwise by switching x and y coords the problem would be easily solved).

I have tried with the Univariate interpolation classes but this is not having the desired effect. How can I use scipy.interpolate to calculate this spline curve?

Answer 1

You need to reconsider how you think about this problem: Actually x is the parameterisation of the curve (which one would usually denote t for time) and y is the x,y co-ordinate:

L = [(x0,y0), (x1,y1), ...]
X = numpy.array(L).T
# Equivalently (but less generally):
# X = [[P[0] for P in L], [ P[1] for P in L ]]

t,X = enumerate(L) # here t[0]==0 and X[0]==(x0,x1,..), X[1]==(y0,y1,..)
# or to name in a more confusing manner but match the docs: x,y = enumerate(L)

Then you can use various scipy.interpolate functions, for example:

f = scipy.interpolate.interp1d(t, X)

.

For example the straight line between (0,0) and (1,1):

f = interp1d((0,1), numpy.array([[0,0],[1,1]]).T )
#          (t0,t1)  numpy.array([[x0,y0],[[x1,y1]]).T
#          (t0,t1)              [[x0,x1],[[y0,y1]]
f(0.5) # array([ 0.5,  0.5])