[[TableOfContents]] = Using B-splines in scipy.signal = Example showing how to use B-splines in scipy.signal to do interpolation. The input points must be equally spaced to use these routine. {{{#!python numbers=disable from numpy import r_, sin from scipy.signal import cspline1d, cspline1d_eval x = r_[0:10] dx = x[1]-x[0] newx = r_[-3:13:0.1] # notice outside the original domain y = sin(x) cj = cspline1d(y) newy = cspline1d_eval(cj, newx, dx=dx,x0=x[0]) from pylab import plot, show plot(newx, newy, x, y, 'o') show() }}} inline:interpolate_figure1.png = N-D interpolation for equally-spaced data = The scipy.ndimage package also contains spline_filter and map_coordinates which can be used to perform N-dimensional interpolation for equally-spaced data. A two-dimensional example is given below: {{{#!python numbers=disable from scipy import ogrid, sin, mgrid, ndimage, array x,y = ogrid[-1:1:5j,-1:1:5j] fvals = sin(x)*sin(y) newx,newy = mgrid[-1:1:100j,-1:1:100j] x0 = x[0,0] y0 = y[0,0] dx = x[1,0] - x0 dy = y[0,1] - y0 ivals = (newx - x0)/dx jvals = (newy - y0)/dy coords = array([ivals, jvals]) newf = ndimage.map_coordinates(fvals, coords) }}} To pre-compute the weights (for multiple interpolation results), you would use {{{#!python numbers=disable coeffs = ndimage.spline_filter(fvals) newf = ndimage.map_coordinates(coeffs, coords, prefilter=False) }}} inline:interpolate_figure2.png = Interpolation of an N-D curve = The scipy.interpolate packages wraps the netlib FITPACK routines (Dierckx) for calculating smoothing splines for various kinds of data and geometries. Although the data is evenly spaced in this example, it need not be so to use this routine. {{{#!python numbers=disable from numpy import arange, cos, linspace, pi, sin, random from scipy.interpolate import splprep, splev # make ascending spiral in 3-space t=linspace(0,1.75*2*pi,100) x = sin(t) y = cos(t) z = t # add noise x+= random.normal(scale=0.1, size=x.shape) y+= random.normal(scale=0.1, size=y.shape) z+= random.normal(scale=0.1, size=z.shape) # spline parameters s=3.0 # smoothness parameter k=2 # spline order nest=-1 # estimate of number of knots needed (-1 = maximal) # find the knot points tckp,u = splprep([x,y,z],s=s,k=k,nest=-1) # evaluate spline, including interpolated points xnew,ynew,znew = splev(linspace(0,1,400),tckp) import pylab pylab.subplot(2,2,1) data,=pylab.plot(x,y,'bo-',label='data') fit,=pylab.plot(xnew,ynew,'r-',label='fit') pylab.legend() pylab.xlabel('x') pylab.ylabel('y') pylab.subplot(2,2,2) data,=pylab.plot(x,z,'bo-',label='data') fit,=pylab.plot(xnew,znew,'r-',label='fit') pylab.legend() pylab.xlabel('x') pylab.ylabel('z') pylab.subplot(2,2,3) data,=pylab.plot(y,z,'bo-',label='data') fit,=pylab.plot(ynew,znew,'r-',label='fit') pylab.legend() pylab.xlabel('y') pylab.ylabel('z') pylab.savefig('splprep_demo.png') }}} inline:splprep_demo.png