spline interpolation coefficients of a line curve in 3d space

Question

I am new to python. I have a line curve in the 3D space defined by a set of given points. Can anyone suggest how I can use the interpolate with spline functions of the scipy package to get the spline coefficients of the curve just like the spline.coeff function in MATLAB? Thank you!

EDIT:

I have used the

tck = interpolate.SmoothBivariateSpline(pts2[:,0], pts2[:,1], pts2[:,2])
test_pts = pts2[:,2]-tck.ev(pts2[:,0], pts2[:,1])
print test_pts

but this is for surfaces apparently and not for line curves pts2 is a Nx3 numpy array containing the coordinates of the points

ok I figured out what I was doing wrong. my input points where too few. now I have another question. The function get_coeffs is supposed to return the spline coefficients at every not. In which order those coefficients are returned? I have an array of 79 tx and 79 ty which represent the knots and I get an array of 1x5625 when I call the function to call the knots

Solution

I too am new to python, but my recent searching led me to a very helpful scipy interpolation tutorial. From my reading of this I concur that the BivariateSpline family of classes/functions are intended for interpolating 3D surfaces rather than 3D curves.

For my 3D curve fitting problem (which I believe is very similar to yours, but with the addition of wanting to smooth out noise) I ended up using scipy.interpolate.splprep (not to be confused with scipy.interpolate.splrep). From the tutorial linked above, the spline coefficients your are looking for are returned by splprep.

The normal output is a 3-tuple, (t,c,k) , containing the knot-points, t , the coefficients c and the order k of the spline.

The docs keep referring to these procedural functions as an "older, non object-oriented wrapping of FITPACK" in contrast to the "newer, object-oriented" UnivariateSpline and BivariateSpline classes. I would have preferred "newer, object-oriented" myself, but as far as I can tell UnivariateSpline only handles the 1-D case whereas splprep handles N-D data directly.

Below is a simple test-case that I used to figure out these functions:

import numpy as np
import matplotlib.pyplot as plt
from scipy import interpolate
from mpl_toolkits.mplot3d import Axes3D


# 3D example
total_rad = 10
z_factor = 3
noise = 0.1

num_true_pts = 200
s_true = np.linspace(0, total_rad, num_true_pts)
x_true = np.cos(s_true)
y_true = np.sin(s_true)
z_true = s_true/z_factor

num_sample_pts = 80
s_sample = np.linspace(0, total_rad, num_sample_pts)
x_sample = np.cos(s_sample) + noise * np.random.randn(num_sample_pts)
y_sample = np.sin(s_sample) + noise * np.random.randn(num_sample_pts)
z_sample = s_sample/z_factor + noise * np.random.randn(num_sample_pts)

tck, u = interpolate.splprep([x_sample,y_sample,z_sample], s=2)
x_knots, y_knots, z_knots = interpolate.splev(tck[0], tck)
u_fine = np.linspace(0,1,num_true_pts)
x_fine, y_fine, z_fine = interpolate.splev(u_fine, tck)

fig2 = plt.figure(2)
ax3d = fig2.add_subplot(111, projection='3d')
ax3d.plot(x_true, y_true, z_true, 'b')
ax3d.plot(x_sample, y_sample, z_sample, 'r*')
ax3d.plot(x_knots, y_knots, z_knots, 'go')
ax3d.plot(x_fine, y_fine, z_fine, 'g')
fig2.show()
plt.show()