Smooth spline representation of an arbitrary contour, f(length) --> x,y

Question

Suppose I have a set of x,y coordinates that mark points along contour. Is there a way that I can build a spline representation of the contour that I can evaluate at a parti

Answer 1

Here is an example using splprep and splev:

import numpy as np
import scipy.interpolate
from matplotlib.pyplot import plot

# x,y coordinates of contour points, not monotonically increasing
x = np.array([2.,  1.,  1.,  2.,  2.,  4.,  4.,  3.])
y = np.array([1.,  2.,  3.,  4.,  2.,  3.,  2.,  1.])

# f: X --> Y might not be a 1:1 correspondence
plot(x, y, '-o')

# get the cumulative distance along the contour
dist = np.sqrt((x[:-1] - x[1:])**2 + (y[:-1] - y[1:])**2)
dist_along = np.concatenate(([0], dist.cumsum()))

# build a spline representation of the contour
spline, u = scipy.interpolate.splprep([x, y], u=dist_along, s=0)

# resample it at smaller distance intervals
interp_d = np.linspace(dist_along[0], dist_along[-1], 50)
interp_x, interp_y = scipy.interpolate.splev(interp_d, spline)
plot(interp_x, interp_y, '-o')