Plotting a curve with equidistant (arc-length) markers

Question

I would like to plot a graph of some experimental data which is sampled at a relatively high rate, but approximates a smooth curve using markers spaced at equal arc-length i

Answer 1

Since matplotlib 1.4, you can use markevery with real numbers to achieve this.

Documentation: http://matplotlib.org/api/lines_api.html#matplotlib.lines.Line2D.set_markevery

Example:

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 10*np.pi, 1000)
y = np.sin(x*2) + np.sin(x + 1)

plt.plot(x, y, marker='o', markevery=0.05)

plt.show()

Answer 2

I think I have put together a relatively good solution. The only problem is taking the data ratio into account in a way that also uses information about the aspect ratio of the final plot. I've not found a reliable way to do this, although this function will accept a data ratio so you can play until the output looks right:

def spacedmarks(x, y, Nmarks, data_ratio=None):
    import scipy.integrate

    if data_ratio is None:
        data_ratio = plt.gca().get_data_ratio()

    dydx = gradient(y, x[1])
    dxdx = gradient(x, x[1])*data_ratio
    arclength = scipy.integrate.cumtrapz(sqrt(dydx**2 + dxdx**2), x, initial=0)
    marks = linspace(0, max(arclength), Nmarks)
    markx = interp(marks, arclength, x)
    marky = interp(markx, x, y)
    return markx, marky

Example of use (this is suitable for pylab mode in iPython):

x = linspace(0, 10*pi, 1000)
y = sin(x*2) + sin(x+1)

plot(x, y)
markx, marky = spacedmarks(x, y, 80)
plot(markx, marky, 'o', color='blue')

Result: