Contour/curve with orientation

Question

How would I plot a curve (in 3d perhaps) with something to show the direction that it's going. For example, to show that a circular plane curve is going clockwise or counterclockwise.

A curve like the one here, http://mathworld.wolfram.com/CauchyIntegralFormula.html

I am not sure even if there is a comparable function right now, so I don't have an example to show you. Thanks for reading.

Edit: I search quite a bit on this, don't think you can do this on gnuplot either.

Answer 1

Interesting question. I have no time for more than a quick and dirty hack, so here we go (liberally inspired from the code in mpl streamplot)

import matplotlib.lines as mlines
import matplotlib.patches as mpatches
import matplotlib.pyplot as plt
import numpy as np

def add_arrow_to_line2D(
    axes, line, arrow_locs=[0.2, 0.4, 0.6, 0.8],
    arrowstyle='-|>', arrowsize=1, transform=None):
    """
    Add arrows to a matplotlib.lines.Line2D at selected locations.

    Parameters:
    -----------
    axes: 
    line: list of 1 Line2D obbject as returned by plot command
    arrow_locs: list of locations where to insert arrows, % of total length
    arrowstyle: style of the arrow
    arrowsize: size of the arrow
    transform: a matplotlib transform instance, default to data coordinates

    Returns:
    --------
    arrows: list of arrows
    """
    if (not(isinstance(line, list)) or not(isinstance(line[0], 
                                           mlines.Line2D))):
        raise ValueError("expected a matplotlib.lines.Line2D object")
    x, y = line[0].get_xdata(), line[0].get_ydata()

    arrow_kw = dict(arrowstyle=arrowstyle, mutation_scale=10 * arrowsize)
    if transform is None:
        transform = axes.transData

    arrows = []
    for loc in arrow_locs:
        s = np.cumsum(np.sqrt(np.diff(x) ** 2 + np.diff(y) ** 2))
        n = np.searchsorted(s, s[-1] * loc)
        arrow_tail = (x[n], y[n])
        arrow_head = (np.mean(x[n:n + 2]), np.mean(y[n:n + 2]))
        p = mpatches.FancyArrowPatch(
            arrow_tail, arrow_head, transform=transform,
            **arrow_kw)
        axes.add_patch(p)
        arrows.append(p)
    return arrows


fig, ax = plt.subplots(1, 1)
t = np.linspace(0., 4*np.pi, 100.)
line = ax.plot(np.log(t+1)*np.cos(t), np.log(t+1)*np.sin(t),"-")
add_arrow_to_line2D(ax, line, arrow_locs=[0.1, 0.2, 0.3, 0.4, 0.6, 0.8, 0.99],
                    arrowsize=1.5)

ax.axis("equal")
ax.set_xlim([-4., 4.])
ax.set_ylim([-4., 4.])
plt.show()