具有方向的轮廓/曲线

Question

我如何用一些曲线绘制曲线（在3d中），以显示它的方向。例如，显示圆形平面曲线顺时针或逆时针方向。

像这里的曲线， http://mathworld.wolfram.com/CauchyIntegralFormula.html

即使现在有类似的功能，我也不确定，所以我没有一个例子可以告诉你。 谢谢你的阅读。

编辑：我在这方面搜索了一下，不要以为你也可以在gnuplot上这样做。

Answer 1

有趣的问题。我没有时间不仅仅是一个快速而又肮脏的黑客，所以我们走了（从mpl streamplot中的代码中获得灵感）

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()