将箭头放在 3d 图中的向量上

I plotted the eigenvectors of some 3D-data and was wondering if there is currently (already) a way to put arrowheads on the lines? Would be awesome if someone has a tip for me.

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

####################################################
# This part is just for reference if
# you are interested where the data is
# coming from
# The plot is at the bottom
#####################################################

# Generate some example data
mu_vec1 = np.array([0,0,0])
cov_mat1 = np.array([[1,0,0],[0,1,0],[0,0,1]])
class1_sample = np.random.multivariate_normal(mu_vec1, cov_mat1, 20)

mu_vec2 = np.array([1,1,1])
cov_mat2 = np.array([[1,0,0],[0,1,0],[0,0,1]])
class2_sample = np.random.multivariate_normal(mu_vec2, cov_mat2, 20)

# concatenate data for PCA
samples = np.concatenate((class1_sample, class2_sample), axis=0)

# mean values
mean_x = mean(samples[:,0])
mean_y = mean(samples[:,1])
mean_z = mean(samples[:,2])

#eigenvectors and eigenvalues
eig_val, eig_vec = np.linalg.eig(cov_mat)

################################
#plotting eigenvectors
################################    

fig = plt.figure(figsize=(15,15))
ax = fig.add_subplot(111, projection='3d')

ax.plot(samples[:,0], samples[:,1], samples[:,2], 'o', markersize=10, color='green', alpha=0.2)
ax.plot([mean_x], [mean_y], [mean_z], 'o', markersize=10, color='red', alpha=0.5)
for v in eig_vec:
    ax.plot([mean_x, v[0]], [mean_y, v[1]], [mean_z, v[2]], color='red', alpha=0.8, lw=3)
ax.set_xlabel('x_values')
ax.set_ylabel('y_values')
ax.set_zlabel('z_values')

plt.title('Eigenvectors')

plt.draw()
plt.show()

要将箭头补丁添加到 3D 绘图中，简单的解决方案是使用FancyArrowPatch类定义于/matplotlib/patches.py。但是，它仅适用于 2D 绘图（在撰写本文时），因为它的posA and posB应该是长度为 2 的元组。

因此我们创建一个新的箭头补丁类，将其命名为Arrow3D，它继承自FancyArrowPatch。我们唯一需要覆盖它的posA and posB。为此，我们发起Arrow3d with posA and posB of (0,0)是。 3D 坐标xs, ys, zs然后使用从 3D 投影到 2Dproj3d.proj_transform()，并将所得的 2D 坐标分配给posA and posB using .set_position()方法，替换(0,0)s。这样我们就可以让 3D 箭头发挥作用。

投影步骤进入.draw方法，它重写了.draw的方法FancyArrowPatch object.

这可能看起来像黑客攻击。但是，那mplot3d目前仅通过提供 3D-2D 投影来提供（再次强调）简单的 3D 绘图功能，并且基本上以 2D 方式进行所有绘图，这不是真正的 3D。

import numpy as np
from numpy import *
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib.patches import FancyArrowPatch
from mpl_toolkits.mplot3d import proj3d

class Arrow3D(FancyArrowPatch):
    def __init__(self, xs, ys, zs, *args, **kwargs):
        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)
        self._verts3d = xs, ys, zs

    def draw(self, renderer):
        xs3d, ys3d, zs3d = self._verts3d
        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
        self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))
        FancyArrowPatch.draw(self, renderer)

####################################################
# This part is just for reference if
# you are interested where the data is
# coming from
# The plot is at the bottom
#####################################################

# Generate some example data
mu_vec1 = np.array([0,0,0])
cov_mat1 = np.array([[1,0,0],[0,1,0],[0,0,1]])
class1_sample = np.random.multivariate_normal(mu_vec1, cov_mat1, 20)

mu_vec2 = np.array([1,1,1])
cov_mat2 = np.array([[1,0,0],[0,1,0],[0,0,1]])
class2_sample = np.random.multivariate_normal(mu_vec2, cov_mat2, 20)

实际绘图。请注意，我们只需要更改一行代码，即添加一个新的箭头艺术家：

# concatenate data for PCA
samples = np.concatenate((class1_sample, class2_sample), axis=0)

# mean values
mean_x = mean(samples[:,0])
mean_y = mean(samples[:,1])
mean_z = mean(samples[:,2])

#eigenvectors and eigenvalues
eig_val, eig_vec = np.linalg.eig(cov_mat1)

################################
#plotting eigenvectors
################################    

fig = plt.figure(figsize=(15,15))
ax = fig.add_subplot(111, projection='3d')

ax.plot(samples[:,0], samples[:,1], samples[:,2], 'o', markersize=10, color='g', alpha=0.2)
ax.plot([mean_x], [mean_y], [mean_z], 'o', markersize=10, color='red', alpha=0.5)
for v in eig_vec:
    #ax.plot([mean_x,v[0]], [mean_y,v[1]], [mean_z,v[2]], color='red', alpha=0.8, lw=3)
    #I will replace this line with:
    a = Arrow3D([mean_x, v[0]], [mean_y, v[1]], 
                [mean_z, v[2]], mutation_scale=20, 
                lw=3, arrowstyle="-|>", color="r")
    ax.add_artist(a)
ax.set_xlabel('x_values')
ax.set_ylabel('y_values')
ax.set_zlabel('z_values')

plt.title('Eigenvectors')

plt.draw()
plt.show()

请检查这个帖子 https://stackoverflow.com/questions/11140163/python-matplotlib-plotting-a-3d-cube-a-sphere-and-a-vector，这激发了这个问题，以了解更多详细信息。