在matplotlib的3d图中将箭头放在矢量上

Question

我绘制了一些3D数据的特征向量，并想知道目前（已经）是否有办法将箭头放在线上？如果有人给我一个提示，那会很棒。

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()

Answer 1

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

因此，我们创建了一个新的箭头补丁类，将其命名为Arrow3D，它继承自FancyArrowPatch。我们唯一需要覆盖其posA和posB。为此，我们使用Arrow3d和posA posB启动(0,0)。然后使用xs, ys, zs将3D坐标proj3d.proj_transform()从3D投影到2D，并使用posA方法将生成的2D坐标分配给posB和.set_position()，替换(0,0)。这样我们就可以使用3D箭头了。

投影步骤进入.draw方法，该方法会覆盖.draw对象的FancyArrowPatch方法。

这可能看起来像黑客。然而，mplot3d目前仅通过提供3D-2D投影提供（再次，仅）简单的3D绘图容量，并且基本上完成2D中的所有绘图，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，我们只需更改代码的一行，即添加新的箭头艺术家：

# 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()

请查看启发了此问题的this post，了解更多详情。

Answer 2

另一种选择：您还可以使用plt.quiver函数，该函数可以非常容易地生成箭头矢量，而无需任何额外的导入或类。

要复制您的示例，您将替换为：

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)

具有：

for v in eig_vec:
    ax.quiver(
        mean_x, mean_y, mean_z, # <-- starting point of vector
        v[0] - mean_x, v[1] - mean_y, v[2] - mean_z, # <-- directions of vector
        color = 'red', alpha = .8, lw = 3,
    )