将箭头放在 matplotlib 的 3d 图中的向量上 [英] Putting arrowheads on vectors in matplotlib's 3d plot

问题描述

我绘制了一些 3D 数据的特征向量，并想知道目前是否(已经)有办法将箭头放在直线上?如果有人给我提示，那就太棒了.

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()

推荐答案

要向 3D 绘图添加箭头补丁，简单的解决方案是使用 /matplotlib/patches 中定义的 FancyArrowPatch 类.py.但是，它仅适用于 2D 绘图(在撰写本文时)，因为它的 posA 和 posB 应该是长度为 2 的元组.

To add arrow patches to a 3D plot, the simple solution is to use FancyArrowPatch class defined in /matplotlib/patches.py. However, it only works for 2D plot (at the time of writing), as its posA and posB are supposed to be tuples of length 2.

因此我们创建了一个新的箭头补丁类，命名为Arrow3D，它继承自FancyArrowPatch.我们唯一需要覆盖它的posA 和posB.为此，我们使用 (0,0) 的 posA 和 posB 启动 Arrow3d.然后使用 proj3d.proj_transform() 将 3D 坐标 xs, ys, zs 从 3D 投影到 2D，并将生成的 2D 坐标分配给 posA 和 posB 使用 .set_position() 方法，替换 (0,0) s.这样我们就可以让 3D 箭头起作用.

Therefore we create a new arrow patch class, name it Arrow3D, which inherits from FancyArrowPatch. The only thing we need to override its posA and posB. To do that, we initiate Arrow3d with posA and posB of (0,0)s. The 3D coordinates xs, ys, zs was then projected from 3D to 2D using proj3d.proj_transform(), and the resultant 2D coordinates get assigned to posA and posB using .set_position() method, replacing the (0,0)s. This way we get the 3D arrow to work.

投影步骤进入 .draw 方法，该方法覆盖了 FancyArrowPatch 对象的 .draw 方法.

The projection steps go into the .draw method, which overrides the .draw method of the FancyArrowPatch object.

这可能看起来像是黑客攻击.但是，mplot3d 目前仅通过提供 3D-2D 投影来提供(再次，仅)简单的 3D 绘图能力，并且基本上以 2D 进行所有绘图，这不是真正的 3D.

This might appear like a hack. However, the mplot3d currently only provides (again, only) simple 3D plotting capacity by supplying 3D-2D projections and essentially does all the plotting in 2D, which is not truly 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)

实物图.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:

Actual drawing. Note that we only need to change one line of your code, which add an new arrow artist:

# 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()

请查看这篇文章，启发了这个问题，了解更多细节.

Please check this post, which inspired this question, for further details.

这篇关于将箭头放在 matplotlib 的 3d 图中的向量上的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！