matplotlib（六）三维作图

写在篇前

  matplotlib也支持三维作图，但是相对于matlab来讲，感觉功能更弱。当然话说回来，三维作图用的场景相对也更少，所以呢，有一定的知识储备就够了。matplotlib绘制三维图形依赖于mpl_toolkits.mplot3d，用法也比较简单，只需要一个关键字参数projection='3d'就可以创建三维Axes。

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

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

 你可能会看到有的教程写的是ax = Axes3D(fig)，这是version1.0.0之前的写法

三维绘图函数

LinePlot

• Axes3D.``plot(xs, ys, *args, zdir=‘z’, **kwargs)

    其他参数向下传递给plot函数

Argument	Description
xs, ys	x、y 坐标
zs	z 坐标，可以是一个标量或一个x*y维矩阵
zdir	当绘制二维图像时的z轴方向

from mpl_toolkits.mplot3d import Axes3D

import numpy as np
import matplotlib.pyplot as plt


plt.rcParams['legend.fontsize'] = 10
fig = plt.figure()
ax = fig.gca(projection='3d')  # get current axes

# Prepare arrays x, y, z
theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)
z = np.linspace(-2, 2, 100)
r = z**2 + 1
x = r * np.sin(theta)
y = r * np.cos(theta)

ax.plot(x, y, z, label='parametric curve')
ax.legend()  # legend content dertermined by label above

plt.show()

ScatterPlot

• Axes3D.``scatter(xs, ys, zs=0, zdir=‘z’, s=20, c=None, depthshade=True, *args, **kwargs)

  返回Patch3DCollection,

    其他参数向下传递给plot函数

  Argument	Description
  xs, ys	x,y坐标点
  zs	z 坐标，可以是一个标量或一个x*y维矩阵，默认是0.
  zdir	当绘制二维图像时的z轴方向
  s	size,即散点大小
  c	颜色映射，其取值可以是非常多类型，有时间专门写一篇讲解
  depthshade	是否渲染景深（或则就说阴影吧），默认是True.

from mpl_toolkits.mplot3d import Axes3D

import matplotlib.pyplot as plt
import numpy as np

# Fixing random state for reproducibility
np.random.seed(19680801)


def randrange(n, vmin, vmax):
    '''
    Helper function to make an array of random numbers having shape (n, )
    with each number distributed Uniform(vmin, vmax).
    '''
    return (vmax - vmin)*np.random.rand(n) + vmin

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

n = 100

# For each set of style and range settings, plot n random points in the box
# defined by x in [23, 32], y in [0, 100], z in [zlow, zhigh].
for c, m, zlow, zhigh in [('r', 'o', -50, -25), ('b', '^', -30, -5)]:
    xs = randrange(n, 23, 32)
    ys = randrange(n, 0, 100)
    zs = randrange(n, zlow, zhigh)
    ax.scatter(xs, ys, zs, c=c, marker=m)

ax.set_xlabel('X Label')
ax.set_ylabel('Y Label')
ax.set_zlabel('Z Label')

plt.show()

WireframePlot

• Axes3D.``plot_wireframe(X, Y, Z, *args, **kwargs)

  Argument	Description
  X, Y,Z	坐标点
  rcount,ccount	采样数，越大采样越多，默认50
  rstride,cstride	采样步长，越小采样越多
  **kwargs	其他参数向下传入Line3DCollection

  from mpl_toolkits.mplot3d import axes3d
  import matplotlib.pyplot as plt
  
  
  fig = plt.figure()
  ax = fig.add_subplot(111, projection='3d')
  
  # Grab some test data.
  X, Y, Z = axes3d.get_test_data(0.05)
  
  # Plot a basic wireframe.
  ax.plot_wireframe(X, Y, Z, rstride=10, cstride=10)
  
  plt.show()
  

SurfacePlot

• Axes3D.``plot_surface(X, Y, Z, *args, norm=None, vmin=None, vmax=None, lightsource=None, **kwargs)

    这个函数算是比较常用的函数，用于绘制三维表面图，让人惊艳的是它的着色效果。

  Argument	Description
  X, Y，Z	坐标点
  rcount,ccount,rstride,cstride	同上
  color	定义surface patch的颜色,type:color-like
  cmap	定义surface patch的颜色，只不过是colorMap,type:colormap
  facecolors	指定单个patch的颜色, type:array-like of colors
  norm	colormap的normalization， type:Normalize
  shade	阴影效果，type:boolean
  vmin, vmax	normalization的边界
  **kwargs	向下传递到Poly3DCollection
  antialiased	抗锯齿，type:boolean

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm

from matplotlib.ticker import LinearLocator, FormatStrFormatter
import numpy as np


fig = plt.figure()
ax = fig.gca(projection='3d')

# Make data.
X = np.arange(-5, 5, 0.25)
Y = np.arange(-5, 5, 0.25)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = np.sin(R)

# Plot the surface.
surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm,
                       linewidth=0, antialiased=False)

# Customize the z axis.
ax.set_zlim(-1.01, 1.01)
ax.zaxis.set_major_locator(LinearLocator(10))
ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))

# Add a color bar which maps values to colors.
fig.colorbar(surf, shrink=0.5, aspect=5)

plt.show()

ContourPlot

• Axes3D.``contour(X, Y, Z, *args, extend3d=False, stride=5, zdir=‘z’, offset=None, **kwargs)

  Argument	Description
  X, Y,Z	Data values as numpy.arrays
  extend3d	是否延申到3d空间 (default: False)
  *stride	（extend3d的）采样步长
  zdir	同上
  offset	绘制轮廓线在zdir垂直的水平面上的投影

    其他位置、关键字参数向下传递到二维contour()函数

from mpl_toolkits.mplot3d import axes3d
import matplotlib.pyplot as plt
from matplotlib import cm

fig = plt.figure()
ax = fig.gca(projection='3d')
X, Y, Z = axes3d.get_test_data(0.05)

# Plot contour curves
cset = ax.contour(X, Y, Z, cmap=cm.coolwarm)

ax.clabel(cset, fontsize=9, inline=1)  # function to label a contour

plt.show()

FilledContourPlot

• Axes3D.``contourf(X, Y, Z, *args, zdir=‘z’, offset=None, **kwargs)

Argument	Description
X, Y,Z	Data values as numpy.arrays
zdir	同上
offset	绘制轮廓线在zdir垂直的水平面上的投影

  其他位置、关键字参数向下传递到二维contourf(),例子请参考上面的contour

PolygonPlot

• Axes3D.``add_collection3d(col, zs=0, zdir=‘z’)

     这个函数挺有趣，但是我没有遇到过这种场景。它可以将三维 collection对象或二维collection对象加入到一个图形中，包括：

  • PolyCollection

  • LineCollection

  • PatchCollection

  from mpl_toolkits.mplot3d import Axes3D  # noqa: F401 unused import
  
  from matplotlib.collections import PolyCollection
  import matplotlib.pyplot as plt
  from matplotlib import colors as mcolors
  import numpy as np
  
  # Fixing random state for reproducibility
  np.random.seed(19680801)
  
  
  def cc(arg):
      '''
      Shorthand to convert 'named' colors to rgba format at 60% opacity.
      '''
      return mcolors.to_rgba(arg, alpha=0.6)
  
  
  def polygon_under_graph(xlist, ylist):
      '''
      Construct the vertex list which defines the polygon filling the space under
      the (xlist, ylist) line graph.  Assumes the xs are in ascending order.
      '''
      return [(xlist[0], 0.), *zip(xlist, ylist), (xlist[-1], 0.)]
  
  
  fig = plt.figure()
  ax = fig.gca(projection='3d')
  
  # Make verts a list, verts[i] will be a list of (x,y) pairs defining polygon i
  verts = []
  
  # Set up the x sequence
  xs = np.linspace(0., 10., 26)
  
  # The ith polygon will appear on the plane y = zs[i]
  zs = range(4)
  
  for i in zs:
      ys = np.random.rand(len(xs))
      verts.append(polygon_under_graph(xs, ys))
  
  poly = PolyCollection(verts, facecolors=[cc('r'), cc('g'), cc('b'), cc('y')])
  ax.add_collection3d(poly, zs=zs, zdir='y')
  
  ax.set_xlabel('X')
  ax.set_ylabel('Y')
  ax.set_zlabel('Z')
  ax.set_xlim(0, 10)
  ax.set_ylim(-1, 4)
  ax.set_zlim(0, 1)
  
  plt.show()
  

BarPlot

• Axes3D.``bar(left, height, zs=0, zdir=‘z’, *args, **kwargs)

   其他参数向下传递给bar函数，返回Patch3DCollection对象

  Argument	Description
  left	条形图水平坐标
  height	条形的高度
  zs	Z方向
  zdir	同上

  from mpl_toolkits.mplot3d import Axes3D  # noqa: F401 unused import
  
  import matplotlib.pyplot as plt
  import numpy as np
  
  # Fixing random state for reproducibility
  np.random.seed(19680801)
  
  
  fig = plt.figure()
  ax = fig.add_subplot(111, projection='3d')
  
  colors = ['r', 'g', 'b', 'y']
  yticks = [3, 2, 1, 0]
  for c, k in zip(colors, yticks):
      # Generate the random data for the y=k 'layer'.
      xs = np.arange(20)
      ys = np.random.rand(20)
  
      # You can provide either a single color or an array with the same length as
      # xs and ys. To demonstrate this, we color the first bar of each set cyan.
      cs = [c] * len(xs)
  
      # Plot the bar graph given by xs and ys on the plane y=k with 80% opacity.
      ax.bar(xs, ys, zs=k, zdir='y', color=cs, alpha=0.8)
  
  ax.set_xlabel('X')
  ax.set_ylabel('Y')
  ax.set_zlabel('Z')
  
  # On the y axis let's only label the discrete values that we have data for.
  ax.set_yticks(yticks)
  
  plt.show()
  

  

Text

• Axes3D.``text(x, y, z, s, zdir=None, **kwargs)

    text的内容其实也很繁杂，需要用一篇内容去探讨，在三维中很重要的一点是要学会二维、三维文字的添加。

  from mpl_toolkits.mplot3d import Axes3D  # noqa: F401 unused import
  
  import matplotlib.pyplot as plt
  
  
  fig = plt.figure()
  ax = fig.gca(projection='3d')
  
  # Demo 1: zdir
  zdirs = (None, 'x', 'y', 'z', (1, 1, 0), (1, 1, 1))
  xs = (1, 4, 4, 9, 4, 1)
  ys = (2, 5, 8, 10, 1, 2)
  zs = (10, 3, 8, 9, 1, 8)
  
  for zdir, x, y, z in zip(zdirs, xs, ys, zs):
      label = '(%d, %d, %d), dir=%s' % (x, y, z, zdir)
      ax.text(x, y, z, label, zdir)
  
  # Demo 2: color
  ax.text(9, 0, 0, "red", color='red')
  
  # Demo 3: text2D
  # Placement 0, 0 would be the bottom left, 1, 1 would be the top right.
  ax.text2D(0.05, 0.95, "2D Text", transform=ax.transAxes)
  
  # Tweaking display region and labels
  ax.set_xlim(0, 10)
  ax.set_ylim(0, 10)
  ax.set_zlim(0, 10)
  ax.set_xlabel('X axis')
  ax.set_ylabel('Y axis')
  ax.set_zlabel('Z axis')
  
  plt.show()
  

写在篇后

  三维绘图不是很常用，主要就是scatterPlot以及surfacePlot稍微更常用。关于三维绘图总结的也有点糙，更多关于matplotlib,可以阅读参考我写的同类文章请参考:

• Matplotlib（一）工作流程
• Matplotlib（二）绘图生命周期
• Matplotlib（三） rcParams 自定义样式控制
• matplotlib（四）核心模式以及注意事项
• matplotlib（五）排版布局