Matplotlib mplot3d 工具包簡介

The mplot3d toolkit adds simple 3D plotting capabilities to matplotlib by supplying an axes object that can create a 2D projection of a 3D scene. The resulting graph will have the same look and feel as regular 2D plots.

建立Axes3D物件

An Axes3D object is created just like any other axes using the projection=‘3d’ keyword. Create a new matplotlib.figure.Figure and add a new axes to it of type Axes3D:
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = fig.add_subplot(111, projection=’3d’)
New in version 1.0.0: This approach is the preferred method of creating a 3D axes.
Note

: Prior to version 1.0.0, the method of creating a 3D axes was di erent. For those using older versions of matplotlib, change ax = fig.add_subplot(111, projection=’3d’) to ax = Axes3D(fig).

要注意的地方

Axes3D展示三維圖形時，其初始檢視中x,y軸與我們一般看的檢視（自己畫的時候的檢視）是反轉的，matlab也是一樣。

可以通過設定初始檢視來改變角度：ax.view_init(30, 35)

Note: 不過這樣圖形可能會因為旋轉而有陰影，也可以通過程式碼中XY軸互換來實現檢視中XY互換。不知道有沒有其它方法，如matlab中就有surf(x,y,z);set(gca,'xdir','reverse','ydir','reverse')這樣命令來實現這個功能[

關於matlab三維圖座標軸原點位置的問題]。

lz總結繪製三維圖形一般流程

建立Axes3D物件

fig = plt.figure()
ax = Axes3D(fig)

再進行座標範圍設定什麼的（可選）

# 計算座標極限值xs = list(itertools.chain.from_iterable([xi[0] for xi in x]))
x_max, x_min = max(xs), min(xs)
ys = list(itertools.chain.from_iterable([xi[1] for xi in x]))
y_max, y_min = max(ys), min(ys)
zs = list
 
(itertools.chain.from_iterable([xi[2] for xi in x]))
z_max, z_min = max(zs), min(zs)
margin = 0.1

再進行繪製，如

plt.scatter(x_new[0], x_new[1], c='r', marker='*', s=50, label='new x')

ax.scatter(xs, ys, zs, c=c, marker=marker, s=50, label=label)

ax.plot_surface(X, Y, Z, rstride=1, cstride=1, label='Discrimination Interface')

再進行一些座標什麼的設定

# 設定圖形展示效果ax.set_xlim(x_min - margin, x_max + margin)
ax.set_ylim(y_min - margin, y_max + margin)
ax.set_zlim(z_min - margin, z_max + margin)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.legend(loc='lower right')
ax.set_title('Plot of class0 vs. class1')
ax.view_init(30, 35)

最後顯示出來

plt.show()

繪製不同三維圖形

Line plots線圖

Scatter plots散點圖

Axes3D.scatter(xs, ys, zs=0, zdir=u'z', s=20, c=u'b', depthshade=True, *args, **kwargs)

Create a scatter plot

Argument	Description
xs, ys	Positions of data points.
zs	Either an array of the same length as xs andys or a single value to place all points inthe same plane. Default is 0.
zdir	Which direction to use as z (‘x’, ‘y’ or ‘z’)when plotting a 2D set.
s	size in points^2. It is a scalar or an array of thesame length as x andy.
c	a color. c can be a single color format string, or asequence of color specifications of lengthN, or asequence ofN numbers to be mapped to colors using thecmap andnorm specified via kwargs (see below). Notethatc should not be a single numeric RGB or RGBAsequence because that is indistinguishable from an arrayof values to be colormapped.c can be a 2-D array inwhich the rows are RGB or RGBA, however.
depthshade	Whether or not to shade the scatter markers to givethe appearance of depth. Default isTrue.

Keyword arguments are passed on to scatter().Returns a Patch3DCollectionNote:scatter(x,y,s=20,c=u'b',marker=u'o',cmap=None,norm=None,vmin=None,vmax=None,alpha=None,linewidths=None,verts=None,**kwargs)

Wireframe plots線框圖

Surface plots曲面圖

引數

x, y, z: x,y,z軸對應的資料。注意z的資料的z.shape是(len(y), len(x))，不然會報錯：ValueError: shape mismatch: objects cannot be broadcast to a single shape

rstride    Array row stride (step size), defaults to 10
cstride    Array column stride (step size), defaults to 10

示例1：

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

fig = plt.figure()
ax = Axes3D(fig)
X = np.arange(-4, 4, 0.25)
Y = np.arange(-4, 4, 0.25)
X, Y = np.meshgrid(X, Y)
R = np.sqrt(X**2 + Y**2)
Z = np.sin(R)

ax.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=plt.cm.hot)
ax.contourf(X, Y, Z, zdir='z', offset=-2, cmap=plt.cm.hot)
ax.set_zlim(-2,2)

# savefig('../figures/plot3d_ex.png',dpi=48)
plt.show()

結果圖形輸出：

示例2：

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

fig = plt.figure()
ax = Axes3D(fig)

x = np.arange(0, 200)
y = np.arange(0, 100)
x, y = np.meshgrid(x, y)
z = np.random.randint(0, 200, size=(100, 200))%3
print(z.shape)

# ax.scatter(x, y, z, c='r', marker='.', s=50, label='')
ax.plot_surface(x, y, z,label='')
plt.show()

Tri-Surface plots三面圖

Contour plots等高線圖

Filled contour plots填充等高線圖

Polygon plots多邊形圖

Axes3D.add_collection3d(col, zs=0, zdir=u'z')

Add a 3D collection object to the plot.

2D collection types are converted to a 3D version bymodifying the object and adding z coordinate information.

Supported are:

• PolyCollection
• LineColleciton
• PatchCollection

繪圖原理是：設定好多面體（如正文體）的頂點座標和所有面對應的頂點，加上一些屬性（如顏色、寬度、透明度）

繪製正方體和四面體示例

#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
__title__ = ''
__author__ = '皮'
__mtime__ = '9/27/2015-027'
__email__ = '[email protected]'"""
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d.art3d import Poly3DCollection

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


# 正文體頂點和麵
verts = [(0, 0, 0), (0, 1, 0), (1, 1, 0), (1, 0, 0), (0, 0, 1), (0, 1, 1), (1, 1, 1), (1, 0, 1)]
faces = [[0, 1, 2, 3], [4, 5, 6, 7], [0, 1, 5, 4], [1, 2, 6, 5], [2, 3, 7, 6], [0, 3, 7, 4]]
# 四面體頂點和麵
# verts = [(0, 0, 0), (1, 0, 0), (1, 1, 0), (1, 0, 1)]
# faces = [[0, 1, 2], [0, 1, 3], [0, 2, 3], [1, 2, 3]]
# 獲得每個面的頂點
poly3d = [[verts[vert_id] for vert_id in face] for face in faces]
# print(poly3d)
# 繪製頂點
x, y, z = zip(*verts)
ax.scatter(x, y, z)
# 繪製多邊形面
ax.add_collection3d(Poly3DCollection(poly3d, facecolors='w', linewidths=1, alpha=0.3))
# ax.add_collection3d(Line3DCollection(poly3d, colors='k', linewidths=0.5, linestyles=':'))

 # 設定圖形座標範圍ax.set_xlabel('X')ax.set_xlim3d(-0.5, 1.5)ax.set_ylabel('Y')ax.set_ylim3d(-0.5, 1.5)ax.set_zlabel('Z')ax.set_zlim3d(-0.5, 1.5)plt.show()

繪製結果截圖

  

Bar plots條形圖

2D plots in 3D三維圖中的二維圖

Text文字圖

Subplotting子圖

matplotlib.mplot3d繪圖例項

matplotlib繪製2維高斯分佈

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
fig = plt.figure()
ax = Axes3D(fig)
rv = stats.multivariate_normal([0, 0], cov=1)
x, y = np.mgrid[-3:3:.15, -3:3:.15]
ax.plot_surface(x, y, rv.pdf(np.dstack((x, y))), rstride=1, cstride=1)
ax.set_zlim(0, 0.2)

# savefig('../figures/plot3d_ex.png',dpi=48)
plt.show()

matplotlib繪製平行z軸的平面

（垂直xy平面的平面）

方程：0*Z + A[0]X + A[1]Y + A[-1] = 0

X = np.arange(x_min - margin, x_max + margin, 0.05)
Z = np.arange(z_min - margin, z_max + margin, 0.05)
X, Z = np.meshgrid(X, Z)
Y = -1 / A[1] * (A[0] * X + A[-1])
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, label='Discrimination Interface')

[mplot3d¶]