python 3D，点成球，螺旋线/面，等高线，莫比乌斯环

点成球

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
PC = []
x = np.arange(-10,11,1)
for i in x: #[1,2]:
    y = list(np.arange(-np.sqrt(100-i**2),np.sqrt(100-i**2)+1 ))
    for it in y:
        PC.append([i,it])

#print(PC)
#print(np.array(PC).shape, PC[-1])
PC_a = []
for i,j in np.array(PC): #ii
    # print(ii)
    # i,j = ii
    print(i,j,-np.sqrt(100-i**2-j**2), np.sqrt(100-i**2-j**2))
    if i**2 + j**2 >= 100:
        continue
    z = list(np.arange(-np.sqrt(100-i**2-j**2), np.sqrt(100-i**2-j**2)+1 ))
    for it in z:
        PC_a.append([i,j,it])
print(PC_a)
print(np.array(PC_a).shape)
PC_a = np.array(PC_a)


fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(PC_a[:,0], PC_a[:,1], PC_a[:,2])

plt.show()

螺旋线、面

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

fig = plt.figure()
ax = Axes3D(fig)#plt.axes(projection='3d')

zline = np.linspace(0,150,1000)
xdata = np.sin(zline)
ydata = np.cos(zline)
ax.plot3D(xdata,ydata,zline,'r')

z = np.array(np.arange(0,150,150/1000))
x = z * np.sin(z)
y = z * np.cos(z)
print(z,x)
ax.scatter(x,y,z,'g')

plt.show()

面 + 莫比坞斯环

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

fig = plt.figure()
ax = Axes3D(fig)#plt.axes(projection='3d')

zline = np.linspace(0,150,1000)
xdata = np.sin(zline)
ydata = np.cos(zline)
ax.plot3D(xdata,ydata,zline,'r')

z = np.array(np.arange(0,150,150/1000))
x = z * np.sin(z)
y = z * np.cos(z)
print(z,x)
ax.scatter(x,y,z,'g')



# 2 contour
def sinBin(x,y):
    return np.sin(np.sqrt(x ** 2 + y ** 2))

X = np.linspace(-6,6,30)
Y = np.linspace(-6,6,30)
X,Y = np.meshgrid(X,Y)

Z = sinBin(X,Y)
fig2 = plt.figure()
ax = Axes3D(fig2)
ax.contour(X,Y,Z,50)#, cmap='binary')

# 3 wireframe 线框图，surface 表面图
fig3 = plt.figure()
ax = Axes3D(fig3)
ax.plot_wireframe(X,Y,Z)
ax.set_title('Wireframe')
ax.set_xlabel(' X ')

fig4 = plt.figure()
ax = Axes3D(fig4)
ax.plot_surface(X,Y,Z)
ax.set_title('surface')

# vector draw
r = np.linspace(0,6,20)
theta = np.linspace(-np.pi*0.9, np.pi*0.9,30)
r,theta = np.meshgrid(r,theta)

X = r * np.sin(theta)
Y = r * np.cos(theta)

Z = sinBin(X,Y)
print(X.shape,Y.shape,Z.shape)
fig5 = plt.figure()
ax = Axes3D(fig5)
ax.plot_surface(X,Y,Z,cmap='viridis')

# ravel, scatter --表面图用了网格坐标（面坐标），
# scatter用了向量坐标，可以用ravel，flatten来转化grid为vetor画图
theta = 2 * np.pi * np.random.random(1000)
r = 6 * np.random.random(1000)
x = np.ravel(r * np.sin(theta))
y = np.ravel(r * np.cos(theta))
z = sinBin(x, y)
print(r.shape,' x ',x.shape, ' y ', y.shape)

fig6 = plt.figure()
ax = Axes3D(fig6)
ax.scatter(x,y,z,cmap='viridis')

theta = 2 * np.pi * np.random.random(1000)
r = 6 * np.random.random(1000)
x = np.squeeze(np.reshape((r * np.sin(theta)),[len(r * np.sin(theta)),1]))
print(x.shape)
y = np.ravel(r * np.cos(theta)) #解开线团
z = sinBin(x, y)
print(r.shape,' x ',x.shape, ' y ', y.shape)

fig6 = plt.figure()
ax = Axes3D(fig6)
ax.scatter(x,y,z,cmap='viridis')

# 4-b trisurf通过三角法覆盖（相邻三个点连接为三角片，然后覆盖为面）

fig7 = plt.figure()
ax = Axes3D(fig7)
ax.plot_trisurf(x,y,z,cmap='viridis')



#结果肯定不像用网格绘制时那样干净，但是这种三角剖分的灵活性允许一些非常有趣的三维图。
# 例如，实际上可以使用此方法绘制三维莫比乌斯带，如下所示。
theta = np.linspace(0,2*np.pi, 30)
w = np.linspace(-0.25,0.25, 8) #环宽度0.25， 20
w, theta = np.meshgrid(w,theta)

# 环面旋转半圈； 精华了，一个是环面的旋转，180度； linspace（0，pi,30);
#另一个是正常的x-y面旋转，它是圆，但是由于环旋转，半径是变化的； 1 + 环长度的sin值
phi = 0.5 * theta

r = 2 + w * np.sin(phi) # r0调节环大小 + 环带宽度
x = np.ravel(r * np.cos(theta)) #矩阵，拉成向量画点
y = np.ravel(r * np.sin(theta))
z = np.ravel(w * np.cos(phi)) #0.25 * np.cos(phi)
print('mobius', x.shape,y.shape,z.shape)

from matplotlib.tri import Triangulation
tri = Triangulation(np.ravel(w), np.ravel(theta))

fig8 = plt.figure()
ax = Axes3D(fig8)
ax.plot_trisurf(x,y,z, triangles = tri.triangles,cmap='viridis')
#ax.scatter(x,y,z)
plt.show()