Matplotlib 3d 散布 plot 最佳拟合平面

Question

Hello I recently made a 3d scatter plot with python (matplotlib) for my bio class, and I wanted to know how I coukd implement a line of best fit, or even a plane or a circle of best fit. But I can't seem to find anything online. This is my code

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
   
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
    
x = [
    180, 183, 191, 180, 190, 190, 180, 165, 182, 187,
    179, 181, 180, 180, 181, 197, 193, 188, 180, 190,
    188, 191, 185, 175, 158, 180, 193, 186, 165, 172,
    168, 181, 178, 172, 189, 189, 185, 181, 188, 188,
    194, 192, 188, 188, 180, 188, 191, 197, 183
]
y = [
    102, 98, 138, 54, 148, 92, 88, 112, 92, 99, 112, 116,
    104, 81, 94, 120, 108, 80, 110, 90, 120, 100, 142, 108,
    138, 96, 74, 96, 129, 130, 134, 140, 126, 94, 90, 128,
    106, 104, 120, 86, 102, 162, 94, 118, 92, 110, 96,
    102, 98
]
z = [
    162, 168, 175, 175, 169, 179, 152, 165, 182, 158,
    155, 167, 164, 160, 175.7, 180, 158, 186, 176, 160,
    199.7, 172, 180, 162, 173, 180, 152, 171, 163, 169,
    179.832, 170, 173, 172, 173, 180, 170, 170, 170, 164,
    170, 164, 170, 177, 173, 166, 172, 167, 159
]

ax.scatter(x, y, z, c='r', marker='o')
        
ax.set_xlabel('Age')
ax.set_ylabel('Heart Rate')
ax.set_zlabel('Height')
    
plt.show()

Answer 1

For computing the line and plane of best fit you can use the scikit-spatial library.

First, convert your coordinates to a Points instance:

import numpy as np

from skspatial.objects import Points

x = [
    180, 183, 191, 180, 190, 190, 180, 165, 182, 187,
    179, 181, 180, 180, 181, 197, 193, 188, 180, 190,
    188, 191, 185, 175, 158, 180, 193, 186, 165, 172,
    168, 181, 178, 172, 189, 189, 185, 181, 188, 188,
    194, 192, 188, 188, 180, 188, 191, 197, 183
]
y = [
    102, 98, 138, 54, 148, 92, 88, 112, 92, 99, 112, 116,
    104, 81, 94, 120, 108, 80, 110, 90, 120, 100, 142, 108,
    138, 96, 74, 96, 129, 130, 134, 140, 126, 94, 90, 128,
    106, 104, 120, 86, 102, 162, 94, 118, 92, 110, 96,
    102, 98
]
z = [
    162, 168, 175, 175, 169, 179, 152, 165, 182, 158,
    155, 167, 164, 160, 175.7, 180, 158, 186, 176, 160,
    199.7, 172, 180, 162, 173, 180, 152, 171, 163, 169,
    179.832, 170, 173, 172, 173, 180, 170, 170, 170, 164,
    170, 164, 170, 177, 173, 166, 172, 167, 159
]

points = Points(np.column_stack((x, y, z)))

To compute the line of best fit do the following:

from skspatial.objects import Line
from skspatial.plotting import plot_3d

line = Line.best_fit(points)

plot_3d(
    points.plotter(c='r', s=10, depthshade=False),
    line.plotter(t_1=-50, t_2=50),
)

Similarly, for the plane of best fit:

from skspatial.objects import Plane
from skspatial.plotting import plot_3d

plane = Plane.best_fit(points)

plot_3d(
    points.plotter(c='r', s=10, depthshade=False),
    plane.plotter(alpha=0.2, lims_x=(-50, 50), lims_y=(-50, 50)),
)

Finally, the circle of best fit can be computed using the circle-fitting-3d library based on the scikit-spatial library. I think that for these points, a circle is not the right model.

from circle_fitting_3d import Circle3D
circle_3d = Circle3D(points)