Created
June 14, 2019 12:36
-
-
Save raacampbell/1c8db957d4f4620c60c3b41e8831d536 to your computer and use it in GitHub Desktop.
3D polynomial surface fit
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
#!/usr/local/bin/python3 | |
# Make a 3d point cloud and fit a surface to it | |
import numpy as np | |
import scipy.linalg | |
from mpl_toolkits.mplot3d import Axes3D | |
import matplotlib.pyplot as plt | |
# some 3-dim points | |
mean = np.array([0.0,0.0,0.0]) | |
cov = np.array([[1.0,-0.2,0.8], [-0.2,1.1,0.0], [0.8,0.0,1.0]]) | |
data = np.random.multivariate_normal(mean, cov, 90) | |
data[:,1] = data[:,1]**2 | |
# regular grid covering the domain of the data | |
r=4 | |
X,Y = np.meshgrid(np.arange(-r, r, 0.5), np.arange(-r, r*2, 0.5)) | |
XX = X.flatten() | |
YY = Y.flatten() | |
order = 1 # 1: linear, 2: quadratic, 3: cubic | |
if order == 1: | |
# best-fit linear plane | |
A = np.c_[data[:,0], data[:,1], np.ones(data.shape[0])] | |
C,_,_,_ = scipy.linalg.lstsq(A, data[:,2]) # coefficients | |
# evaluate it on grid | |
Z = C[0]*X + C[1]*Y + C[2] | |
# or expressed using matrix/vector product | |
#Z = np.dot(np.c_[XX, YY, np.ones(XX.shape)], C).reshape(X.shape) | |
elif order == 2: | |
# best-fit quadratic curve | |
A = np.c_[np.ones(data.shape[0]), data[:,:2], np.prod(data[:,:2], axis=1), data[:,:2]**2] | |
C,_,_,_ = scipy.linalg.lstsq(A, data[:,2]) | |
# evaluate it on a grid | |
Z = np.dot(np.c_[np.ones(XX.shape), XX, YY, XX*YY, XX**2, YY**2], C).reshape(X.shape) | |
elif order == 3: | |
# best-fit cubic curve | |
A = np.c_[np.ones(data.shape[0]), data[:,:2], np.prod(data[:,:2], axis=1), data[:,:2]**2, data[:,:2]**3] | |
C,_,_,_ = scipy.linalg.lstsq(A, data[:,2]) | |
# evaluate it on a grid | |
Z = np.dot(np.c_[np.ones(XX.shape), XX, YY, XX*YY, XX**2, YY**2, XX**3, YY**3], C).reshape(X.shape) | |
# plot points and fitted surface | |
fig = plt.figure() | |
ax = fig.gca(projection='3d') | |
ax.plot_surface(X, Y, Z, rstride=1, cstride=1, alpha=0.2) | |
ax.scatter(data[:,0], data[:,1], data[:,2], c='r', s=50) | |
plt.xlabel('X') | |
plt.ylabel('Y') | |
ax.set_zlabel('Z') | |
ax.axis('equal') | |
ax.axis('tight') | |
plt.show() |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment