Spline interpolation in 3D in python

Question

I am searching the equivalent Matlab command

Vq = interp3(X,Y,Z,V,Xq,Yq,Zq)

in Python. In Matlab I can use the method \'spline\' interpolation,

Answer 1

Spline interpolation on for 3+ dimensions can be done using scipy.interpolate.Rbf as your described. For plotting purposes you can use a smaller resolution (1000 points is a good rule of thumb), and when you want to evaluate your spline, you can interpolate on much greater than 132000 points without problem (see example below).

Can you add a Minimal, Complete, and Verifiable example for what you are trying to do in matlab? This will explain why do you need to create a grid space with a resolution of 132000 points. Also, please note, there is a curse of dimensionality. Matlab uses a cubic spline or a piecewise polynomial which can be dangerous due to overfitting. I recommend you used a more sane method for training on 51 datapoints and applying to 132000+ datapoints. This is a great example on polynomial curve fitting and model selection.

Example:

Generate data:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d

%matplotlib inline
import random
# set seed to reproducible
random.seed(1)
data_size = 51
max_value_range = 132651
x = np.array([random.random()*max_value_range for p in range(0,data_size)])
y = np.array([random.random()*max_value_range for p in range(0,data_size)])
z = 2*x*x*x + np.sqrt(y)*y + random.random()
fig = plt.figure(figsize=(10,6))
ax = axes3d.Axes3D(fig)
ax.scatter3D(x,y,z, c='r')

Fit spline and interpolate

x_grid = np.linspace(0, 132651, 1000*len(x))
y_grid = np.linspace(0, 132651, 1000*len(y))
B1, B2 = np.meshgrid(x_grid, y_grid, indexing='xy')
Z = np.zeros((x.size, z.size))

import scipy as sp
import scipy.interpolate
spline = sp.interpolate.Rbf(x,y,z,function='thin_plate',smooth=5, episilon=5)

Z = spline(B1,B2)
fig = plt.figure(figsize=(10,6))
ax = axes3d.Axes3D(fig)
ax.plot_wireframe(B1, B2, Z)
ax.plot_surface(B1, B2, Z,alpha=0.2)
ax.scatter3D(x,y,z, c='r')

Fit spline on large data

predict_data_size = 132000
x_predict = np.array([random.random()*max_value_range for p in range(0,predict_data_size)])
y_predict = np.array([random.random()*max_value_range for p in range(0,predict_data_size)])
z_predict = spline(x_predict, y_predict)
fig = plt.figure(figsize=(10,6))
ax = axes3d.Axes3D(fig)
ax.plot_wireframe(B1, B2, Z)
ax.plot_surface(B1, B2, Z,alpha=0.2)
ax.scatter3D(x_predict,y_predict,z_predict, c='r')