3D curve kriging

This example shows how to use the 3D curve kriging method to interpolate a 3D curve:

\[z = f(x, y)\]

In this example, we use the following equation to generate a 3D curve for illustration:

\[x=\sin(t), y= \cos(t), z= \cos(8t)\]

Note that the function name is possibly been modified in future versions.

import numpy as np
from polytex.kriging.mdKrig import buildKriging, interp

import matplotlib.pyplot as plt

Prepare the data for kriging interpolation

The data for kriging interpolation should be an array of xy data in shape of (n, 2) and an array of z data in shape of (n, 1).

t_rad = np.linspace(0, 2 * np.pi, 10)

xy = np.hstack((np.sin(t_rad).reshape(-1, 1), np.cos(t_rad).reshape(-1, 1)))
z = np.cos(8 * t_rad)

Build the kriging model

The kriging model is built by the function buildKriging(). The possible drift functions are: lin, quad, and cub, namely, the linear, quadratic and cubic drift functions. The default drift function is lin. The possible covariance functions are: lin, and cub. Nugget effect (nugg) is used for the smoothing of the curve.

expr = buildKriging(xy, z, 'lin', 'cub', nugg=100)

zInterp = interp(xy, expr)

Plot the result

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
# ax.plot(xy[:, 0], xy[:, 1], z, '--', label='data')
ax.plot(xy[:, 0], xy[:, 1], zInterp, label='interp/nugg=1')
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('z')
ax.legend()
plt.show()