Interpolation of unstructured grids.
The interpolation of this object is based on a
R*Tree structure. To begin with, we start by building this
object. By default, this object considers the WGS-84 geodetic coordinate system.
But you can define another one using the class
import matplotlib.pyplot import numpy import pyinterp mesh = pyinterp.RTree()
Then, we will insert points into the tree. The class allows you to add points
using two algorithms. The first one called
packing, will enable you to enter the values in the tree at
once. This mechanism is the recommended solution to create an optimized
in-memory structure, both in terms of construction time and queries. When this
is not possible, you can insert new information into the tree as you go along
Populates the search tree
When the tree is created, you can interpolate data with three algorithms:
When comparing an RBF to IDW, IDW will never predict values higher than the maximum measured value or lower than the minimum measured value. However, RBFs can predict values higher than the maximum values and lower than the minimum measured values.
The window function restricts the analyzed data set to a range near the point of interest. The weighting factor decreases the effect of points further away from the interpolated section of the point.
We start by interpolating using the IDW method
STEP = 1 / 32 mx, my = numpy.meshgrid(numpy.arange(X0, X1 + STEP, STEP), numpy.arange(Y0, Y1 + STEP, STEP), indexing='ij') idw, neighbors = mesh.inverse_distance_weighting( numpy.vstack((mx.ravel(), my.ravel())).T, within=False, # Extrapolation is forbidden k=11, # We are looking for at most 11 neighbors radius=600000, num_threads=0) idw = idw.reshape(mx.shape)
Interpolation with RBF method
Interpolation with a Window Function
Let’s visualize our interpolated data
fig = matplotlib.pyplot.figure(figsize=(10, 20)) ax1 = fig.add_subplot(311) pcm = ax1.pcolormesh(mx, my, idw, cmap='jet', shading='auto', vmin=0, vmax=1) ax1.set_title('IDW interpolation') ax2 = fig.add_subplot(312) pcm = ax2.pcolormesh(mx, my, rbf, cmap='jet', shading='auto', vmin=0, vmax=1) ax2.set_title('RBF interpolation') ax3 = fig.add_subplot(313) pcm = ax3.pcolormesh(mx, my, wf, cmap='jet', shading='auto', vmin=0, vmax=1) ax3.set_title('Window function interpolation') fig.colorbar(pcm, ax=[ax1, ax2, ax3], shrink=0.8) fig.show()
Total running time of the script: ( 1 minutes 19.325 seconds)