Unstructured grid

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 Spheroid.

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 using the insert method.

SIZE = 2000
X0, X1 = 80, 170
Y0, Y1 = -45, 30
lons = numpy.random.uniform(low=X0, high=X1, size=(SIZE, ))
lats = numpy.random.uniform(low=Y0, high=Y1, size=(SIZE, ))
data = numpy.random.random(size=(SIZE, ))

Populates the search tree

mesh.packing(numpy.vstack((lons, lats)).T, data)

When the tree is created, you can interpolate data with three algorithms:

• Inverse Distance Weighting or IDW

• Radial Basis Function or RBF

• Window Function

Note

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

rbf, neighbors = mesh.radial_basis_function(
    numpy.vstack((mx.ravel(), my.ravel())).T,
    within=False,  # Extrapolation is forbidden
    k=11,  # We are looking for at most 11 neighbors
    radius=600000,
    rbf='thin_plate',
    num_threads=0)
rbf = rbf.reshape(mx.shape)

Interpolation with a Window Function

wf, neighbors = mesh.window_function(
    numpy.vstack((mx.ravel(), my.ravel())).T,
    within=False,  # Extrapolation is forbidden
    k=11,
    radius=600000,
    wf='parzen',
    num_threads=0)
wf = wf.reshape(mx.shape)

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()