Irregular Data Grid Contour Plotting

Introduction

This lab demonstrates how to create a contour plot of irregularly spaced data in Python using Matplotlib. The contour plot shows the 2D distribution of data values using iso-contours or contour lines. In this example, we will compare a contour plot of irregularly spaced data interpolated on a regular grid versus a tricontour plot for an unstructured triangular grid.

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Import necessary libraries

We start by importing the necessary libraries for this example: matplotlib.pyplot and numpy. Additionally, we import matplotlib.tri for triangulation of the data.

import matplotlib.pyplot as plt
import numpy as np
import matplotlib.tri as tri

Generate random data

We generate random data using NumPy's np.random.uniform method. We generate npts = 200 data points with x and y values between -2 and 2. We also calculate the z values using the function z = x * np.exp(-x**2 - y**2).

np.random.seed(19680801)
npts = 200
x = np.random.uniform(-2, 2, npts)
y = np.random.uniform(-2, 2, npts)
z = x * np.exp(-x**2 - y**2)

Interpolation on a grid

We create a contour plot of irregularly spaced data coordinates via interpolation on a grid. We first create grid values for x and y using np.linspace. We then linearly interpolate the data (x, y) on a grid defined by (xi, yi) using tri.LinearTriInterpolator. We plot the interpolated data with the usual axes.Axes.contour.

ngridx = 100
ngridy = 200
xi = np.linspace(-2.1, 2.1, ngridx)
yi = np.linspace(-2.1, 2.1, ngridy)

triang = tri.Triangulation(x, y)
interpolator = tri.LinearTriInterpolator(triang, z)
Xi, Yi = np.meshgrid(xi, yi)
zi = interpolator(Xi, Yi)

fig, ax1 = plt.subplots()
cntr1 = ax1.contourf(xi, yi, zi, levels=14, cmap="RdBu_r")
ax1.plot(x, y, 'ko', ms=3)
ax1.set(xlim=(-2, 2), ylim=(-2, 2))
ax1.set_title('Contour Plot of Irregularly Spaced Data Interpolated on a Grid')
fig.colorbar(cntr1, ax=ax1)
plt.show()

Tricontour

We plot the same data using a tricontour plot by directly supplying the unordered, irregularly spaced coordinates to axes.Axes.tricontour.

fig, ax2 = plt.subplots()
cntr2 = ax2.tricontourf(x, y, z, levels=14, cmap="RdBu_r")
ax2.plot(x, y, 'ko', ms=3)
ax2.set(xlim=(-2, 2), ylim=(-2, 2))
ax2.set_title('Tricontour Plot of Irregularly Spaced Data')
fig.colorbar(cntr2, ax=ax2)
plt.show()

Summary

This lab demonstrated how to create a contour plot of irregularly spaced data in Python using Matplotlib. We compared a contour plot of irregularly spaced data interpolated on a regular grid versus a tricontour plot for an unstructured triangular grid. The axes.Axes.contour and axes.Axes.tricontour methods were used to create the contour plots.