Contour plots

• Last Updated : 22 Jan, 2021

A contour plot is a graphical method to visualize the 3-D surface by plotting constant Z slices called contours in a 2-D format. The contour plot is an alternative to a 3-D surface plot

The contour plot is formed by:

• Vertical axis: Independent variable 2
• Horizontal axis: Independent variable 1
• Lines: iso-response values, can be calculated with the help (x,y).

The independent variable usually restricted to a regular grid. The actual techniques for determining the correct iso-response values are rather complex and almost always computer-generated.

The contour plot is used to depict the change in Z values as compared to X and Y values. If the data (or function) do not form a regular grid, you typically need to perform a 2-D interpolation to form a regular grid.

For one variable data, a run sequence/ histogram is considered necessary. For two-variable data, a scatter plot is considered necessary. The contour plots can also polar co-ordinates (r,theta) instead of traditional rectangular (x, y, z) coordinates.

Types of Contour Plot:

• Rectangular Contour plot: A projection of 2D-plot in 2D-rectangular canvas. It is the most common form of the contour plot.
• Polar contour plot: Polar contour plot is plotted by using the polar coordinates r and theta. The response variable here is the collection of values generated while passing r and theta into the given function, where r is the distance from origin and theta is the angle from the positive x axis.
• Ternary contour plot: Ternary contour plot is used to represent the relationship between 3 explanatory variables and the response variable in the form of a filled triangle.

Contour plot can be plotted in different programming languages:

• Python/ Matplotlib: Contour plot can be plotted using plt.contour or plt.contourf functions, where plt is matplotlib.pyplot. The difference between these two that plot.contour generates hollow contour plot, the plt.contourf generated filled.
• Matlab: functions such as contourf (2d-plot) and contour3 (3D-contour) can be used for contour plotting
• R: can create a contour plot with filled.contour functions in R.

Implementations:

• Rectangular Contour Plot: Below is the sample code for plotting rectangular contour plots in Python and matplotlib.

Python3

 #  importsimport numpy as npimport matplotlib.pyplot as plt## define a functiondef func(x, y):    return np.sin(x) ** 2 +  np.cos(y) **2# generate 50 values b/w 0 a5x = np.linspace(0, 5, 50)y = np.linspace(0, 5, 50)  # Generate combination of gridsX, Y = np.meshgrid(x, y)Z = func(X, Y)  # Draw rectangular contour plotplt.contour(X, Y, Z, cmap='gist_rainbow_r'); • Polar Contour plot: For plotting polar contour plot we need to define first r and theta. Below is the sample code for plotting polar contour plots using matplotlib subplots.

Python3

 # generate r and theta arraysrad_arr = np.radians(np.linspace(0, 360, 20))r_arr = np.arange(0, 1, .1)# define functiondef func(r, theta):  return r * np.sin(theta)   r, theta = np.meshgrid(r_arr, rad_arr)# get the values of response variablesvalues = func(r,theta)  # plot the polar coordinatesfig, ax = plt.subplots(subplot_kw=dict(projection='polar'))ax.contourf(theta, r, values, cmap='Spectral_r')  plt.show() Polar contour plot

• Ternary Contour Plot: Matplotlib does not provide a definitive API for plotting Ternary Contour plot, however, there are many other package which does that. IN this example, we will be using Plotly library.

Python3

 # install & import plotly! pip install plotlyimport plotly.figure_factory as ff  # Define variablesa = np.array([0. , 0. , 0., 0., 1./3, 1./3, 1./3, 2./3, 2./3, 1.])b = np.array([0., 1./3, 2./3, 1., 0., 1./3, 2./3, 0., 1./3, 0.])c = 1 - a - b# Define function that generates response variablefunc = (a - 0.02) * b * (a - 0.5) * (b - 0.4) * (c - 1)**2  # plot ternary contourfig = ff.create_ternary_contour(np.array([a, b, c]), func,                                pole_labels=['a', 'b', 'c'],                                interp_mode='cartesian',                                colorscale='Viridis',)fig.show() Ternary Contour plot

References:

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