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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

 `#  imports``import` `numpy as np``import` `matplotlib.pyplot as plt``#``# define a function``def` `func(x, y):``    ``return` `np.sin(x) ``*``*` `2` `+`  `np.cos(y) ``*``*``2``# generate 50 values b/w 0 a5``x ``=` `np.linspace(``0``, ``5``, ``50``)``y ``=` `np.linspace(``0``, ``5``, ``50``)`` ` `# Generate combination of grids``X, Y ``=` `np.meshgrid(x, y)``Z ``=` `func(X, Y)`` ` `# Draw rectangular contour plot``plt.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 arrays``rad_arr ``=` `np.radians(np.linspace(``0``, ``360``, ``20``))``r_arr ``=` `np.arange(``0``, ``1``, .``1``)``# define function``def` `func(r, theta):``  ``return` `r ``*` `np.sin(theta) `` ` `r, theta ``=` `np.meshgrid(r_arr, rad_arr)``# get the values of response variables``values ``=` `func(r,theta)`` ` `# plot the polar coordinates``fig, 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 plotly``import` `plotly.figure_factory as ff`` ` `# Define variables``a ``=` `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 variable``func ``=` `(a ``-` `0.02``) ``*` `b ``*` `(a ``-` `0.5``) ``*` `(b ``-` `0.4``) ``*` `(c ``-` `1``)``*``*``2`` ` `# plot ternary contour``fig ``=` `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: My Personal Notes arrow_drop_up