## Overview:

- Contour plot is a collection of contour lines.

- Each contour is a curve that is a resultant of cutting a surface by a plane.

- Every contour need not form a curve. Some of the resultant contours can be a straight line as well.

- Here is the formal definition of a contour plot:
- A level curve of a function
*f(x,y)*is the curve of points*(x,y)*where*f(x,y)*is some constant value, on every point of the curve. Different level curves produced for the*f(x,y)*for different values of c - can be put together as a plot, which is called a level curve plot or a contour plot.

- A level curve of a function

- Every contour line in a contour plot is drawn for different value of z, each value a constant.

## Applications of Contour Plots:

- A contour plot in cartography represents levels of equal elevation with respect to a base level.

- A contour line that connects places with the same temperature is called an
*isotherm*. Remember, a level curve of*f(x,y)*has the same value z in all the points of*x,y*that curve passes through

- If a level curve is to be drawn for ocean depth where the ocean depth is the same on the places it connects it is called an
*isobath*.

## Drawing a Contour Plot using Python and Matplotlib:

- Create a list of x points

- Create a list of y points

- From x and y form a matrix of z values.

- Call the contour() function of matplotlib.pyplot module and display the plot.

## Example 1:

import numpy as np # List of points in x axis # List of points in y axis # X and Y points are from -6 to +6 varying in steps of 2 # Z values as a matrix # Populate Z Values (a 7x7 matrix) - For a circle x^2+y^2=z # Print x,y and z values # Set the x axis and y axis limits # Provide a title for the contour plot # Set x axis label for the contour plot # Set y axis label for the contour plot # Create contour lines or level curves using matplotlib.pyplot module # Display z values on contour lines # Display the contour plot |

Output 1:

## Example 2:

Here is the python program that plots the contour plots or level curves for a saddle surface which is a hyperbolic paraboloid.

import numpy as np import matplotlib.pyplot as plot # List of points in x axis # List of points in y axis # X and Y points are from -4 to +4 varying in steps of 2 # Z values as a matrix # Populate Z Values (a 5x5 matrix) - For a saddle surface/hyperbolic paraboloid, x^2-y^2=z # Print x,y and z values # Set the x axis and y axis limits # Provide a title for the contour plot # Set x axis label for the contour plot # Set y axis label for the contour plot # Create contour lines for the Hyperbolic Paraboloid using matplotlib.pyplot module # Display z values on contour lines # Display the contour plot |