How To Plot a Function of Two Variables in MATLAB?

MATLAB provides various built-in functions to plot a function of two variables with the help of different types of plots like mesh, surface, scatter plots, etc. In this tutorial, I am going to explain the process of plotting a function of two variables in MATLAB.

Plot a Function of Two Variables in MATLAB

The step-by-step process to plot a function of two variables in MATLAB is explained below.

• Step (1) − Define the range of x and y points.

• Step (2) − Create a grid of x and y points. For this, use the "meshgrid" function in MATLAB.

Syntax

[X, Y] = meshgrid(x, y);

• Step (3) − Define a function in two variables that you need to plot.

• Step (4) − Create a plot of the function.

Hence, plotting a function of two variables in MATLAB is a simple four step process.

Let us understand the above given algorithm with the help of MATLAB examples.

Plot a Function of Two Variables Using Mesh Plot

In MATLAB, we have a function "mesh" that is used to plot a 3D surface plot of a function. We can use it to plot a function of two-variables.

Example

The following example demonstrates how we can use the "mesh" function to plot a function of two-variables.

% MATLAB code to plot function of two-variable using mesh surface plot
% Define the range of x and y points
x = linspace(-5, 5, 50);
y = linspace(-5, 5, 50);

% Create a grid of x and y points
[X, Y] = meshgrid(x, y);

% Define a function of two variables
Z = X.^2 + Y.^2;

% Plot the function using the mesh surface plot
mesh(X, Y, Z);
title('Two Variable Function Mesh Plot');
xlabel('X-axis');
ylabel('Y-axis');
zlabel('Z-axis');

Output

Plot a Function of Two Variables Using Surface Plot

In MATLAB, we can also plot a function of two-variables using the surface plot. For this, there is a built-in function in MATLAB library named, "surf" that plots a 3D surface plot for the defined function.

Example

Let us see an example to understand how to use the "surf" function to plot a function of two variables in MATLAB.

% MATLAB code to plot a function of two-variable using surface plot
% Define the range of x and y points
x = linspace(-5, 5, 50);
y = linspace(-5, 5, 50);

% Create a grid of x and y points
[X, Y] = meshgrid(x, y);

% Define a function of two variables
Z = X.^2 + Y.^2;

% Plot the function using the 3D surface plot
surf(X, Y, Z);
title('Two Variable Function Surface Plot');
xlabel('X-axis');
ylabel('Y-axis');
zlabel('Z-axis');

Output

Plot a Function of Two Variables Using Scatter Plot

We can also plot a function of two variable using the scatter plot. For this, we have a built-in function "scatter" in MATLAB.

Example

Here is an example demonstrating how to plot a function of two variables using the scatter plot.

% MATLAB code to plot a function of two-variable using scatter plot
% Define the range of x and y points
x = linspace(-5, 5, 50);
y = linspace(-5, 5, 50);

% Create a grid of x and y points
[X, Y] = meshgrid(x, y);

% Define a function of two variables
Z = X.^2 + Y.^2;

% Plot the function using the scatter plot
scatter(X(:), Y(:), Z(:), 'green'); 
title('Two Variable Function Scatter Plot');
xlabel('X-axis');
ylabel('Y-axis');
colorbar;	% Z values

Output

Plot a Function of Two Variables Using Contour Plot

In MATLAB, we can plot a function of two variables using the contour plot. For this, we use the "contour" function in MATLAB.

Example

The following example shows the MATLAB code implementation to plot a function of two variables using the contour plot.

% MATLAB code to plot a function of two-variable using contour plot
% Define the range of x and y points
x = linspace(-5, 5, 50);
y = linspace(-5, 5, 50);

% Create a grid of x and y points
[X, Y] = meshgrid(x, y);

% Define a function of two variables
Z = X.^2 + Y.^2;

% Plot the function using the contour plot
contour(X, Y, Z);
title('Two Variable Function Contour Plot');
xlabel('X-axis');
ylabel('Y-axis');
colorbar;	% Z values

Output

Conclusion

In MATLAB, we can plot a function of two variables using different types of plots. In this tutorial, I explained the step-by-step process and examples in MATLAB to plot a function of two variables. You can try all these codes with different functions as well.