How to Use surf in MATLAB for 3D Surface Plots

In MATLAB, use the surf function to create 3D surface plots by passing matrices for X, Y, and Z coordinates. It visualizes data as a colored surface, helping you see relationships between variables in three dimensions.

Syntax

The basic syntax of surf is:

• surf(Z): Creates a surface plot using matrix Z for height values, with X and Y as indices.
• surf(X,Y,Z): Uses matrices X and Y for coordinates and Z for height.
• surf(..., C): Specifies color data C for the surface.

This function plots a 3D colored surface where colors represent height or specified data.

matlab

surf(Z)
surf(X,Y,Z)
surf(X,Y,Z,C)

Example

This example creates a 3D surface plot of the function z = sin(sqrt(x^2 + y^2)). It shows how to generate X and Y grids, compute Z, and plot with surf.

matlab

x = linspace(-5,5,50);
y = linspace(-5,5,50);
[X,Y] = meshgrid(x,y);
Z = sin(sqrt(X.^2 + Y.^2));
surf(X,Y,Z)
title('3D Surface plot of z = sin(sqrt(x^2 + y^2))')
xlabel('X axis')
ylabel('Y axis')
zlabel('Z axis')

Output

A 3D colored surface plot window appears showing wave-like surface with axes labeled X, Y, Z.

Common Pitfalls

Common mistakes when using surf include:

• Passing vectors instead of matrices for X, Y, and Z. Use meshgrid to create coordinate matrices.
• Not matching the sizes of X, Y, and Z. All must be the same size.
• Using surf with very large matrices can slow down rendering.

matlab

x = -5:5; y = -5:5; % vectors
% Z = sin(sqrt(x.^2 + y.^2)); % error: sizes mismatch
% Correct way:
[X,Y] = meshgrid(x,y);
Z = sin(sqrt(X.^2 + Y.^2));
surf(X,Y,Z)

Quick Reference

Usage	Description
surf(Z)	Surface plot with Z heights, X and Y as indices
surf(X,Y,Z)	Surface plot with specified X, Y coordinates
surf(X,Y,Z,C)	Surface plot with color data C
meshgrid(x,y)	Create coordinate matrices for X and Y
xlabel('label')	Label X axis
ylabel('label')	Label Y axis
zlabel('label')	Label Z axis
title('text')	Add title to plot

Key Takeaways

Use surf with matrices X, Y, and Z to create 3D surface plots in MATLAB.

Generate coordinate grids with meshgrid to match sizes of X, Y, and Z.

Colors on the surface represent height or specified color data.

Always label axes and add titles for clear visualization.

Avoid size mismatches and large matrices for better performance.