mesh and surf for surfaces in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of mesh and surf with sine wave

What is the output of the following MATLAB code snippet that uses mesh and surf to plot a sine wave surface?

MATLAB

x = linspace(-2*pi, 2*pi, 30);
y = linspace(-2*pi, 2*pi, 30);
[X,Y] = meshgrid(x,y);
Z = sin(sqrt(X.^2 + Y.^2));
figure;
mesh(X,Y,Z);
figure;
surf(X,Y,Z);

A Two figures: first shows a wireframe sine wave surface, second shows a colored smooth sine wave surface

B Two figures: both show flat planes with no wave pattern

C One figure with two overlapping plots of sine wave surfaces

D Error because meshgrid is used incorrectly

💡 Hint

Recall that mesh shows wireframe and surf shows colored surface.

mesh function plots a wireframe grid of the surface, while surf plots a colored surface with shading. Both use the same data, so the sine wave pattern appears in both but with different visual styles.

❓ Predict Output

intermediate

Effect of shading on surf plot

What will be the visual difference after running this MATLAB code?

MATLAB

x = linspace(-3,3,50);
y = linspace(-3,3,50);
[X,Y] = meshgrid(x,y);
Z = exp(-X.^2 - Y.^2);
figure;
surf(X,Y,Z);
shading flat;

A The code will produce an error because shading is not a valid function

B The surface will have flat color patches without smooth color transitions

C The plot will show only the wireframe without any color fill

D The surface will have smooth color gradients with lighting effects

💡 Hint

Check what shading flat does to surface plots.

shading flat removes smooth color interpolation and lighting, resulting in flat color patches on each face of the surface.

🔧 Debug

advanced

Identify the error in meshgrid usage

What error does this MATLAB code produce and why?

MATLAB

x = 1:5;
y = 1:5;
[X,Y] = meshgrid(x);
Z = X + Y;
mesh(X,Y,Z);

A No error, code runs and plots a surface

B Error: meshgrid requires two input vectors, but only one was given

C Error: Z matrix dimensions do not match X and Y

D Error: mesh function requires three input arguments

💡 Hint

Recall that meshgrid can accept one or two vector inputs.

No error occurs. MATLAB's meshgrid function accepts a single input vector, producing X and Y as square matrices both of size length(x)-by-length(x). Here, it creates 5x5 matrices, Z = X + Y is valid, and mesh plots the surface successfully.

❓ Predict Output

advanced

Number of grid points in meshgrid output

How many points are in the X matrix created by this code?

MATLAB

x = linspace(0,1,40);
y = linspace(0,2,60);
[X,Y] = meshgrid(x,y);

A 40

B 100

C 2400

D 60

💡 Hint

Remember meshgrid creates matrices with rows = length(y) and columns = length(x).

X is a matrix with size length(y) rows and length(x) columns, so total elements = 60 * 40 = 2400.

🧠 Conceptual

expert

Difference between mesh and surf in 3D plotting

Which statement correctly describes the difference between mesh and surf functions in MATLAB?

A <code>mesh</code> automatically adds lighting, <code>surf</code> does not

B <code>mesh</code> creates a 2D plot, <code>surf</code> creates a 3D plot

C <code>mesh</code> requires fewer input arguments than <code>surf</code>

D <code>mesh</code> creates a wireframe surface without color filling, while <code>surf</code> creates a colored surface with shading

💡 Hint

Think about how the surface looks visually with each function.

mesh draws a grid-like wireframe surface without color filling, while surf draws a solid surface with color and shading effects.