contour plots in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Basic Contour Plot

What will be the output of this MATLAB code snippet that creates a contour plot?

MATLAB

x = -2:0.2:2;
y = -2:0.2:2;
[X,Y] = meshgrid(x,y);
Z = X.^2 + Y.^2;
contour(X,Y,Z,5);

A A contour plot with 5 contour lines representing levels of Z = X^2 + Y^2

B A 3D surface plot of Z = X^2 + Y^2

C A scatter plot of points (X,Y) colored by Z values

D An error because contour requires a vector input, not matrices

💡 Hint

Recall that contour plots show lines of constant value for a function of two variables.

The code creates a grid of points and calculates Z = X^2 + Y^2 at each point. The contour function then draws 5 contour lines representing levels of Z. It does not create a 3D plot or scatter plot, and the inputs are valid matrices for contour.

❓ Predict Output

intermediate

Contour Plot with Specified Levels

What does this MATLAB code produce?

MATLAB

x = linspace(-3,3,50);
y = linspace(-3,3,50);
[X,Y] = meshgrid(x,y);
Z = sin(X).*cos(Y);
contour(X,Y,Z,[-0.5 0 0.5]);

A An error because contour levels must be positive

B A contour plot with default number of contour lines ignoring specified levels

C A filled contour plot with colors between levels -0.5, 0, and 0.5

D A contour plot with exactly three contour lines at levels -0.5, 0, and 0.5

💡 Hint

Check how contour levels are specified as a vector of values.

The contour function draws contour lines at the exact levels specified in the vector [-0.5 0 0.5]. It does not fill the areas between contours (that would be contourf). Negative levels are allowed.

🔧 Debug

advanced

Identify the Error in Contour Plot Code

This MATLAB code is intended to plot contours of Z = X^2 - Y^2, but it produces an error. What is the cause?

MATLAB

x = -2:0.1:2;
y = -2:0.2:2;
[X,Y] = meshgrid(x,y);
Z = X^2 - Y^2;
contour(X,Y,Z);

A Using ^ operator on matrices instead of element-wise .^ causes an error

B meshgrid inputs must be column vectors, not row vectors

C contour requires Z to be a vector, not a matrix

D The variable Z is not defined before calling contour

💡 Hint

Check how powers are applied to arrays in MATLAB.

In MATLAB, ^ is matrix power and requires square matrices. X and Y are matrices, so X^2 and Y^2 cause an error. The element-wise power operator .^ should be used instead.

📝 Syntax

advanced

Syntax Error in Contour Plot Command

Which option contains the correct syntax to plot contours of Z with 10 levels in MATLAB?

MATLAB

x = -1:0.1:1;
y = -1:0.1:1;
[X,Y] = meshgrid(x,y);
Z = exp(-X.^2 - Y.^2);

A contour(X,Y,Z,levels=10);

B contour(X,Y,Z,10);

C contour(X,Y,Z,levels 10);

D contour(X,Y,Z,10,);

💡 Hint

Check MATLAB function argument syntax carefully.

MATLAB contour function takes the number of contour levels as a numeric argument without keywords or commas. Options A, B, and D have invalid syntax.

🚀 Application

expert

Number of Contour Lines in Complex Plot

Given the code below, how many contour lines will be drawn by MATLAB's contour function?

MATLAB

x = linspace(-2,2,100);
y = linspace(-2,2,100);
[X,Y] = meshgrid(x,y);
Z = sin(3*X).*cos(2*Y);
contour(X,Y,Z);

A Exactly 5 contour lines because of the sine and cosine frequencies

B An error because contour requires explicit contour levels

C Approximately 10 contour lines (default number)

D No contour lines because Z contains negative values

💡 Hint

If contour levels are not specified, MATLAB chooses a default number.

When contour levels are not specified, MATLAB automatically selects about 10 contour levels spanning the range of Z values, regardless of the function's frequency.