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.

Practice

1. What does a contour plot in MATLAB primarily represent?

easy

A. A 3D surface plot

B. Lines connecting points with the same value

C. A bar chart of values

D. A scatter plot of points

Solution

1. Step 1: Understand contour plot purpose

   A contour plot shows curves that connect points with equal values on a grid.

2. Step 2: Compare with other plot types

   3D surface plots show height as a surface, bar charts show bars, scatter plots show points, so they differ.

3. Final Answer:

   Lines connecting points with the same value -> Option B

4. Quick Check:

   Contour plot = lines of equal value [OK]

Hint: Contour plots connect equal values with lines [OK]

Common Mistakes:

• Confusing contour plots with 3D surface plots
• Thinking contour plots show individual points
• Mixing contour plots with bar charts

2. Which of the following is the correct syntax to create a basic contour plot in MATLAB using matrices X, Y, and Z?

easy

A. contour(X, Y, Z)

B. plot(X, Y, Z)

C. contourplot(X, Y, Z)

D. surface(X, Y, Z)

Solution

1. Step 1: Recall MATLAB contour syntax

   The function to create contour plots is contour(X, Y, Z).

2. Step 2: Eliminate incorrect functions

   plot() is for 2D plots, contourplot() is not a MATLAB function, surface() creates 3D surfaces.

3. Final Answer:

   contour(X, Y, Z) -> Option A

4. Quick Check:

   Use contour() for contour plots [OK]

Hint: Use contour(X,Y,Z) to plot contours [OK]

Common Mistakes:

• Using plot() instead of contour()
• Typing contourplot() which is invalid
• Using surface() which makes 3D plots

3. What will be the output of the following MATLAB code?

X = 1:3; Y = 1:3; [Xg,Yg] = meshgrid(X,Y); Z = Xg.^2 + Yg.^2; contour(Xg, Yg, Z, 3);

medium

A. An error because contour needs vectors, not matrices

B. A 3D surface plot of Z values

C. A scatter plot of points (Xg, Yg, Z)

D. A contour plot with 3 contour lines representing levels of Z

Solution

1. Step 1: Understand meshgrid and Z calculation

   meshgrid creates grids Xg and Yg; Z is sum of squares, a smooth surface.

2. Step 2: Interpret contour call with 3 levels

   contour with 3 as last argument draws 3 contour lines at different Z levels.

3. Final Answer:

   A contour plot with 3 contour lines representing levels of Z -> Option D

4. Quick Check:

   contour with level count = contour lines count [OK]

Hint: Last argument in contour sets number of lines [OK]

Common Mistakes:

• Thinking contour creates 3D surface plots
• Believing contour requires vectors, not matrices
• Confusing contour with scatter plots

4. Identify the error in this MATLAB code snippet for contour plotting:

X = 1:5; Y = 1:5; Z = X + Y; contour(X, Y, Z);

medium

A. contour requires only two arguments

B. X and Y must be matrices, not vectors

C. Z must be a matrix matching grid size, not a vector

D. No error, code runs fine

Solution

1. Step 1: Check dimensions of X, Y, Z

   X and Y are vectors; Z is vector sum, not a matrix grid.

2. Step 2: Understand contour input requirements

   contour needs Z as matrix matching X, Y grid sizes; here Z is vector, causing error.

3. Final Answer:

   Z must be a matrix matching grid size, not a vector -> Option C

4. Quick Check:

   Z size mismatch causes error [OK]

Hint: Z must be matrix matching X,Y grid for contour [OK]

Common Mistakes:

• Passing vector Z instead of matrix
• Assuming contour accepts vector inputs
• Ignoring dimension mismatch errors

5. You want to plot contour lines only at specific Z values: 5, 10, and 15. Which MATLAB command correctly achieves this given matrices X, Y, and Z?

hard

A. contour(X, Y, Z, [5 10 15])

B. contour(X, Y, Z, 3)

C. contour(X, Y, Z, 'Levels', [5 10 15])

D. contour(X, Y, Z, 'LineLevels', [5 10 15])

Solution

1. Step 1: Recall contour level specification syntax

   To specify exact contour levels, pass a vector of levels as the fourth argument.

2. Step 2: Evaluate options for specifying levels

   contour(X, Y, Z, [5 10 15]) uses vector [5 10 15] correctly; contour(X, Y, Z, 3) sets number of lines, not levels; options C and D use invalid syntax.

3. Final Answer:

   contour(X, Y, Z, [5 10 15]) -> Option A

4. Quick Check:

   Use vector of levels as 4th argument [OK]

Hint: Pass vector of levels as 4th argument to contour [OK]

Common Mistakes:

• Using number instead of vector for levels
• Trying unsupported name-value pairs
• Confusing level count with specific levels