contour plots in MATLAB - Step-by-Step Execution

Concept Flow - contour plots

Define grid points X, Y

↓

Calculate Z = f(X,Y)

↓

Call contour(X,Y,Z)

↓

MATLAB draws contour lines

↓

Display plot with contour levels

Contour plots show lines connecting points with the same value on a 2D grid. We create X and Y grids, compute Z values, then draw contour lines.

Execution Sample

MATLAB

x = -2:0.5:2;
y = -2:0.5:2;
[X,Y] = meshgrid(x,y);
Z = X.^2 + Y.^2;
contour(X,Y,Z);

This code creates a grid from -2 to 2, computes Z as X squared plus Y squared, then draws contour lines of Z.

Execution Table

Step	Action	Variables	Result/Output
1	Create vector x	x = [-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]	Vector x created
2	Create vector y	y = [-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]	Vector y created
3	Generate grid matrices	X, Y from meshgrid(x,y)	X and Y matrices of size 9x9 created
4	Calculate Z values	Z = X.^2 + Y.^2	Z matrix with squared sums created
5	Call contour plot	contour(X,Y,Z)	Contour lines drawn on plot
6	Display plot	Figure window shows contour plot	Visual contour plot appears
7	End	All variables set	Execution complete

💡 All steps completed, contour plot displayed

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
x	undefined	[-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]	[-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]	[-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]	[-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]	[-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]
y	undefined	undefined	[-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]	[-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]	[-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]	[-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]
X	undefined	undefined	undefined	9x9 matrix with repeated x columns	9x9 matrix with repeated x columns	9x9 matrix with repeated x columns
Y	undefined	undefined	undefined	9x9 matrix with repeated y rows	9x9 matrix with repeated y rows	9x9 matrix with repeated y rows
Z	undefined	undefined	undefined	undefined	9x9 matrix with values X.^2 + Y.^2	9x9 matrix with values X.^2 + Y.^2

Key Moments - 3 Insights

Why do we use meshgrid to create X and Y matrices instead of just vectors?

meshgrid creates full 2D grids for X and Y so each point pairs with every other, allowing calculation of Z at every (x,y) point. See execution_table step 3.

What does the dot operator (.^2) do in Z = X.^2 + Y.^2?

The dot means element-wise squaring of each matrix element, so each X and Y value is squared individually before adding. See execution_table step 4.

How does contour know which lines to draw from Z?

contour finds points where Z has the same value and connects them with lines. This is done automatically when calling contour(X,Y,Z) in step 5.

Visual Quiz - 3 Questions

Look at the variable_tracker table, what is the size of matrix Z after step 4?

A 9x1

B 9x9

C 1x9

D Undefined

💡 Hint

Check variable_tracker row for Z at After Step 4 column

At which step in the execution_table does MATLAB draw the contour lines?

A Step 3

B Step 2

C Step 5

D Step 6

💡 Hint

Look for 'Call contour plot' action in execution_table

If we change x and y to have larger ranges, how would the contour plot change?

A More contour lines over a bigger area

B Fewer contour lines

C No change in contour lines

D Plot will be empty

💡 Hint

Think about how grid size affects the plot area and contour lines

Concept Snapshot

contour(X,Y,Z) draws lines connecting points with equal Z values.
X and Y are 2D grids from meshgrid(x,y).
Z is calculated element-wise for each (X,Y).
Use dot operators for element-wise math.
Contour lines visualize levels of Z on 2D plane.

Full Transcript

Contour plots in MATLAB show lines where a function has the same value on a 2D grid. First, vectors x and y define points. meshgrid creates matrices X and Y pairing all x and y points. Then Z is calculated element-wise as X squared plus Y squared. Calling contour(X,Y,Z) draws lines connecting points with equal Z values. The plot appears in a figure window. This step-by-step process helps visualize how contour plots are made.

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