contour plots in MATLAB - Step-by-Step Execution

Concept Flow - contour plots

Define grid points X, Y

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Calculate Z = f(X,Y)

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Call contour(X,Y,Z)

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MATLAB draws contour lines

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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.