mesh and surf for surfaces in MATLAB - Step-by-Step Execution

Concept Flow - mesh and surf for surfaces

Define X, Y grid points

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Calculate Z values for each (X,Y)

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Call mesh(X,Y,Z) to draw wireframe

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Call surf(X,Y,Z) to draw colored surface

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View 3D plot with grid or color shading

First, create grid points X and Y, then compute Z values. Use mesh to draw a wireframe surface and surf to draw a colored surface.

Execution Sample

MATLAB

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

This code creates a grid from -2 to 2, calculates Z as X squared plus Y squared, then draws a wireframe mesh and a colored surface.

Execution Table

Step	Action	Variables	Result/Output
1	Create vector x from -2 to 2 step 0.5	x	x = [-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]
2	Create vector y from -2 to 2 step 0.5	y	y = [-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]
3	Create grid matrices X and Y using meshgrid(x,y)	X, Y	X and Y are 9x9 matrices with grid coordinates
4	Calculate Z = X.^2 + Y.^2 element-wise	Z	Z is 9x9 matrix with squared sums
5	Call mesh(X,Y,Z)	Plot	Wireframe 3D plot appears showing surface shape
6	Call surf(X,Y,Z)	Plot	Colored 3D surface plot appears showing surface shape
7	End of script	-	Plots displayed, execution stops

💡 All commands executed, plots rendered, script ends

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 grid	9x9 matrix grid	9x9 matrix grid
Y	undefined	undefined	undefined	9x9 matrix grid	9x9 matrix grid	9x9 matrix grid
Z	undefined	undefined	undefined	undefined	9x9 matrix of sums	9x9 matrix of sums

Key Moments - 3 Insights

Why do we use meshgrid before calculating Z?

meshgrid creates matrices X and Y that hold all grid points, so Z can be calculated element-wise for each (X,Y) pair, as shown in step 3 and 4 of the execution_table.

What is the difference between mesh and surf plots?

mesh draws a wireframe grid showing the surface shape (step 5), while surf draws a colored surface with shading (step 6), making it easier to see height differences.

Why does Z use element-wise power .^ instead of ^?

Because X and Y are matrices, .^ squares each element individually (step 4). Using ^ would try matrix multiplication, causing an error.

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what does Z represent?

A A single number representing total sum

B A vector of x values squared

C A matrix of sums of squares of X and Y elements

D A matrix of random values

💡 Hint

Check step 4 in execution_table where Z is calculated as X.^2 + Y.^2 element-wise

At which step does the wireframe mesh plot appear?

A Step 3

B Step 5

C Step 4

D Step 6

💡 Hint

Look at the 'Action' column in execution_table for mesh(X,Y,Z) call

If we change the step size in x and y from 0.5 to 1, how does variable_tracker for x change after step 1?

A x becomes [-2 -1 0 1 2]

B x becomes [-2 -1.5 -1 -0.5 0 0.5 1 1.5 2]

C x becomes [-2 -1 0 1 2 3]

D x remains undefined

💡 Hint

Check how x is created in step 1 with range and step size

Concept Snapshot

meshgrid(x,y) creates X,Y grids for coordinates
Z = f(X,Y) computes surface heights element-wise
mesh(X,Y,Z) draws wireframe surface
surf(X,Y,Z) draws colored shaded surface
Use .^ for element-wise power on matrices
Plots show 3D surface shapes clearly

Full Transcript

This example shows how to create 3D surface plots in MATLAB using mesh and surf. First, vectors x and y are created from -2 to 2 with step 0.5. Then meshgrid creates matrices X and Y holding all grid points. Next, Z is calculated as the sum of squares of X and Y elements. The mesh function draws a wireframe plot of the surface, while surf draws a colored surface plot. The code uses element-wise power .^ to square each element of X and Y. The execution table traces each step, showing variable values and plot actions. Key moments clarify why meshgrid is needed, the difference between mesh and surf, and the importance of element-wise operations. The visual quiz tests understanding of Z's meaning, when plots appear, and how changing step size affects variables. This helps beginners see how MATLAB builds and displays 3D surfaces step-by-step.