mesh and surf for surfaces in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the mesh function do in MATLAB?

The mesh function creates a wireframe 3D surface plot, showing grid lines without filled faces, which helps visualize the shape of a surface.

beginner

How is surf different from mesh in MATLAB?

surf creates a 3D surface plot with colored, filled faces, making the surface look solid and easier to interpret compared to the wireframe style of mesh.

beginner

What inputs do mesh and surf require?

Both functions typically require matrices X, Y, and Z of the same size, where Z contains the height values and X, Y define the grid coordinates.

beginner

How can you create the grid matrices X and Y for plotting surfaces?

You can use the meshgrid function with vectors for x and y to create matrices X and Y that define the grid points for surface plotting.

beginner

What is a simple example to plot z = sin(sqrt(x^2 + y^2)) using mesh and surf?

Create vectors x and y, use meshgrid to get X and Y, compute Z = sin(sqrt(X.^2 + Y.^2)), then call mesh(X,Y,Z) or surf(X,Y,Z) to plot.

What does the MATLAB mesh function display?

A A bar chart

B A 2D line plot

C A wireframe 3D surface plot

D A filled 3D surface plot

mesh shows a wireframe grid representing the surface shape without filled faces.

Which function shows a colored, filled 3D surface in MATLAB?

A mesh

B surf

C plot

D scatter

surf creates a solid 3D surface with colored faces.

What MATLAB function helps create grid matrices X and Y from vectors?

A meshgrid

B linspace

C plot

D surf

meshgrid converts vectors into coordinate matrices for surface plotting.

If X, Y, and Z are matrices of the same size, which is true?

A They cannot be used for 3D plots

B They must be vectors

C Only <code>Z</code> needs to be a matrix

D They can be used as inputs to <code>mesh</code> or <code>surf</code>

mesh and surf require X, Y, and Z matrices of the same size.

What does the dot operator (e.g., .^2) do in MATLAB surface calculations?

A Element-wise operation on matrices

B Matrix multiplication

C Logical AND

D Transpose

The dot operator applies the operation element-wise, which is needed for surface calculations.

Explain how to create a 3D surface plot using mesh and surf in MATLAB.

Think about how to prepare the grid and height data before plotting.

Describe the visual difference between mesh and surf plots.

Imagine looking at a fishing net versus a solid sheet.

Practice

1. What is the main difference between mesh and surf functions in MATLAB when plotting 3D surfaces?

easy

A. mesh creates a wireframe surface, while surf creates a colored surface.

B. mesh plots 2D graphs, while surf plots 3D graphs.

C. mesh only works with matrices, surf only works with vectors.

D. mesh colors the surface, surf shows only edges.

Solution

1. Step 1: Understand the function outputs

   mesh draws a grid-like wireframe of the surface without filling colors.

2. Step 2: Compare with surf

   surf draws a colored surface that fills the area between grid lines, showing height with color.

3. Final Answer:

   mesh creates a wireframe surface, while surf creates a colored surface. -> Option A

4. Quick Check:

   Wireframe vs colored surface = A [OK]

Hint: Remember: mesh = wireframe, surf = colored surface [OK]

Common Mistakes:

• Thinking mesh colors the surface
• Confusing 2D and 3D plotting
• Assuming mesh only works with vectors

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

easy

A. mesh(X, Y);

B. mesh(X, Y, Z);

C. mesh(X, Z, Y);

D. meshplot(X, Y, Z);

Solution

1. Step 1: Recall mesh function syntax

   The correct syntax for mesh requires three inputs: X, Y, and Z matrices representing coordinates.

2. Step 2: Check options

   Only mesh(X, Y, Z); matches the correct order and function name. mesh(X, Y); misses Z, B uses invalid function meshplot, C swaps Y and Z incorrectly.

3. Final Answer:

   mesh(X, Y, Z); -> Option B

4. Quick Check:

   Correct function and argument order = D [OK]

Hint: Syntax: mesh(X, Y, Z) with all three matrices [OK]

Common Mistakes:

• Using wrong function name like meshplot
• Swapping Y and Z arguments
• Omitting one of the required inputs

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

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

medium

A. A colored surface plot with smooth shading.

B. A flat 2D grid with no height variation.

C. An error because meshgrid is used incorrectly.

D. A 3D wireframe surface showing a paraboloid shape.

Solution

1. Step 1: Understand meshgrid and Z calculation

   meshgrid creates matrices X and Y for grid points. Z is calculated as sum of squares, forming a paraboloid shape.

2. Step 2: Understand mesh plotting

   mesh plots a wireframe 3D surface of Z over X and Y, showing the paraboloid shape as a grid.

3. Final Answer:

   A 3D wireframe surface showing a paraboloid shape. -> Option D

4. Quick Check:

   meshgrid + paraboloid + mesh = wireframe paraboloid [OK]

Hint: meshgrid creates grids; mesh plots wireframe surface [OK]

Common Mistakes:

• Thinking mesh creates colored surface
• Assuming meshgrid returns vectors, not matrices
• Expecting 2D plot instead of 3D

4. Identify the error in this MATLAB code snippet:

X = 0:0.5:2; Y = 0:0.5:2; Z = X.^2 + Y.^2; surf(X, Y, Z);

medium

A. Z must be a matrix matching sizes of X and Y, not vectors.

B. surf requires only two inputs, not three.

C. X and Y must be row vectors, not column vectors.

D. The operator .^ is invalid for vectors.

Solution

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

   X and Y are vectors, but Z is calculated element-wise and is also a vector, not a matrix matching grid points.

2. Step 2: Understand surf input requirements

   surf expects X, Y, Z matrices of the same size, usually created by meshgrid. Here, Z is not a matrix matching X and Y.

3. Final Answer:

   Z must be a matrix matching sizes of X and Y, not vectors. -> Option A

4. Quick Check:

   surf needs matching matrix sizes = C [OK]

Hint: Use meshgrid to create X, Y matrices before surf [OK]

Common Mistakes:

• Passing vectors instead of matrices to surf
• Misunderstanding element-wise operations
• Thinking surf accepts vector inputs directly

5. You want to plot the surface of the function z = sin(x) * cos(y) over the range x = -pi to pi and y = -pi to pi. Which MATLAB code correctly creates a colored surface plot using surf?

hard

A. x = -pi:pi; y = -pi:pi; Z = sin(x) * cos(y); surf(x, y, Z);

B. x = linspace(-pi, pi, 50); y = linspace(-pi, pi, 50); Z = sin(x) .* cos(y); surf(x, y, Z);

C. x = linspace(-pi, pi, 50); y = linspace(-pi, pi, 50); [X, Y] = meshgrid(x, y); Z = sin(X) .* cos(Y); surf(X, Y, Z);

D. X = -pi:pi; Y = -pi:pi; Z = sin(X) + cos(Y); mesh(X, Y, Z);

Solution

1. Step 1: Create grid points for x and y

   Use linspace to create vectors from -pi to pi with enough points, then use meshgrid to create matrices X and Y.

2. Step 2: Calculate Z values element-wise

   Calculate Z as sin(X) .* cos(Y) using element-wise multiplication to get matrix Z matching X and Y.

3. Step 3: Plot with surf

   Use surf(X, Y, Z) to plot the colored surface correctly.

4. Final Answer:

   x = linspace(-pi, pi, 50); y = linspace(-pi, pi, 50); [X, Y] = meshgrid(x, y); Z = sin(X) .* cos(Y); surf(X, Y, Z); -> Option C

5. Quick Check:

   meshgrid + element-wise .* + surf = B [OK]

Hint: Use meshgrid and element-wise .* for surface plots [OK]

Common Mistakes:

• Using * instead of .* for element-wise multiplication
• Not using meshgrid to create X and Y matrices
• Using vectors directly in surf without matching sizes