mesh and surf for surfaces in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a grid of points using meshgrid.

MATLAB

x = -2:0.5:2;
y = -2:0.5:2;
[X, Y] = [1](x, y);

Drag options to blanks, or click blank then click option'

Ameshgrid

Bplot

Clinspace

Dsurf

Attempts:

3 left

💡 Hint

Common Mistakes

Using linspace instead of meshgrid.

Trying to use plot to create coordinate matrices.

The meshgrid function creates matrices for X and Y coordinates from vectors x and y, which is needed for 3D surface plotting.

2fill in blank

medium

Complete the code to calculate Z as the sum of squares of X and Y.

MATLAB

Z = [1].^2 + Y.^2;

Drag options to blanks, or click blank then click option'

AY

BX

CZ

Dx

Attempts:

3 left

💡 Hint

Common Mistakes

Using lowercase x instead of matrix X.

Forgetting the dot before the power operator.

We use X squared plus Y squared to get the surface height Z.

3fill in blank

hard

Fix the error in the code to plot the surface using surf.

MATLAB

surf(X, Y, [1]);

Drag options to blanks, or click blank then click option'

AZ

Bplot

CY

Dx

Attempts:

3 left

💡 Hint

Common Mistakes

Passing x or y instead of Z to surf.

Trying to use plot instead of surf.

The surf function needs the Z matrix for heights, so we pass Z.

4fill in blank

hard

Fill both blanks to create a mesh plot and label the axes.

MATLAB

mesh(X, Y, Z);
xlabel('[1]');
ylabel('[2]');

Drag options to blanks, or click blank then click option'

AX-axis

BY-axis

CZ-axis

DSurface

Attempts:

3 left

💡 Hint

Common Mistakes

Labeling axes incorrectly or swapping labels.

Using 'Z-axis' label for x or y axis.

We label the x-axis as 'X-axis' and the y-axis as 'Y-axis' to describe the plot clearly.

5fill in blank

hard

Fill all three blanks to create a surface plot with title and color bar.

MATLAB

surf(X, Y, Z);
title('[1]');
colorbar;
shading [2];
view([3]);

Drag options to blanks, or click blank then click option'

A3D Surface Plot

Binterp

C[45 30]

Dflat

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'flat' shading which is less smooth.

Not setting a proper view angle for 3D visualization.

The title describes the plot, 'interp' smooths colors, and view sets the angle to [45 30].

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