Why 3D plots show complex relationships in MATLAB - See It in Action

Why 3D plots show complex relationships

📖 Scenario: Imagine you are a scientist studying how two factors affect a result. You want to see how these two factors together change the result. A 3D plot helps you see this complex relationship clearly.

🎯 Goal: You will create a simple 3D plot in MATLAB to show how two variables affect a result. This will help you understand why 3D plots are useful for showing complex relationships.

📋 What You'll Learn

Create two vectors representing two variables

Create a grid of points from these vectors

Calculate a result based on these two variables

Plot the result in a 3D surface plot

💡 Why This Matters

🌍 Real World

Scientists and engineers often study how two factors together affect a result, like temperature and pressure affecting a chemical reaction. 3D plots help visualize these complex effects.

💼 Career

Understanding 3D plotting is useful for data analysis, research, and engineering jobs where visualizing relationships between multiple variables is important.

1

Create two vectors for variables

Create two vectors called x and y using linspace. Set x from 0 to 5 with 50 points, and y from 0 to 5 with 50 points.

MATLAB

% Create vectors x and y using linspace
% Your code here

Need a hint?

Use linspace(start, end, number_of_points) to create vectors.

2

Create a grid of points from vectors

Use meshgrid with x and y to create matrices X and Y that hold all combinations of x and y.

MATLAB

x = linspace(0, 5, 50);
y = linspace(0, 5, 50);
% Create grid matrices X and Y using meshgrid
% Your code here

Need a hint?

meshgrid creates matrices for all pairs of x and y.

3

Calculate the result using X and Y

Calculate a matrix Z where each element is sin(X) + cos(Y). Use element-wise operations with sin and cos.

MATLAB

x = linspace(0, 5, 50);
y = linspace(0, 5, 50);
[X, Y] = meshgrid(x, y);
% Calculate Z as sin(X) + cos(Y)
% Your code here

Need a hint?

Use element-wise operations with sin and cos on matrices.

4

Plot the 3D surface

Use surf to create a 3D surface plot of Z over X and Y. Then use xlabel, ylabel, and zlabel to label the axes as 'X axis', 'Y axis', and 'Z axis'.

MATLAB

x = linspace(0, 5, 50);
y = linspace(0, 5, 50);
[X, Y] = meshgrid(x, y);
Z = sin(X) + cos(Y);
% Plot the surface and label axes
% Your code here

Need a hint?

Use surf(X, Y, Z) to plot. Label axes with xlabel, ylabel, and zlabel.