askvity

How to Rotate a Cube in Matlab

Published in Matlab 3D Rotation 4 mins read

Rotating a cube in Matlab, specifically rotating the points defining the cube's vertices, can be achieved by defining rotation angles, converting them to a rotation matrix, and then multiplying the matrix containing the cube's vertex coordinates by this rotation matrix.

Based on the provided reference, here's a step-by-step guide on how to perform this rotation using Euler angles and a Direction Cosine Matrix (DCM).

Understanding the Rotation Process

At its core, rotating a 3D object like a cube in Matlab involves transforming the coordinates of its vertices. A common method is to use matrix multiplication, where the vertex coordinates are represented as a matrix (let's call it P), and the rotation is represented by a rotation matrix (often a DCM). Multiplying P by the rotation matrix yields the new, rotated coordinates.

The provided reference demonstrates this using Euler angles (roll, pitch, yaw) which are first converted into a DCM.

Steps to Rotate a Cube (or its Vertices)

Follow these steps, referencing the provided code snippets:

Step 1: Define the Rotation Angles

You need to specify the desired rotation around each axis. The reference uses roll, pitch, and yaw angles.

roll = -0.3064;
pitch = -1.2258;
yaw = 9.8066;
  • Roll: Rotation around the X-axis.
  • Pitch: Rotation around the Y-axis.
  • Yaw: Rotation around the Z-axis.

These angles are typically defined in radians in Matlab's aerospace functions, although degree versions (angle2dcm) exist. The specific values provided are:

  • roll = -0.3064
  • pitch = -1.2258
  • yaw = 9.8066

Step 2: Convert Angles to a Direction Cosine Matrix (DCM)

A DCM is a 3x3 matrix that represents the rotation in 3D space. Matlab's angle2dcm function converts Euler angles (yaw, pitch, roll, in that specific order for the default 'ZYX' rotation sequence) into a DCM.

dcm = angle2dcm(yaw, pitch, roll);

The dcm variable will now hold the 3x3 rotation matrix corresponding to the specified yaw, pitch, and roll values.

Step 3: Apply the Rotation to the Cube's Points

Assume you have a matrix P where each row represents the [x, y, z] coordinates of one vertex of the cube. To rotate these points, you multiply the matrix P by the dcm matrix.

P = P * dcm;

If P is an nx3 matrix (where n is the number of vertices), the result P * dcm will be a new nx3 matrix containing the coordinates of the rotated vertices. The original P is overwritten with the rotated coordinates.

Note: This step assumes P already contains the initial coordinates of the cube's vertices. A cube has 8 vertices. You would need to define these coordinates before this step.

Step 4: Plot the Rotated Cube

Once the points in P have been rotated, you can plot them to visualize the rotated cube. If P contains the vertex coordinates, you can use plot3.

plot3(P(:,1), P(:,2), P(:,3)) % rotated cube.

This command plots the points in 3D space using the first column of P for x-coordinates, the second for y-coordinates, and the third for z-coordinates. To make it look like a solid cube, you would typically also plot the edges connecting the vertices, or use functions like patch or surf with appropriate face definitions based on the vertex indices in P. However, the provided reference only shows plotting the points.

Summary of Steps

Here is a summary of the core steps based on the reference:

  1. Define roll, pitch, yaw angles.
  2. Calculate the dcm matrix using angle2dcm(yaw, pitch, roll).
  3. Multiply the matrix of cube points P by dcm: P = P * dcm.
  4. Plot the resulting points: plot3(P(:,1),P(:,2),P(:,3)).

This method allows you to rotate any set of 3D points, making it suitable for rotating the vertices of a cube.

Related Articles