Understanding 3D Rotation Transformations

Click For Summary
SUMMARY

This discussion focuses on the principles of 3D rotation transformations, specifically how trigonometric conventions from 2D translate into three dimensions. The positive x-axis, y-axis, and z-axis have specific orientations, and the discussion raises questions about the consistency of these conventions when axes are repositioned. The user aims to apply this understanding to create matrix transformations for controlling the orientation of 3D shapes, highlighting the importance of correctly determining rotation signs. The reference to the Wikipedia article on rotation matrices provides foundational knowledge for constructing these transformations.

PREREQUISITES
  • Understanding of Cartesian coordinate systems
  • Familiarity with trigonometric functions and their applications in geometry
  • Knowledge of matrix operations, specifically 3x3 rotation matrices
  • Basic concepts of 3D graphics and transformations
NEXT STEPS
  • Study the properties of 3D rotation matrices in detail
  • Learn about Euler angles and their application in 3D rotations
  • Explore quaternion mathematics for representing 3D orientations
  • Investigate the implications of axis transformations on rotation conventions
USEFUL FOR

This discussion is beneficial for students and professionals in physics, computer graphics, and engineering who are working with 3D transformations and seeking to deepen their understanding of rotation conventions and matrix applications.

student6587
Messages
1
Reaction score
0
Hello,

First time posting to Physics Forums.

I have been thinking about rotation transformations and am a bit confused on how trig works in 3D.

In 2D, convention says the positive x-axis points to the right, the positive y-axis points upward, and positive angles are measured from the positive x-axis in a counter-clockwise fashion. Proper insertion of a third dimension has the positive z-axis pointing toward the viewer.

How do these rules translate to other perspectives of the 3 cartesian axes? For example, if the positive x-axis points to the left, the positive z axis points up, and the positive y-axis points toward the viewer. Is positive rotation still counter-clockwise? What axis is this angle measured from?

I suspect that the convention is arbitrary but there must be some criteria for consistency. A little bit of context: ultimately, I want to use this knowledge to construct matrix transformations to control the orientation of a simple 3D shape. When I try to work these out by hand, I keep getting the signs wrong.

Thanks!
 
Physics news on Phys.org

Similar threads

Undergrad Calculating Pitch and Roll Relative to a Velocity Vector from IMU Data
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Displacement-Rotation Algorithm
  • · Replies 2 ·
Replies
2
Views
2K
High School Rotating a point in 3-space through an angle about some vector
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Not all reflections in 2D are 3D rotations?
  • · Replies 9 ·
Replies
9
Views
3K
MHB Finding the Rotation Matrix for 60 Degree Rotation around (1,1,1) Axis
  • · Replies 27 ·
Replies
27
Views
5K
Undergrad Rotation of a point in R3 about the y-axis
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Rotate a shape back to its original position with the fewest rotations
  • · Replies 21 ·
Replies
21
Views
5K
Undergrad Did I figure-out z-translation of 2D-coordinates correctly?
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Passive Transformation and Rotation Matrix
  • · Replies 1 ·
Replies
1
Views
4K
Graduate How to Calculate the Rotation Axis Incorporating Translation?
  • · Replies 8 ·
Replies
8
Views
2K