Coordinate System Transformation

Click For Summary

Discussion Overview

The discussion revolves around the topic of coordinate system transformations, specifically focusing on the conversion between a global coordinate system defined by a motion capture device and a local coordinate system defined by a person's pelvis. The participants explore the mathematical implications of rotating points in space based on these coordinate systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Historical

Main Points Raised

  • One participant describes the need to rotate points in a global coordinate system to align with a local coordinate system defined by the orientation of a person's pelvis.
  • The participant provides the unit vectors for both the global and local coordinate systems, noting that the local system is oriented closely to the global system.
  • There is a suggestion that a rotation matrix could be derived to facilitate the transformation between the two coordinate systems.
  • Another participant references orthogonal matrices and suggests searching for related topics in orthogonal groups, indicating a potential mathematical approach to the problem.
  • A later reply indicates that the original question has been resolved and published, suggesting that the discussion may not be as active or relevant to current inquiries.
  • One participant emphasizes the importance of avoiding empty threads and encourages revisiting older discussions to provide insights for future readers.

Areas of Agreement / Disagreement

There is no clear consensus among participants regarding the current relevance of the original question, as one participant notes it has been resolved while others engage with the mathematical concepts involved. The discussion reflects a mix of historical context and ongoing exploration of related mathematical principles.

Contextual Notes

The discussion includes references to mathematical concepts such as rotation matrices and orthogonal groups, but lacks detailed exploration of the specific mathematical steps required for the transformation. The original problem's resolution is mentioned but not elaborated upon.

Who May Find This Useful

This discussion may be of interest to students and professionals in fields related to mathematics, physics, and engineering, particularly those dealing with coordinate transformations and motion capture technology.

dhume878
Messages
6
Reaction score
1
Hey everyone,

I'm working on my degree and have started getting into some deeper lin alg than I took previously regarding coordinate system transformations. I was hoping someone might be able to shed some light on it for me. I'll do my best to explain the problem ..

I have a global coordinate system for a volume in space created by a motion capture device. Thus three unit vectors representing the x, y and z vectors of the global space are
[1 0 0
0 1 0
0 0 1]

I then have a person standing in space, with markers on their hips in such a way I can determine a local system for the person's pelvis. The unit vectors representing this local system are as follows

[0.9625 -0.0326 -0.266
0.0268 0.9999 -0.0256
0.2671 0.6175 0.9627]

So the local system is oriented very close to the global system.

I then calculate two points in space, but in the global space. I in essence need to rotate them about the origin of my local system as much as my local system is rotated from my global system.

I'm sure I sound like a bumbling goon, but I hope you guys can make heads or tails of this. I'm guessing there's a way to come up with a rotation matrix from system 1 to system 2, and from there .. hmm.. somehow translate my points about the origin of my local system.

I can clarify anything if need be.
 
Physics news on Phys.org
I appreciate the response after 8 years. This was the question of a young academic, which has since been solved, published, and laid to rest. However I would point people toward the wiki article on rotation matrices as opposed to orthogonality wrt to the relevance of the question. https://en.wikipedia.org/wiki/Rotation_matrix
 
  • Like
Likes   Reactions: Greg Bernhardt
We currently try to avoid any empty threads, which implies to work through old ones, such that anyone who stops by has at least a hint on how to proceed.
 
  • Like
Likes   Reactions: dhume878

Similar threads

Undergrad Derivation of equations of stress tensor transformation
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Passive Transformation and Rotation Matrix
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad "Map" point between coordinate systems
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Non orthogonal basis and the lines of its coordinate grid
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Spacetime coordinate smoothness requirement
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Transforming Vectors and Tensors
  • · Replies 8 ·
Replies
8
Views
3K
MHB How to Visualize Vectors and Subspaces in a Coordinate System?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Coordinate System Transformation: Lowering/Raising Indices Explained
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Coordinate transformation of a vector of magnitude zero
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Is a Gravitational Field Real or Just a Coordinate Transformation Artifact?
  • · Replies 40 ·
2
Replies
40
Views
5K