Euler Angle transformation, help

In summary, the conversation discusses the need for euler angles in the probe's frame of reference to create a 3-D visualization of what the camera on the tip of the probe would see. The person is struggling with making rotation transformations using euler angles for vectors and is looking for suggestions on how to solve this problem. They mention that one solution would be to have a formula that gives the instantaneous transformation between the two coordinate systems. They also mention having data available such as the vector between the two coordinate systems, the orientation of the probe at any instance of time, and the rotation matrix between both coordinate systems at any given instance of time. Finally, they mention figuring out a solution by writing a program that constantly gives the difference in the euler angles of
  • #1
spaderdabomb
49
0
I'm doing a research project currently and basically what I have is a camera measuring a probe. I have designed the camera to give the orientation of the probe using euler angles in the camera's frame of reference. This was working for most of my data, but now I need a 3-D visualization of what the camera on the tip of the probe would see. In order to do that, I now need to know the euler angles in the probe's frame of reference.

I know how to make rotation transformations using euler angles for vectors, but for some reason this problem is confusing me. I need euler angles in one frame where I have the euler angles in another frame. Suggestions on how to make this work are greatly appreciated, thanks!

EDIT: An easy way would be IF I KNEW the angles between the two coordinate systems, but unfortunately one of the coordinate systems (the probe) is constantly changing. So it is a little more complex than simply adding angles and subtracting them. All I need though I guess, is a formula that gives me the instantaneous transformation. Then I can just put that into my MATLAB code and I'll have all the data I need.

DATA AVAILABLE:

- Vector between two coordinate systems
- Orientation of probe at any instance of time (but changing in time)
- Euler angles of probe in camera's reference frame
- Rotation matrix between both coordinate systems at any given instance of time
 
Last edited:
Physics news on Phys.org
  • #2
Think I figured it out. All I had to do was write a program that constantly gave the difference in the euler angles of the two coordinate systems. Then I took the original vector (pointing in the -z direction of my probe's coordinate system) and did the inverse transformation using the inverse of the rotation matrix given by the euler angles. Finally, I did took that vector and normalized it so I had a unit vector in my new coordinate system pointing in the correct direction.
 

1. What are Euler angles and how are they used in transformation?

Euler angles are a set of three angles that describe the orientation of an object in a three-dimensional space. They are used in transformation to represent the rotation of an object around its three axes.

2. How do you convert between Euler angles and other representations of orientation?

There are various methods for converting between Euler angles and other representations of orientation, such as rotation matrices and quaternions. The conversion process involves using trigonometric functions and specific formulas depending on the type of Euler angles used (e.g. Tait-Bryan angles or proper Euler angles).

3. What are the advantages and disadvantages of using Euler angles for transformation?

One advantage of using Euler angles is that they are intuitive and easy to visualize. However, they can suffer from the problem of gimbal lock, where one axis becomes aligned with another and the rotation becomes ambiguous. They also have singularities at certain orientations, which can make calculations and conversions more complex.

4. How do Euler angles differ from other methods of representing orientation?

Euler angles differ from other methods of representing orientation in that they use a sequence of rotations around fixed axes, rather than a single rotation around an arbitrary axis. This can make them more intuitive for certain applications, but also leads to the aforementioned issues with gimbal lock and singularities.

5. What are some real-world applications of Euler angles?

Euler angles are commonly used in aerospace engineering, robotics, and computer graphics, among other fields. They are also used in motion capture technology for animation and in flight simulation for controlling aircraft movements.

Similar threads

Replies
18
Views
931
Replies
7
Views
855
  • Classical Physics
Replies
8
Views
1K
Replies
2
Views
2K
Replies
1
Views
1K
  • Classical Physics
Replies
5
Views
1K
Replies
6
Views
1K
  • Classical Physics
Replies
1
Views
461
  • Classical Physics
Replies
1
Views
496
  • Classical Physics
Replies
4
Views
2K
Back
Top