Coordinate System Transformation

In summary, the person is trying to solve a problem where they need to rotate points in space around the origin of a local system, in order to rotate them relative to the global system.
  • #1
dhume878
6
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.
 
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  • #3
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
 
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Likes Greg Bernhardt
  • #4
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.
 
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Likes dhume878

Question 1: What is a coordinate system transformation?

A coordinate system transformation is the process of converting coordinates from one reference system to another. This is often necessary when working with data from different sources or when using different mapping systems.

Question 2: Why do we need coordinate system transformation?

Coordinate system transformation allows for data to be accurately compared and integrated from multiple sources. It also helps to ensure that measurements and locations are represented correctly on different maps or in different coordinate systems.

Question 3: What are the common types of coordinate systems?

The most common types of coordinate systems are geographic coordinate systems (such as latitude and longitude), projected coordinate systems (such as UTM or State Plane), and local coordinate systems (such as Cartesian coordinates).

Question 4: How do you perform a coordinate system transformation?

Coordinate system transformation can be performed using mathematical equations, specialized software, or by manually reprojecting coordinates. The method used will depend on the complexity of the transformation and the accuracy required.

Question 5: What are some potential errors or challenges when performing a coordinate system transformation?

Some potential errors or challenges when performing a coordinate system transformation include data loss or distortion, incorrect datum conversions, and differences in precision between different coordinate systems. It is important to carefully consider the accuracy and limitations of each coordinate system before performing a transformation.

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