How Do Rotation Matrices Impact Coordinate Systems and Object Transformations?

[Leo Authersh]

Can anyone give me geometric and intuitive insight on Rotation matrices which has two sets of coordinates after Transformation?

 

[fresh_42]

Can you be a bit more precise? What don't you understand exactly? And what, which cannot be found already here:
https://en.wikipedia.org/wiki/Rotation_matrix

 

[Leo Authersh]

Can you be a bit more precise? What don't you understand exactly? And what, which cannot be found already here:
https://en.wikipedia.org/wiki/Rotation_matrix

Hi, Now I understood. In the above picture, they have the vector fixed and rotated the axes. I couldn't understood it at first. Thank you for your answer :)

 

[WWGD]

I think the post refers to two coordinate systems. Before- and After- rotation.

 

[Leo Authersh]

I think the post refers to two coordinate systems. Before- and After- rotation.

Yes it is. Here they rotated the axes instead of vector.

 

[fresh_42]

Yes it is. Here they rotated the axes instead of vector.

Yeah, this is really a bit difficult to distinguish sometimes: changing the coordinates or changing the object and how does it affect the matrix? It's easy to get confused if one doesn't keep track of what is what and in which coordinate system. A tip is better to write some extra lines than to search for errors afterwards. I always tell students when it comes to calculations: write it down step by step, because writing is fast, thinking is slow.

 

[Leo Authersh]

Yeah, this is really a bit difficult to distinguish sometimes: changing the coordinates or changing the object and how does it affect the matrix? It's easy to get confused if one doesn't keep track of what is what and in which coordinate system. A tip is better to write some extra lines than to search for errors afterwards. I always tell students when it comes to calculations: write it down step by step, because writing is fast, thinking is slow.

I believe thinking is fast. But if we write down each step we can save all the cognition for solving a specific step which otherwise would be wasted in memorizing the already solved steps. But that's just for me :)