Mapping points in different Coordinate Systems

[gabrigoo]

Hello everyone,

I have been trying to solve this problem for a few days but haven't been able to come up with a solution.

Imagine you have two coordinate systems: Coordinate System 1 and Coordinate System 2. The location and orientation of these coordinate systems are unknown. There is a point in space called P1. The location of this point with respect to Coordinate System 1 and Coordinate System 2 is known. There is also an additional point in space called P2. For this point, the location is only known for Coordinate System 1.


How can you get the location of P2 with respect to Coordinate System 2?

Here is a schematic drawing of the problem:

 

[lev888]

Hello everyone,

I have been trying to solve this problem for a few days but haven't been able to come up with a solution.

Imagine you have two coordinate systems: Coordinate System 1 and Coordinate System 2. The location and orientation of these coordinate systems are unknown. There is a point in space called P1. The location of this point with respect to Coordinate System 1 and Coordinate System 2 is known. There is also an additional point in space called P2. For this point, the location is only known for Coordinate System 1.


How can you get the location of P2 with respect to Coordinate System 2?

Here is a schematic drawing of the problem:View attachment 30172

You can rotate system 2 around P1 keeping P1 coordinates constant. This changes P2 coordinates. So I don't think solution exists.

 

[gabrigoo]

I was thinking that if 3 points are known then I could get a transformation matrix T to map every point. Does this make sense?