Projection between two coordinate systems

I have two coordinate systems as the picture shown. I know the origin and unit vectors of the two coordinate systems. now, I want to project the coordinates in one coordinate system to another system. how could I do using Matlab? Thanks in advance!

Answer 1

[Honglei Chen]

Let's use coodinate system g as the reference and assume your coordinates are Pg = [xg;yg;zg]. For coordinate system l, the orgin is Ol = [xolg;yolg;zolg] and the three unit vectors are Xlg, Ylg, and Zlg. So you can define the transform matrix as [Xlg Ylg Zlg]. Then the new coordinate Pl can be represented as

Pl = M.'*(Pg-Ol)

If you have access to Phased Array System Toolbox, then you can try using

<https://www.mathworks.com/help/phased/ref/local2globalcoord.html>

or

<https://www.mathworks.com/help/phased/ref/global2localcoord.htm> l

depending on which one you want to use as a reference.

HTH

[Yang Lu]

Thank you for your response. However, what I want to know is how to project a line(coordinates) from one system to another?

[Honglei Chen]

Could you be more specific? From my perspective, a line is a collection of points, so you can just line up multiple points in Pg and everything should work as is.

HTH

[Yang Lu]

I am sorry for that I did not make clear. I got a series of coordinates of one profile in one coordinate system and now I want to project all the coordinates to another coordinate system. Hope the following picture can help to understand my question. So I can get the coordinates in the current coordinate system. I do not think the active and passive coordinate transformation is useful here.

Merci!