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How to changes X Y coordinate System and get value point?

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Hi all,
Following is described of my question.
Suppose that, I have XY coordinate and 2 points (a,b)
Now, I create new XY coordinate with a is original point.
C is one point of x'ay' coordinate.
So, How to convert C position to xy coordinate??
or in opposite, if C is one point of xy coordinate, how to get position of C in x'y' coordinate??
Do anyone have idea, please help me.
Thank you so much.

Risposta accettata

Jiri Hajek
Jiri Hajek il 9 Dic 2022
Hi, you need to use matrix transformations of coordinates as described e.g. here: https://en.wikipedia.org/wiki/Kinematics#Matrix_representation
  3 Commenti
Jiri Hajek
Jiri Hajek il 12 Dic 2022
OK. I'll try to explain the basic concept. In order to generalize transformation of coordinates for your point in a plane, you will always need at most two elementary transformations. One of them is rotation and the other is translation.
In your illustrations, you have the original and final coordinate systems, but to fully understand the complete transformation between your two coordinate systems, you will need to plot also a third coordinate system, which incorporates just one of the transformation steps (doesn't matter if rotation or translation).
To actually transform your coordinates, you have to perform one transform after the other. Offset (translation) is simple, but for the rotation, you need a matrix transform, see e.g. here.
galaxy
galaxy il 18 Dic 2022
Modificato: galaxy il 18 Dic 2022
Sorry for feedback late
I got it.
Thank you for your anwser.

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