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

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.

Answer 1

[Jiri Hajek]

Hi, you need to use matrix transformations of coordinates as described e.g. here: https://en.wikipedia.org/wiki/Kinematics#Matrix_representation

[galaxy]

@Jiri Hajek

thank you for your comment.

But, I am not understood, can you help me to explain.

[Jiri Hajek]

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]

@Jiri Hajek

Sorry for feedback late

I got it.

Thank you for your anwser.