# Transforming a point from one coordinate system to another

I am trying to map the position of an object in one image to another. I have four points in one image with corresponding points in another image so as to bound an area say A. Now, if I have points in A from one image, how do I get the coordinate of the points in the second image.

It must be noted that the first image has oblique coordinates while the second one is orthogonal. Also, I do not have any other information such as the angle between the two coordinate systems. I only have four points in both the images that encompass all my required points (in area A) within them.

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More work is required for other coordinate systems, e.g. changing from to polar coordinates to Cartesian coordinates. If a point has polar coordinates $(r,\theta)$ then it has Cartesian coordinates $$(x,y) = (r\cos\theta,r\sin\theta).$$