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When the coordinates of certain points have been determined in a coordinate system, there is often the need to know the coordinates of the points in another coordinate system. The calculation of the coordinates of the points in the second system based on the coordinates in the first system and the relationship between the two coordinate systems is referred to as coordinate transformation. This entry describes coordinate transformations between Cartesian coordinate systems.

For example, in Figure 1, if the 2D coordinates of points A, B, C, and D in the x-y system are known, they can be transformed into the X-Y system if the relationship between the two systems is known.

In general, coordinate transformations between Cartesian systems can be expressed as


where (x, y, z) and (X, ...

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