Affine & Curvilinear Transformations
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Coordinate transformations are required when you need to register different sets of coordinates for objects in the same area that may have come from maps of different (and sometimes unknown) projections. There are two ways to look at coordinate transformations: 1)Move objects on a fixed coordinate system so that the coordinates change. 2)Hold the objects fixed and move the coordinate system (this is the more useful way to consider transformations for GIS purposes).
Missouri Spatial Data Information Service