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Projecting Ellipsoid Points to a Map Using a Map Projection

Additional distortion to point locations, and therefore distances and angles, are introduced by the map projection that is used to project points from the ellipsoid to the map. Two projection techniques are used for all zones in the State Plane Coordinate System of the U.S., except for one zone in Alaska. These two map projections are the Lambert Conformal Conic and the Transverse Mercator. The Transverse Mercator is also the map projection used by the Universal Transverse Mercator coordinate system and Canada’s MTM system. The ratio of distances on the map to distances on the ellipsoid is called the scale factor. Normally a goal of the cartographer is to keep the map scale as close to 1.0 as possible for the mapped area to minimize distortion. For the Lambert Conformal Conic and Transverse Mercator projections, the map scale will vary from point to point, but will be conformal, that is it will be the same in all directions at a point. For the U.S. State Plane Coordinate System, most states are divided into multiple zones to minimize distortion introduced by the map projection. Some states are small enough in area or have a shape that is ideally suited for the map projection, allowing them to be mapped without being subdivided into multiple zones.