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Ultimately, the goal is very straightforward relating each position on one surface, the reference ellipsoid, to a corresponding position on another surface as faithfully as possible and then flattening that second surface to accommodate Cartesian coordinates. In fact, the whole procedure is in the service of moving from geographic to Cartesian coordinates and back again. These days, the complexities of the mathematics are handled with computers. Of course, that was not always the case. Map projections in which shape is preserved are known as conformal or orthomorphic. Orthomorphic means right shape. In a conformal projection, the angles between intersecting lines and curves retain their original form on the map. In other words, between short lines, meaning lines under about 10 miles, a 45º angle on the ellipsoid is a 45º angle on the map. It also means that the scale is the same in all directions from a point; in fact, it is this characteristic that preserves the angles. These aspects were certainly a boon for all State Plane Coordinate users. On long lines, angles on the ellipsoid are not exactly the same on the map projection. Nevertheless, the change is small and systematic. Actually, all three of the projections that were used in the designs of the original State Plane Coordinate Systems were conformal. Each system was originally based on the North American Datum 1927, NAD27. Along with the Oblique Mercator projection, which was used on the panhandle of Alaska, the two primary projections were the Lambert Conic Conformal Projection and the Transverse Mercator projection. Today, they're in North American Datum of 1983, NAD83 2011 (2010.0).