GEOG 862
GPS and GNSS for Geospatial Professionals

Secant Projections

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Secant Projections
Source: GPS for Land Surveyors

As mentioned, when a conic or a cylindrical map projection surface is made secant, it intersects the ellipsoid, and the map is brought close to its surface. For example, the conic and cylindrical projections shown in the illustration cut through the ellipsoid. The map is projected both inward and outward onto it and there is no distortion on the two lines of exact scale, standard lines. They are created along the small circles where the cone and the cylinder intersect the ellipsoid. They are called small circles because they do not describe a plane that goes through the center of the Earth, as do the previously mentioned great circles. Between the standard lines, the map is under the ellipsoid, and outside of the standard lines, the map is above it. That means that between the standard lines, a distance from one point to another is actually longer on the ellipsoid than it is shown on the map, and outside the standard lines, a distance on the ellipsoid is shorter than it is on the map. Any length that is measured along a standard line is the same on the ellipsoid and on the map, which is why another name for standard parallels is lines of exact scale.  They are called standard parallels in the case of a Lambert projection that is illustrated at the top here. The lower picture is Transverse Mercator projection and the lines of exact scale neither meridians of longitude nor parallels of latitude, but are rather complex curves,