Three-Dimensional Intersection—A Vector Approach

by William E. Ball, Jr., (M.ASCE), Engrg. Analyst; U.S. Dept. of the Interior, Bureau of Land Mgmt., Portland, OR,


Serial Information: Journal of the Surveying and Mapping Division, 1973, Vol. 99, Issue 1, Pg. 63-78


Document Type: Journal Paper

Abstract: Systems of equations are derived and computational routines are outlined that can be used to determine the geodetic coordinates and elevation of a point by three-dimensional intersection using horizontal and vertical angles only. Equations are similarly derived and a computational routine is outlined that can be used to compute the geodetic coordinates and elevation of a point using horizontal angles, vertical angles, and slope distances. In both cases angles are used that have been measured from two or more points having known geodetic coordinates and elevations to a point of unknown position. All data consist of direct field measurements in the form of horizontal angles, vertical angles, and slope distance corrected only for refraction. The equations are exact with respect to a reference ellipsoid, but corrections may be required wherever the actual topographic surface differs significantly from the surface of the reference ellipsoid.

Subject Headings: Geodetic surveys | Computing in civil engineering | Intersections | Slopes | Distance measurement | Topography | Vector analysis

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