Geoscience Reference
In-Depth Information
Chapter 6
Gauss and UTM Conformal Projections
and the Plane Rectangular Coordinate
System
In Chap.
5
we established the relationship between geodetic elements on the Earth's
surface and those on the ellipsoid. This chapter further establishes the
corresponding relationship between geodetic elements on the ellipsoid and those
on the plane. We will discuss the corresponding relationship between geodetic
coordinates, geodesic direction, geodesic distance, and geodetic azimuth, and their
corresponding counterparts on the plane. Such corresponding relationship is real-
ized through mathematical projection methods, of which there are many. This
chapter, however, is primarily concerned with the two conformal (orthomorphic)
projections used in geodetic survey, i.e., the Gauss projection and the Universal
Transverse Mercator (UTM) projection and establishes the projection relationship
between the geodetic coordinate system and plane coordinate system, as well as the
relationship between the geodetic control network on the ellipsoid and that on the
plane.
6.1 Overview of Projection
6.1.1 Aims of Projection
The reference ellipsoid is the datum for geodetic computations (of geodetic coor-
dinates, geodetic azimuth, and geodesic distance, etc.) and for study of the shape
and size of the Earth (computations of vertical deflection and height anomaly).
Geodetic coordinates on the ellipsoid are the fundamentals for geodetic survey. One
of the roles of geodetic survey is to determine the coordinates of surface points to
control topographic mapping. Maps are flat, so the coordinates of geodetic points
used to control mapping have to be plane coordinates, otherwise they will be
unrelated, for one belongs to the plane system and the other the ellipsoid system.
Establishing the corresponding relationship between geodetic coordinates and
plane coordinates therefore becomes necessary, which is called projection. Within
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