Courses - GPS 443
GPS 443 Conformal Mapping Model
(catalog description): Conformal mapping of the ellipsoidal
surface, meridian convergence, point scale factor; State Plane
Coordinate systems, Transverse Mercator, Equatorial Mercator,
Lambert Conformal with one or two standard parallels, polar
azimuthal, and UTM; reduction of observations, computations on the
conformal map and relation to the surface of the earth; review of
complex variables. Prerequisite: GPS 441, GPS 442, equivalent or
consent, Lec. 1, Cr. 1
The popularity of the State Plane
Coordinate Systems in the U.S.A. makes the conformal mapping model
very important. The former are a patchwork of transverse Mercator
and Lambert conformal mappings spanning the U.S.
We look in detail at the meaning
of conformality and the mathematical conditions that lead to such
a property. We introduce the point scale factor, line scale
factor, and the meridian convergence and derive the mapping
equations that map the ellipsoidal surface to the conformal map
and vice versa. We further derive and discuss the so-called
mapping elements that allow us to convert the 2D ellipsoidal
surface model observations to conformal mapping model
observations, and adjust networks on the conformal map.
The conformal mapping model is
the most "abstract model", in the sense that physical observations
must first be reduced to the 3D geodetic model, then to the 2D
ellipsoidal model, and finally, to the conformal mapping model. It
is of course also important to apply these reductions in the
reverse whenever angles and distance on the map are to be used on
the physical surface of the earth.
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