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Introduction.
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The South African Gauss
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The South African Gauss
Contents
Introduction.
Why?
What is the Gauss conform system?
Which latitude?
Some definitions and notation.
Sign and axes convention.
The constants of the spheroid.
The constraints.
More definitions, conventions and a cartesian coordinate system.
Converting from Geodetic to Geocentric latitude.
Implications of the conform constraint.
Small Displacements on the surface of the earth.
Small displacements on the map.
Matching the Angles across the projection.
Specifying the boundary conditions.
Resolving differences with original references.
Complex Variable approach to finding the solution to the transform equations.
Calculating L(t).
Calculating the inverse
.
Conformal latitude.
Expansion of
in powers of the eccentricity.
The inverse of
.
Newton-Raphson method for finding the inverse of
.
In summary.
Appendix I. The Transverse Cylindrical Coordinate system.
Appendix II Power series solutions suitable for the tropics.
Power series of
in terms of t
The inverse of
as a power series.
Expanding L, the distance along the central meridian from the equator.
Expanding R as a Taylor series of an analytic function.
Matching terms in the power series.
Inverting the transform.
References.
About this document ...
John Carter
Fri Feb 21 14:23:22 SAT 1997
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