The South African Gauss Conform map projection system.

by John Carter - ece@dwaf.gov.za

Institute for Water Quality Studies.

Department of Water and Sanitation.

• 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 ...

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