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3.4.4.7 New Zealand Map Grid

This projection system typifies the most recent development in the design and formulation of map projections where, by more complex mathematics yielding formulas readily handled by modern computers, it is possible to maintain the conformal property and minimize scale distortion over the total extent of a country area without being tied to a particular zone distributed about a set line such as a central meridian or standard parallel. Thus both North and South Islands of New Zealand, previously treated not very satisfactorily in two zones of a Transverse Mercator projection can now be projected as one zone of what resembles most closely an oblique Mercator but which, instead of being based on a minimum scale factor straight central line, has a central line which is a complex curve roughly following the trend of both North and South Islands. The projected coordinate system achieves this by a form of double projection where a conformal projection of the ellipsoid is first made to say an oblique Stereographic projection and then the Cauchy-Riemann equations are invoked in order to further project the rectangular coordinates on this to a modification in which lines of constant scale can be made to follow other than the normal great or small circles of Central meridians or standard parallels. Snyder classifies this projection and others like it as a modified Stereographic projection. The mathematical treatment of the New Zealand Map Grid is covered by a publication by the New Zealand Department of Lands and Survey Technical Circular 1973/32 by I.F. Stirling.

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