THE INVERSE MODIFIED POLYCONIC PROJECTION
| Autor: | G V Haines |
|---|---|
| Rok vydání: | 1987 |
| Předmět: |
Power series
Iterative method Lambert conformal conic projection Orthographic projection in cartography Mathematical analysis Geometry Latitude Azimuth symbols.namesake symbols Astrophysics::Earth and Planetary Astrophysics Polyconic projection Linear approximation Earth-Surface Processes Mathematics |
| Zdroj: | Cartographica: The International Journal for Geographic Information and Geovisualization. 24:14-24 |
| ISSN: | 1911-9925 0317-7173 |
| DOI: | 10.3138/gh1h-3r48-g47h-75x2 |
| Popis: | Two projections are used on many small-scale maps of Canada: a Lambert conformal conic projection south of 80°N and a modified polyconic projection north of 80°N. The inverse of the latter projection is mathematically derived in the present paper. Latitude is derived by the Newton-Raphson iterative method, starting with an initial linear approximation which has zero error at 80°N and at the pole. The azimuth of the projected radius vector is then calculated analytically from the iteratively derived latitude, and longitude is in turn derived analytically from the azimuth. Defining error as the spherical arc distance between correct and derived positions, the maximum error of the initial derivation is .05°. The maximum error after one Newton-Raphson iteration is .0002° and after two iterations is .00000001°. The inverse of the matching Lambert projection is derived from a power series in eccentricity squared. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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