engleski

Determination of Standard Parallels Based on Parameters of Normal Aspect Conical Projections

The following normal aspect conic projections are analysed in detail: conformal, equal-area, equidistant along meridians, equidistant along parallels and gnomonic perspective. Parameters which fully define a map projection are determined by setting certain conditions which have to be met. These conditions are usually expressed using relations which the linear scale has to meet. Then, projection parameters are obtained which are usually expressed with latitudes corresponding to standard parallels, i.e. parallels along which there is no distortion in the projection. This paper emphasises on a reverse procedure: one has to determine standard parallels for known projection parameters. It is shown that the problem is reduced to solving a non-linear equation (for conformal projections and equidistant conic projections along meridians) or quadratic equation (for equal-area projections). This is equivalent to finding a root of appropriate functions. Special emphasis is put on normal aspect conic projections with only one standard parallel. It is demonstrated that the normal aspect conic projection which is equidistant along parallels and the normal aspect conic gnomonic projection can only have one standard parallel, while the conformal, equal-area and equidistant along meridians projections can have two such parallels.

cartography; conic map projections; standard parallels

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