Map projection aspects

ABSTRACT

A projection aspect is usually defined in references as the relation to the so-called auxiliary surface. However, such surfaces do not usually exist in map projection theory, which raises the issue of defining projection aspects without reference to auxiliary surfaces. This paper explains how projection aspects can be defined in two ways which are not mutually exclusive. According to the first definition, the aspect is the position of a projection axis in relation to the axis of geographic parameterization of a sphere. The projection axis is the axis of the pseudogeographic parameterization of a sphere, based on which the basic equations of map projection are defined. The basic equations of map projection are selected according to agreement and/or custom. According to this definition, aspects can be normal, transverse or oblique. According to the second definition, an aspect is the representation of the area in the central part of a map, and can be polar, equatorial or oblique. Therefore, it is possible for a map projection to have a normal and polar aspect, but it can also have a normal and equatorial aspect. The second definition is not recommended for use, due to its ambiguity.

RÉSUMÉ

L’aspect d’une projection est généralement défini en référence à la relation avec la surface auxiliaire. Pourtant de telles surfaces n’existent généralement pas dans la théorie des projections cartographiques, ce qui pose le problème de définir l’aspect sans définir de surfaces auxiliaires. Ce papier explique comment l’aspect d’une projection peut être défini de deux façons qui ne sont pas mutuellement exclusives. Selon la première définition, l’aspect est la position de l’axe de la projection en relation avec l’axe de la paramétrisation géographique de la sphère. L’axe de la projection est l’axe de parametrisation pseudogéographique de la sphère à partir duquel les équations de base de la projection sont définies. Les équations de base de la projection sont sélectionnées en fonction d’un accord et/ou des habitudes. A partir de cette définition, l’aspect peut être normal, transverse ou oblique. Selon la deuxième définition, l’aspect est la représentation de la surface sur la partie centrale de la carte et peut être polaire, équatoriale ou oblique. Ainsi une projection cartographique peut avoir un aspect normal et polaire, mais il peut aussi avoir un aspect normal et équatorial. La seconde définition est donc à éviter, compte tenu de son ambiguïté.

KEYWORDS:

• Projection aspect
• normal aspect
• transverse aspect
• oblique aspect
• polar aspect
• equatorial aspect

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes on contributors

Miljenko Lapaine studied Mathematics and graduated from the Faculty of Science, University of Zagreb, in the field of Theoretical Mathematics. He completed the postgraduate studies in Geodesy, in the field of Cartography at the Faculty of Geodesy in Zagreb by defending his Master's thesis A Modern Approach to Map Projections. He obtained his PhD from the same Faculty with a dissertation entitled Mapping in the Theory of Map Projections. He has been a full professor since 2003. He has published more than 900 papers, several textbooks and monographs. Prof. Lapaine is the Chairman of the ICA Commission on Map Projections, a founder and President of the Croatian Cartographic Society and the Executive editor of the Cartography and Geoinformation journal.

Nedjeljko Frančula is professor emeritus at the Faculty of Geodesy, University of Zagreb. He obtained his Dipl. Ing. from the University in Zagreb (1962) and PhD from the University in Bonn (1971), both in geodesy. He worked on the application of computers for solving geodetic and cartographic problems for more than 30 years and introduced digital cartography into the undergraduate and postgraduate studies at the Faculty of Geodesy in Zagreb. He published about 500 scientific and professional papers. From 1976 to 1986, he was a deputy editor of the Geodetski list, and from 1987 to 1995 the journal's editor in chief. He has been a full member of the Croatian Academy of Engineering in Department of Civil Engineering and Geodesy since 1998. In March 2008 he was named Member Emeritus.