HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...

The starting point for this article is the fact that each spatial object i is characterized by three coordinates: x (latitude), y (longitude) and zi(by tradition elevation). The discussion is organized around three axes. First, the author reviews some of main problems encountered when representing a volume (ellipsoid) on a plane (map). Second, some elementary principles of cartography are discu...

I. Prefatory Notes 1. Fields and slopes. A function of two variables is called a “field” by the physicists, maybe because it might be describing a topography in which the height of the surface above, say sea level, is a function of two coordinates, say the longitude and latitude. To be precise, physics would call this a scalar field (because the height is a single number at each point) in two d...