• The geographical view of oceanic space

Maps would represent the world on a flat surface or attempt to suggest its curvature. A plane representation of the earth necessarily preserves certain dimensions or proportions, but also leads to distortions in other aspects; the cartographer has to select which  projection is best suited to the purpose of the map.

The 'Mercator projection' (1569) is meant for sailors, who need to follow a predetermined course; priority is thus given to preserving straight lines as straight lines, sacrificing other less important elements of spatial representation, e.g. the relative size of continents.

In the early 19th century, new types of projection were invented, which represented correctly the relative superficies of countries, enabling statesmen to judge of their weight,  but distorted shapes and lines.

• Circular vision in naval battle scenes

On a different scale, the issue of the projection of a circular space on a flat canvas arises in marine painting. Some naval scenes would attempt to give a panoramic vision.