What cartesian coordinate system is best for preserving direction?

The Transverse Mercator projection is specifically designed to preserve directional accuracy over small areas. This projection is ideal for regions with a north-south extent because it maintains angles, making it particularly useful for navigation and mapping where precise direction is crucial. In the Transverse Mercator, the central meridian is straight, and distortions in scale are minimized along this line, which means that distances and angles can be measured accurately in relation to it.

This projection is widely used for topographic maps and by various surveying and engineering applications due to its ability to represent the earth's curvature accurately over relatively small areas, allowing for reliable directional representations.

In contrast, other projections, like Albers Equal Area, are designed to preserve area but not necessarily direction, which would lead to distortions in angles. The Equidistant Conic projection helps maintain distances but does not focus on direction, and the Azimuthal projection, while good for direction from a central point, does not preserve direction across all areas effectively. Therefore, for applications requiring accurate directional representation, the Transverse Mercator is the most appropriate choice.