Map Projections

Map making is fundamentally an exercise in translation—converting the three-dimensional reality of our Earth, or more precisely its geoid shape, onto a two-dimensional surface. Geometrically, this transformation is inherently flawed; it is impossible to represent a sphere accurately on a flat plane without introducing some form of distortion. This challenge is compounded when we consider the Earth’s varied topography and other three-dimensional features.

Given these constraints, the cartographer’s task becomes one of strategic compromise. The key to successful map-making lies not in avoiding distortion altogether, but in making informed decisions about which aspects of the Earth’s surface to preserve and which to sacrifice, based on the intended use of the map.

For example, a map designed for navigation might prioritize accurate representation of angles and directions, even if this means distorting the relative sizes of landmasses. Conversely, a thematic map that highlights population density or climate zones would need to maintain the correct proportions of areas, potentially at the expense of angular accuracy.

A sphere is not a developable surface but is the closest geometrical form to the shape of the earth i.e., the Geoid. The shapes that form a developable surface are 2-dimensional geometric shapes like the Cone, Cylinder and Circle.

When we construct maps, we try to represent four geographical characteristics: Area, Shape, Bearing, and Distance. There can also be a fifth type in which none of the above features are preserved. 

Classification based on preservation :

Based on certain attributes, the following types of projections can be made…

Preservation	Projections
of area	Equal Area or Homolographic Projection
of shape	Orthomorphic Projection
of bearing	Azimuthal Projection
of distance	Equidistant Projection
none	Aphylactic Projection

Classification based on Development :

Perspective Map Projections

Map projections are techniques used to represent the three-dimensional Earth’s surface on a two-dimensional plane. These projections can be categorized based on three main factors: the type of developable surface used, the viewpoint or perspective, and the projection aspect.

Types of Surfaces:

• Cylinder: The Earth’s surface is projected onto a cylinder that touches the globe along a central meridian or equator.
• Cone: The surface is projected onto a cone that intersects the globe along one or two parallels (lines of latitude).
• Plane: The projection is made onto a plane that tangents or cuts through the Earth’s surface at a specific point or along a line.

Viewpoints or Perspectives:

• Center (Gnomonic Projection): The light source is directly above the surface’s centre, creating accurate angles but highly distorted distances and areas.
• Periphery or Antipodal (Stereographic Projection): The light source is located at the surface’s opposite pole, resulting in conformal projections that preserve angles but distort shapes and areas.
• Infinity (Orthographic Projection): The light source is infinitely far away, producing equal-angle projections that maintain the correct appearance of angles and shapes but distort sizes and distances.

Projection Aspects:

• Polar: The central meridian of the projection passes through one of the Earth’s poles.
• Equatorial (or Transverse): The central meridian is the Earth’s equator, or, in the case of a transverse projection, a meridian 90 degrees from the equator.
• Oblique: The central meridian is neither through a pole nor the equator, slanting across the globe to best represent a specific region.

Non-Perspective Map Projections

Non-perspective map projections, also known as mathematical or analytical projections, do not simulate projecting the Earth’s surface onto a developable surface (like a cylinder, cone, or plane) from a specific viewpoint. Instead, they use mathematical formulas to transform geographic coordinates (latitude and longitude) into planar coordinates (x and y). These projections are commonly used when exact geometric accuracy isn’t the main priority, and they can be categorized based on the property they prioritize most:

1. Conformal Projections: These projections preserve local angles, meaning that small shapes retain their true angles and form, though area and distance can be distorted. Examples include the Lambert Conformal Conic projection and the Stereographic projection when used in a non-perspective sense. Although the Mercator projection is technically a perspective cylindrical projection, it is often discussed with conformal projections because of its ability to preserve angles.
2. Equal-Area (or Equi-Area) Projections: These projections ensure that the relative areas of regions are maintained, though their shapes and angles might be distorted. Examples include the Albers Equal-Area Conic projection, the Lambert Azimuthal Equal-Area projection, and the Mollweide projection.
3. Equidistant Projections: These preserve true distances along specific lines (typically the central meridian or the equator) or between certain points. Elsewhere, distances, angles, and shapes may be distorted. Examples include the Equirectangular projection and the Central Cylindrical projection. The Robinson projection, while primarily a compromise projection, also maintains some equidistant properties.
4. Compromise Projections: These aim to balance the preservation of angles, areas, and distances, without perfectly preserving any of them. The Robinson projection is a well-known example, designed for aesthetic purposes, while others like the Winkel Tripel and Van der Grinten projections similarly seek a balanced view.

Non-perspective projections are selected based on the map’s intended purpose, often prioritizing area, shape, or distance depending on the region being mapped. This makes them especially useful for various applications, including global or regional maps, where distortion trade-offs are necessary.