Map Projections: Dimensions, Geometry, and Classifications

Types of Map Projections by Preserved Dimension

1. Equidistant Projections
These projections preserve distances along specific directions, typically along straight lines known as automecoic lines. Linear deformation occurs in other directions. The linear anamorphosis, calculated as the ratio of the projected distance to the true distance, equals 1 along automecoic lines. Equidistant projections are useful for measuring distances from a central point.
2. Conformal Projections
These projections preserve angles between intersecting curves and lines. The angular anamorphosis represents the difference between the angle on the sphere and the corresponding angle on the map. Conformal projections are commonly used for nautical charts, often employing parallel meridians.
3. Equivalent (Equal-Area) Projections
These projections preserve the area of any shape on the map. The surface anamorphosis is the ratio of the map area to the corresponding real-world area. Equivalent projections are frequently used for thematic maps and land parcel representation.
4. Aphylactic (Compromise) Projections
These projections do not perfectly preserve any of the above magnitudes (distance, angle, or area) but aim to minimize overall distortion, keeping anamorphosis values relatively low.

Geometric Classification of Map Projections

By Position of the Projection Source:
Projections are categorized based on the position of the point of view or projection vertex, the design center (point of tangency), and the projected plane. Planar projections involve projecting onto a flat plane, while development projections involve projecting onto a developable surface like a cone or cylinder.
I. Planar Projections
Key characteristics of planar projections include:

• Circles passing through the projection vertex are projected as straight lines.
• Points equidistant from the vertex are equidistant from the center of the projection.
• Surfaces equidistant from the center of projection exhibit the same degree of deformation.

Classification of Planar Projections:
A. By Position of the Projection Center:

1. Plane perpendicular to the Earth's axis, centered on a pole: Polar or equatorial projections.
2. Plane perpendicular to the equator, centered on the equator: Meridional or transverse projections.
3. Plane perpendicular to any other point: Oblique, direct, horizontal, or overhead projections.

B. By Projection Vertex:

1. Gnomonic (Central) Projection: Point of view at the Earth's center. Projects the entire hemisphere. Great circles (shortest paths) are represented as straight lines. Distortion increases significantly away from the center of projection.
2. Stereographic Projection: Point of view opposite the projection center. Conformal projection. Can represent a hemisphere. Circles on the sphere are projected as circles on the plane. Scale is constant along circles centered on the projection center. Rhumb lines (lines of constant bearing) are projected as logarithmic spirals.
3. Orthographic Projection: Point of view at infinity. Maximum field of view is a hemisphere.
4. Scenographic Projection: Point of view at a finite distance outside the Earth. Examples include Ahir (1.71 R), Parent (1.594 R), Lowry (1.69 R), and Fiorini (1.76 R) projections, where R is the Earth's radius.