Map projection perspective refers to a specific method of transformation used in cartography, distinct from other mathematical approaches. Within the broader concept of map projection, which is the system of transformation of the spherical surface onto a plane surface, perspective projections are those that can be geometrically visualized as projecting features from a globe onto a flat surface (or a surface that can be flattened, like a cone or cylinder) using a simulated light source.
The reference defines map projection as:
It is the system of transformation of the spherical surface onto a plane surface. It is carried out by an orderly and systematic representation of the parallels of latitude and the meridians of longitude of the spherical earth or part of it on a plane surface on a conveniently chosen scale.
Perspective projections are a way this "orderly and systematic representation" can be achieved.
Understanding Perspective Projections
Think of a translucent globe with a light source inside or outside it. If you wrap a piece of paper around the globe (say, as a cylinder or a cone) or hold a flat sheet of paper against it, the light shining through the globe's features (like continents or grid lines) will cast shadows onto the paper. The resulting pattern on the paper, when unrolled or viewed, is a perspective map projection.
The key element is the location of the simulated light source (the perspective point) relative to the globe. This location determines the specific type of perspective projection and influences how geographical features are distorted when transferred from the sphere to the flat map.
Types of Perspective Projections Based on Light Source Location
Perspective projections onto a flat plane (a planar or azimuthal projection) are the most common examples illustrating the concept of the light source location. The plane is typically tangent to the globe at a specific point.
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Gnomonic Projection: The light source is placed at the center of the globe.
- Characteristic: All great circles (including all meridians and the equator) are shown as straight lines.
- Use: Ideal for navigation as the shortest distance between two points on the globe (a segment of a great circle) is a straight line on the map. Area and shape distortion increase rapidly away from the center point.
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Stereographic Projection: The light source is placed on the surface of the globe directly opposite the tangent point of the projection plane.
- Characteristic: This is a conformal projection, meaning it preserves local shapes and angles.
- Use: Often used for mapping polar regions or hemispheres.
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Orthographic Projection: The light source is placed at an infinite distance from the globe, as if rays of light are coming from the sun far away.
- Characteristic: Represents the Earth as it appears from outer space. Areas near the edge are severely compressed.
- Use: Primarily for pictorial or illustrative purposes, showing the Earth's appearance.
Other Perspective Projections
While planar projections most clearly demonstrate the light source concept, perspective can also be applied conceptually to projections onto other surfaces:
- Cylindrical Perspective: Imagine a cylinder wrapped around the globe. The light source can be at the center, on the surface, or at infinity, casting shadows onto the cylinder. When unrolled, this creates a rectangular map. The standard Mercator projection, while often presented geometrically, is typically derived mathematically but could be visualized with a specific perspective point, though its common derivation is tangential.
- Conical Perspective: Imagine a cone placed over the globe. A light source inside or outside the globe projects features onto the cone. When unrolled, this creates a fan-shaped map. Conical projections are useful for mapping mid-latitude regions.
Why Perspective Matters
Understanding the perspective principle helps visualize how the 3D spherical surface is transformed into a 2D map. It highlights that this process inevitably introduces distortions in properties like area, shape, distance, and direction. The choice of perspective point (or the mathematical equivalent in non-perspective projections) influences which distortions are minimized or which properties are preserved, aligning the map with its intended use (e.g., navigation, area measurement, education).
While many modern projections are derived using complex mathematical formulas rather than a simple geometric perspective model, the concept of perspective remains a fundamental way to understand the underlying principles of how spherical coordinates are systematically represented on a plane surface, as described in the definition of map projection.
Summary of Perspective Projection Types (Planar)
| Projection Type | Light Source Location | Key Property/Characteristic | Primary Use Cases |
|---|---|---|---|
| Gnomonic | Center of the globe | Great circles are straight lines; high distortion | Navigation (shortest routes) |
| Stereographic | Opposite the tangent point on surface | Conformal (preserves local shapes/angles) | Polar maps, hemispheres |
| Orthographic | Infinite distance (like sunlight) | Earth as seen from space; high edge compression | Illustrative maps |
In conclusion, "map projection perspective" most commonly refers to the class of map projections that can be conceptualized using a geometric projection of the globe's features from a specific point (the light source) onto a projection surface. It's a tangible way to understand one system of transformation used to convert the Earth's sphere into a flat map.
