Maps are essential tools for visualizing and understanding spatial information. They are essentially information packages derived from various data sources, including satellite imagery and attribute data, processed and presented in a visual format. A crucial aspect of map creation is map projection.
In cartography and geodesy, a map projection is a systematic transformation of the latitudes and longitudes of locations from the surface of a sphere or ellipsoid into locations on a plane. Simply put, it’s the method used to represent the 3D surface of the Earth on a 2D flat map. This process is necessary because the Earth is a sphere (or more accurately, an oblate spheroid), and flattening a curved surface onto a plane inevitably introduces some distortion.
The purpose of map projections is to transfer geographical patterns or elements from the Earth’s curved surface onto a flat surface using mathematical formulas, aiming to achieve specific desired properties in the resulting map. These properties can include preserving shape, area, distance, or direction, but no single projection can perfectly preserve all of them simultaneously across the entire map.
Map projections are fundamental in geodesy for transforming points, lines, and angles from the Earth’s surface onto a flat plane using projection formulas. Ideally, a map projection should maintain certain characteristics of the original features on the Earth. These characteristics are often categorized into:
- Distance: Maintaining accurate distances on the map, corresponding to true distances on the Earth’s surface at a given scale.
- Shape (Angles): Preserving the true shapes or angles of features as they appear on the Earth.
- Area: Representing areas on the map in proportion to their actual areas on the Earth.
However, due to the inherent distortion when flattening a sphere, map projections are classified based on which of these properties they prioritize preserving, leading to various types suited for different purposes.
Categories of Map Projections
Map projections can be categorized in several ways, depending on the criteria used for classification. Here are some common classifications:
1. Based on Projection Surface
This classification is based on the geometric shape onto which the Earth’s surface is conceptually projected. Imagine shining a light through a transparent globe onto a developable surface – a surface that can be flattened without stretching or tearing (like a cylinder, cone, or plane).
- Cylindrical Projections:
These projections are conceptually created by wrapping a cylinder around the globe. The cylinder touches the globe at a line of tangency, typically the equator or a meridian. Points on the globe are then projected onto this cylinder. When the cylinder is unrolled, it forms a rectangular map grid.
Alt text: Illustration depicting a cylindrical map projection, showing the globe enclosed within a cylinder and projected outwards.
A well-known example of a cylindrical projection is the **Mercator projection**, popularized by the Flemish cartographer Gerardus Mercator in 1569. While famous for navigation due to its preservation of local shape and direction (making rhumb lines straight), it significantly distorts areas, especially at higher latitudes, making areas near the poles appear much larger than they are in reality.- Conical Projections:
Conical projections involve projecting the globe onto a cone. The cone touches the globe along a circle of tangency, typically a parallel of latitude. These projections are most accurate near the standard parallel and are well-suited for mapping mid-latitude regions with an east-west orientation.
Alt text: Diagram showing a conical map projection, with the globe inside a cone, projecting surface features onto the cone.
Conical projections are particularly useful for representing regions like the United States or Europe, which are elongated latitudinally.
- Azimuthal (Planar or Zenithal) Projections:
Azimuthal projections project the Earth’s surface onto a flat plane. This plane can be tangent to the globe at any point, but is often tangent at the North Pole, South Pole, or the Equator. Azimuthal projections are particularly useful for showing directions accurately from the center point of the projection.
Alt text: Image illustrating an azimuthal map projection, demonstrating projection onto a flat plane tangent to the globe’s surface.
They are commonly used for polar maps and for representing global navigation routes centered on a specific location. Distortion increases rapidly away from the center point in azimuthal projections.
- Conventional Projections:
This category encompasses projections that do not neatly fit into the cylindrical, conical, or azimuthal classifications. These are often mathematically derived projections designed to minimize distortion for specific regions or purposes, without being based on simple geometric shapes. Examples include sinusoidal and Robinson projections, which are often used for world maps to offer a visually balanced representation, even if they involve some distortion of all properties.
2. Based on Aspect or Case (Orientation of Projection Surface)
This classification depends on the orientation of the projection surface relative to the Earth’s axis.
- Normal (Equatorial or Polar) Projections: In normal aspect, the axis of the projection surface (cylinder or cone) or the central point of the plane is aligned with the Earth’s polar axis. For cylindrical projections, the cylinder is tangent along the equator (equatorial). For azimuthal projections, the plane is tangent at the North or South Pole (polar).
- Oblique Projections: The axis or central point is oriented at an angle between the poles and the equator. This can be useful for regions that are not aligned with cardinal directions.
- Transverse (Meridian or Equatorial) Projections: The axis or central point is perpendicular to the Earth’s polar axis. For cylindrical projections, the cylinder is tangent along a meridian (transverse or meridional), like in the Transverse Mercator projection, which is highly accurate along a narrow zone around the central meridian and is used for many large-scale mapping systems. For azimuthal projections, the plane is tangent at a point on the equator (equatorial azimuthal).
3. Based on Preserved Property (Distortion)
As no projection can perfectly preserve all properties, projections are often classified by the property they prioritize minimizing distortion for.
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Conformal Projections (Shape-Preserving):
Conformal projections preserve local shapes and angles. This means that small circles on the Earth appear as circles on the map, and angles between lines are correctly represented locally. The Mercator projection is a classic example. Conformal projections are crucial for navigation and кадастрал mapping where accurate shape representation is important. However, they distort areas, especially away from standard lines or points. -
Equal Area Projections (Area-Preserving or Equivalent):
Equal area projections maintain the correct proportions of areas. A region on the map has the same area relative to the total map area as the corresponding region on the Earth has to the total Earth surface area. These projections distort shapes, especially at larger scales, but are essential for thematic maps where accurate areal comparisons are needed, such as population density maps or land use maps. Examples include the Albers Equal Area Conic and the Mollweide projection. -
Equidistant Projections (Distance-Preserving):
Equidistant projections preserve distances from one or two points to all other points on the map, or along certain lines. No projection can preserve distances from all points to all other points. Azimuthal Equidistant projections, for example, preserve distances from the central point of the projection. These are useful for measuring distances from a central location, such as in airline distance maps or seismic maps.
4. Based on Tangent or Secant Case
This refers to how the projection surface intersects with the reference globe or ellipsoid.
- Tangent Projections: The projection surface touches the globe at a single point (for azimuthal projections) or along a line (for cylindrical and conical projections). Distortion is minimal at the point or line of tangency and increases with distance from it.
- Secant Projections: The projection surface intersects the globe. For conical and cylindrical projections, the surface cuts into the globe, resulting in two lines of intersection (standard lines). For azimuthal projections, a secant case is less common. Secant projections have reduced overall distortion compared to tangent projections because distortion is spread out between the standard lines, and there are areas of “under-projection” and “over-projection” that partially compensate for each other.
- Non-Tangent and Non-Secant Projections: These are more complex mathematical projections that do not rely on simple geometric tangency or secancy. They are designed to optimize specific properties or minimize overall distortion in more sophisticated ways.
The selection of a map projection is crucial and depends heavily on:
- Purpose and Required Accuracy of the Map: What the map will be used for dictates which properties are most important to preserve.
- Geographic Location, Shape, and Extent of the Area to be Mapped: The region’s location and shape influence which projection type is most suitable. For example, polar regions are best represented with azimuthal projections, while mid-latitude zones might be better suited for conical projections.
- Characteristics to be Maintained: Whether shape, area, distance, or direction is most critical for the map’s intended use guides the choice of projection type.
Understanding the different types of map projections and their inherent distortions is essential for anyone working with maps, ensuring that the chosen projection is appropriate for the intended application and interpretation of spatial data.
