2D Map Projections: Mercator vs Mollweide vs Orthographic |…

What are Map Projections?

Map projections are mathematical functions that transform the spherical Earth onto a flat surface. This transformation is necessary for creating maps but introduces distortions in area, shape, distance, or direction.

The choice of projection depends on the purpose of the map and the region it covers.

Mercator Projection

Developed by Gerardus Mercator in 1569, this cylindrical projection is widely used for navigation because it preserves angles and shapes locally. However, it distorts areas near the poles.

The formula for the Mercator projection is given by: x = λ - λ₀; y = ln(tan(π/4 + φ/2)), where λ is longitude, φ is latitude, and λ₀ is the central meridian.

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Mollweide Projection

Invented by Karl B. Mollweide in 1805, this equal-area projection minimizes area distortion at the expense of shape accuracy, especially near the poles.

The formula for the Mollweide projection is: x = 2 * sqrt(2) * λ / π * cos(φ); y = sqrt(2) * sin(φ), where φ and λ are latitude and longitude respectively.

Orthographic Projection

This perspective projection represents the Earth as if viewed from an infinite distance, making it useful for visualizing globes or celestial bodies. It preserves angles but distorts areas and shapes.

The formula for orthographic projection is: x = 2 * R * cos(φ) * cos(λ); y = 2 * R * cos(φ) * sin(λ), where φ and λ are latitude and longitude, and R is the radius of the Earth.

Frequently asked questions

Why do different projections exist?

Different projections serve various purposes. Some preserve angles (like Mercator), others minimize area distortion (like Mollweide), while some are best for visualizing spherical surfaces (like Orthographic).

Which projection is best for navigation?

The Mercator projection is ideal for navigation because it preserves local angles and shapes, making it easier to plot courses on a map.

How does the Mollweide projection handle area distortion?

Mollweide's equal-area property ensures that areas are accurately represented relative to each other, though shapes near the poles become distorted.

What is the main use of Orthographic projections?

Orthographic projections are used for visualizing globes and celestial bodies because they provide a realistic perspective view from an infinite distance.

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