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The shortest point between two points on Earth is called a great circle route. Unlike rhumb lines, such lines appear curved on a conformal projection (Figure 5.5.4). Of course, the literal shortest path from Providence to Rome is actually a straight line: but you'd have to travel beneath Earth's surface to travel it. When we talk about the ...
Sep 10, 2024 · Here’s why: Geodesics on a Sphere: A great circle is the largest possible circle that can be drawn on a sphere, where the circle’s center is also the center of the sphere. This makes great circles the geodesic or “straight line” path in spherical geometry. Shortest Path: On a flat surface (Euclidean geometry), the shortest distance ...
a. Shape. A projection that maintains shape is ‘conformal’. For example a 2x2 square becomes a 1x1 or 4x4 square. Stretching in one direction is matched by stretching in the other: that is, the scale factors are equal at a point in the two directions (i.e. there is 'equal-stretching'). Circles (“Tissot’s Indicatrix”) ->.
Now the straight line is the great circle, and the curved one is the loxodrome. These lines are the same as in the Mercator above, but the projection changes their appearance. When a projection preserves great circle routes as straight lines, we call it an azimuthal projection. Unfortunately, much like the equidistant projections, it only works ...
A gnomonic projection, also known as a central projection or rectilinear projection, is a perspective projection of a sphere, with center of projection at the sphere's center, onto any plane not passing through the center, most commonly a tangent plane. Under gnomonic projection every great circle on the sphere is projected to a straight line ...
These projections preserve the direction from a single point, with all straight lines drawn from the center of the map representing a great circle route. Key point: all azimuthal map projections are planar, but not all planar projections are azimuthal. Azimuthal projections preserve angles from a standard point across the entire globe.
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Can a projection preserve great circle routes as straight lines?
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Why do we need a map projection?
The Gnomonic projection is another member of the azimuthal projection family (maps projected to a plane surface that is tangent to the globe at a single point), and it has the distinction of being the only map projection on which any straight line represents a great-circle arc. Whereas on the Azimuthal Equidistant projection only straight lines that originate at the map's central point show ...
