What is Gnomonic Projection?

Information about Gnomonic Projection

Examples of gnomonic projections.


The gnomonic map projection displays all great circles as straight lines.

Thus the shortest route between two locations in reality corresponds to that on the map. This is achieved by projecting, with respect to the center of the Earth (hence perpendicular to the surface), the Earth's surface onto a tangent plane. The least distortion occurs at the tangent point. Less than half of the sphere can be projected onto a finite map.

Since Meridians and the Equator are great circles, they are always shown as straight lines.
  • If the tangent point is one of the Poles then the meridians are radial and equally spaced. The equator is at infinity in all directions. Other parallels are depicted as concentric circles.
  • If the tangent point is on the equator then the meridians are parallel but not equally spaced. The equator is a straight line perpendicular to the meridians. Other parallels are depicted as hyperbolae.
  • In other cases the meridians are radially outward straight lines from a Pole, but not equally spaced. The equator is a straight line that is perpendicular to only one meridian (which again demonstrates that the projection is not conformal).
As for all azimuthal projections, angles from the tangent point are preserved. The map distance from that point is a function r(d) of the true distance d, given by



where R is the radius of the Earth. The radial scale is



and the transverse scale



so the transverse scale increases outwardly, and the radial scale even more.

The gnomonic projection is said to be the oldest map projection, developed by Thales in the 6th century BC.

Gnomonic projections are used in seismic work because seismic waves tend to travel along great circles. They are also used by navies in plotting direction finding bearings, since radio signals travel along great circles.

External links

References

Snyder, John P. (1987). Map Projections - A Working Manual. U.S. Geological Survey Professional Paper 1395. United States Government Printing Office, Washington, D.C..  This paper can be downloaded from USGS pages
Views
Graphical projections
  • Perspective projection
  • Parallel projection
  • Orthographic projection
  • Plan, or floor plan view
  • Section

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  • Great circle is a circle on the surface of a sphere.
  • Great Circle is also a fictional organization from Andromeda Nebula, a novel by Ivan Yefremov
A great circle
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MAP may refer to:
  • MAP, the ISO 639 alpha-3 for Austronesian languages
  • MAP (band), an indie band from Riverside, California
  • Maghreb Arab Press, the official Moroccan news agency
  • Malawi Against Polio

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EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001. Their greatest hit, their debut single "time after time", peaked at #13 in the Oricon singles chart.
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tangent has two distinct but etymologically-related meanings: one in geometry and one in trigonometry.

Geometry

In plane geometry, a line is tangent to a curve, at some point, if both line and curve pass through the point with the oppsite direction.
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A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface. In mathematics, a sphere is the set of all points in three-dimensional space (R3
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equator is an imaginary line on the Earth's surface equidistant from the North Pole and South Pole. It thus divides the Earth into a Northern Hemisphere and a Southern Hemisphere. The equators of other planets and astronomical bodies are defined analogously.
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Polish people, or Poles, (Polish: Polacy) are a western Slavic ethnic group of Central Europe, living predominantly in Poland. Poles are sometimes defined as people who share a common Polish culture and are of Polish descent.
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The word infinity comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end") which arise in philosophy, mathematics, and theology.
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Parallels may refer to:
  • Parallels (album), an album by progressive metal band Fates Warning
  • Parallels (solitaire), a solitaire card game which is played with two decks of playing cards
  • "Parallels" (TNG episode), an episode of

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circle is the set of all points in a plane at a fixed distance, called the radius, from a given point, the centre.

Circles are simple closed curves which divide the plane into an interior and exterior.
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hyperbola (Greek ὑπερβολή literally 'overshooting' or 'excess') is a type of conic section defined as the intersection between a right circular conical surface and a plane which cuts through both halves
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conformal map is a function which preserves angles.

More formally, a map

w = f(z)


is called conformal (or angle-preserving) at z0
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This article has been tagged since June 2007.
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Transverse may refer to:
  • Transversality, a concept related to the intersection of manifolds in topology
  • Transverse City, an album by Warren Zevon

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Thales of Miletos (Θαλῆς ὁ Μιλήσιος, ca. 624 BC–ca. 546 BC), was a pre-Socratic Milesian[] philosopher and one of the Seven Sages of Greece.
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The 6th century BC started the first day of 600 BC and ended the last day of 501 BC.

Overview

In the Near East, the first half of this century was dominated by the Neo Babylonian or Chaldean
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Seismology (from the Greek seismos = earthquake and λόγος,logos = knowledge ) is the scientific study of earthquakes and the propagation of elastic waves through the Earth.
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navy is the branch of a country's military forces principally designated for naval warfare and amphibious warfare (marines) namely lake- or ocean-borne combat operations and related functions.
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Direction finding (DF) refers to the establishment of the direction from which a received signal was transmitted. This can refer to radio or other forms of wireless communication.
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Radio is the wireless transmission of signals, by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space.
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