What Is Gnomonic Projection?

A gnomonic map projection is a map projection that depicts all great circles as straight lines, with any straight-line segment on a gnomonic map displaying a geodesic, the shortest route between the segment’s two endpoints.

This is accomplished by projecting spherical surface points onto a tangent plane, with each landing where a ray from the sphere’s center passes through the point on the surface and subsequently onto the plane.

There is no distortion at the tangent point, but it increases fast away from it. A finite map can only fit less than half of the sphere. As a result, a rectilinear photographic lens based on the gnomonic principle can only image 180 degrees.

History

Thales devised the gnomonic projection in the sixth century BC, and it is said to be the oldest map projection. In a nodus-based sundial, the path of the shadow-tip or light-spot follows the same hyperbolae generated by parallels on a gnomonic map.

Projection Properties

The gnomonic projection qualities are described in the subsections below.

Graticule

An azimuthal projection is gnomonic. The meridians project as straight lines originating at the pole in the polar aspect. Angles between meridians are correct.

The parallels are made out of unequally spaced concentric circles. Their distance from the pole increases rapidly. The equator cannot be depicted in a polar orientation.

The meridians appear as straight vertical lines in the equatorial perspective. Their spacing widens as one moves away from the central meridian.

The equator is depicted as a straight line parallel to the meridians. Another type of parallel is a convex curve that bends away from the equator. Neither pole is visible. All great circles, regardless of their aspect, project as straight lines.

Distortion

The conformal and equal-area properties of the gnomonic projection are not present. The aberrations in shape, area, and distance increase as one move away from the center.

Within a 30° radius of the center, there is significant distortion. Only at the center of the projection are directions and angles exact.

Variants

In ArcGIS, there are three options. The sphere-based Earth models are correctly supported by all three variations.

ArcGIS Pro 1.0 and later, as well as ArcGIS Desktop 9.3 and later, support the gnomonic variety. The radius is calculated using the semimajor axis.

ArcGIS Pro 1.0 and later, as well as ArcGIS Desktop 9.3 and later, support the gnomonic auxiliary sphere variant. The sphere supplied by the Auxiliary Sphere Type option is used in this variation.

ArcGIS Pro 1.2 and later, as well as ArcGIS Desktop 10.4 and later, support the gnomonic ellipsoidal variation. This is the only form of the three that appropriately supports ellipsoidal projection.

Usage

Because seismic waves tend to move in large circles, gnomonic projections are used in seismic work. Because radio signals travel in large circles, they are also employed by warships to plot direction finding bearings.

Meteors also travel in large circles, with the IMO’s suggested set of star charts for visual meteor observations being the Gnomonic Atlas Brno 2000.0.

Pilots of aircraft and ships use the projection to determine the shortest path between their starting point and their destination.

The gnomonic projection is widely employed in photography, where it is referred to as rectilinear projection.

Because they are equal, the same viewer that is used to produce photographic panoramas can also be used to render gnomonic maps (view as a 360° interactive panorama).

In astronomy, the gnomonic projection is utilized when the tangent point is centered on the object of interest.

The sphere being projected in this example is the celestial sphere, R = 1, rather than the Earth’s surface.

Parameters

Gnomonic parameters are as follows:

• False Northing
• Longitude of the Center
• Center’s Latitude
• False Easting

The following are the Gnomonic auxiliary sphere parameters:

• False Northing
• Longitude of Center
• Center’s Latitude
• False Easting

Gnomonic chart

Based on the gnomonic projection, this map is highly useful in great circle sailing. This is a perspective projection in which a portion of a spherical surface is projected from the sphere’s center onto a plane surface tangential to the surface of the sphere.

This projection’s main feature is that large circular arcs are projected as straight lines.

To draw a great circle on a Mercator chart—the projection being a somewhat complex curve that is always concave to the equator—the route is first drawn on a gnomonic chart by linking the plotted coordinates of departure and destination with a straight line.

The Mercator chart is used to identify the positions of a succession of points on this line that are taken from the gnomonic chart. The needed projection of the great circle route on the Mercator chart is then constructed by drawing a fair curve across these spots.

Hugh Godfray’s 1858 publication of two polar gnomonic maps covering the greater part of the planet, one for the northern and one for the southern hemispheres, popularized the gnomonic chart.

Although it was widely assumed that Godfray invented this method of great circle sailing, it is worth noting that a complete explanation of the construction of a polar gnomonic chart, along with a detailed example of a great circle route from the Lizard to the Bermudas, appeared in Samuel Sturmey’s Mariners’ Mirror in 1669.

Limitations of Gnomonic projection

The gnomonic projection is constrained by its perspective point and cannot project a line 90° or more from the center point. This means that neither the equatorial nor polar aspects can project the equator. More than one-third of the earth should not be mapped using this projection.

The gnomonic projection is not useful for mapping most large land masses on the globe.

It fails to accurately portray small scale topographic features such as lakes, volcanoes, and many other smaller features.

It is a bit heavy when printed on paper due to the use of several types of lines (line segments and arcs) in order to describe the curved surface of the earth.

The gnomonic projection cannot be used for accurate maps of major cities in mountainous regions where the Mercator is preferred.

Advantages of Gnomonic projection

Since the gnomonic projection presents all parallel lines as straight, it is a very simple method of drawing a map.

Gnomonic maps are usually affordable to print.

They have an angular orientation and thus can be used as providing a lay-flat perspective display. This makes them supremely appropriate for wall maps or for recreating large three-dimensional scenes in miniature models or dioramas.

Gnomic’s superior ability to depict topography allows it to be used for high quality photo mapping.

Topographic data can be rendered in a more accurate and detailed form with gnomonic maps than with most others.

Summary

The gnomonic projection is a perspective, equal-area map projection. It draws parallels and meridians as straight lines radiating from the center of the map.

The projection’s name is derived from the Greek word for “Earth.” This perspective projection has numerous applications, particularly in aerial photography and ocean navigation.

The gnomonic projection has been used for centuries to draw maps of the Earth’s surface, with longitude being represented as an angular measurement from a central meridian.

The projection was used to chart the islands of the southern hemisphere by Captain William Bligh, and it is still used today by mariners to plot great circle routes on a Mercator chart.

In the future, this map may be used more widely in location-based services and tourism, as the smartphone technology enables easy capture of GPS, then geotagging.

The gnomonic projection is heavily employed in photography where it is referred to as rectilinear projection.

FAQs

What is Gnomonic projection?

A gnomonic map projection is a map projection that depicts all great circles as straight lines, with any straight-line segment on a gnomonic map displaying a geodesic, the shortest route between the segment’s two endpoints.

What is a gnomonic projection used for?

The gnomonic projection is suited for navigational charts at enormous scales, displaying less than one-sixth of the earth. It has been used to create global globes using polyhedral mapping.

What do Gnomonic projections preserve?

The gnomonic map projection depicts all large circles as straight lines. In other terms, it observes surface data from the center of the Earth. As a result, the shortest route between two points in reality matches to the shortest route on the map.

What is zenithal gnomonic projection?

A zenithal gnomonic polar projection is one in which the light source is at the center of the projecting globe and the tangent plane touches either of the two poles. The parallels of latitude are concentric rings.

The meridians of longitude are straight lines extending from the center.

What is the difference between Mercator and Gnomonic projections?

Mercator projection maps are useful in navigation because they can mark any location on the globe. The gnomonic projection puts points from a globe onto a piece of paper that touches the globe at a single location.

These projections are used to map small areas. They are frequently used for road and weather maps.

How many gnomonic charts are there?

There are fifteen charts available covering the world’s oceans: North Atlantic, South Atlantic, North Pacific, South Pacific, and Indian Ocean.

Is a gnomonic projection the same as a topographic map?

A gnomonic projection is created by projecting points and lines from a globe onto a sheet of paper that contacts the globe at a single location. Topographic maps depict changes in height of the Earth’s surface.

What best describes a gnomonic chart?

Based on the gnomonic projection, this map is highly useful in great circle sailing. This is a perspective projection in which a portion of a spherical surface is projected from the sphere’s center onto a plane surface tangential to the surface of the sphere.

What are the advantages and disadvantages of gnomonic projection?

Advantages- The latitude and longitude show as a grid, making it simple to pinpoint spots with a ruler; it is extremely accurate at the equator. Disadvantages- At the poles, distances between regions and their areas are altered. What exactly is a gnomonic projection?

What does the Homolosine projection show best?

The Goode homolosine projection (or interrupted Goode homolosine projection) is a globe map projection that is pseudo cylindrical, equal-area, and composite. Because of its equal-area characteristic, it is excellent for presenting the spatial distribution of phenomena.

When was gnomonic projection invented?

Thales devised the gnomonic projection in the sixth century BC, and it is said to be the oldest map projection. In a nodus-based sundial, the path of the shadow-tip or light-spot follows the same hyperbolae generated by parallels on a gnomonic map.

What is the difference between a gnomonic chart and Mercator chart?

Lines of longitude and latitude are parallel on a Mercator projection chart. Meridians converge and lines of latitude are curved on gnomonic projection charts. A rhumb line course of 040° crosses each meridian (line of longitude) at the same angle.

What is gnomonic chart with sample?

In passage planning, Gnomonic Charts are used to draw big circle routes as straight lines. All great circles are represented as straight lines using a gnomonic map projection, resulting in each line segment on a gnomonic map showing the shortest route between the segment’s two endpoints.

What are routeing charts?

Routeing Charts are essential for ocean trip passage planning since they feature routes and distances between key ports, ocean currents, ice limitations, load lines, and wind roses. They also include forecasts for meteorological and oceanic conditions for each month of the year.

Which map projection is the most accurate?

AuthaGraph. This is without a doubt the most accurate map projection available. In fact, the AuthaGraph World Map is so perfectly proportioned that it suddenly folds into a three-dimensional world.

Hajime Narukawa, a Japanese architect, invented this projection in 1999 by evenly splitting a spherical surface into 96 triangles.

What is the most widely used projection in marine navigation?

The Mercator projection, invented in 1569 by a Flemish cartographer and geographer named Geradus Mercator, is one of the most well-known map projections. Because of its capacity to portray lines of continuous true direction, it became the standard map projection for nautical purposes.

What are disadvantages of azimuthal projections?

The entire Earth cannot be represented by a perspective azimuthal projection. If you need to have a map of the complete world, then a perspective-based azimuthal projection cannot produce a usable conclusion.

What does the orthographic projection preserve?

This is a perspective projection of the globe onto a tangent plane from an infinite distance (i.e., orthogonally); consequently, the map has the appearance of a globe.

Orthographic projections are highly popular for local regions, such as the region surrounding a city, when scale and relative appearance must be kept.

What is a Mollweide projection map?

The Mollweide projection is an equal-area pseudo cylindrical map projection that depicts the world as an ellipse with axes in a 2:1 ratio. It is also known as a Babinet, elliptical, homolographic, or homalographic projection. Karl B. Mollweide was the first to mention Mollweide.