Werner projection

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Werner projection of the world Werner projection SW.jpg
Werner projection of the world
Woodcut Werner projection from 1536 Map-heart-054.jpg
Woodcut Werner projection from 1536

The Werner projection is a pseudoconic equal-area map projection sometimes called the Stab-Werner or Stabius-Werner projection. Like other heart-shaped projections, it is also categorized as cordiform. Stab-Werner refers to two originators: Johannes Werner (14661528), a parish priest in Nuremberg, refined and promoted this projection that had been developed earlier by Johannes Stabius (Stab) of Vienna around 1500.

Map projection Systematic representation of the surface of a sphere or ellipsoid onto a plane

A map projection is a way to "flatten" a globe's surface into a plane in order to make a map. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane.

Heart (symbol) symbol representing the heart

The heart shape is an ideograph used to express the idea of the "heart" in its metaphorical or symbolic sense as the center of emotion, including affection and love, especially romantic love.

Johannes Werner German mathematician

Johann(es) Werner was a German mathematician. He was born in Nuremberg, Germany, where he became a parish priest. His primary work was in astronomy, mathematics, and geography, although he was also considered a skilled instrument maker.

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The projection is a limiting form of the Bonne projection, having its standard parallel at one of the poles (90°N/S). [1] [2] Distances along each parallel and along the central meridian are correct, as are all distances from the north pole.

Bonne projection map projection

The Bonne projection is a pseudoconical equal-area map projection, sometimes called a dépôt de la guerre, modified Flamsteed, or a Sylvanus projection. Although named after Rigobert Bonne (1727–1795), the projection was in use prior to his birth, in 1511 by Sylvano, Honter in 1561, De l'Isle before 1700 and Coronelli in 1696. Both Sylvano and Honter’s usages were approximate, however, and it is not clear they intended to be the same projection.

See also

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Mercator projection Map projection for navigational use that distorts areas far from the equator

The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because of its unique property of representing any course of constant bearing as a straight segment. Such a course, known as a rhumb or, mathematically, a loxodrome, is preferred by navigators because the ship can sail in a constant compass direction to reach its destination, eliminating difficult and error-prone course corrections. Linear scale is constant on the Mercator in every direction around any point, thus preserving the angles and the shapes of small objects and fulfilling the conditions of a conformal map projection. As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation starts infinitesimally, but accelerates with latitude to become infinite at the poles. So, for example, landmasses such as Greenland and Antarctica appear far larger than they actually are relative to landmasses near the equator, such as Central Africa.

Geographic coordinate system Coordinate system

A geographic coordinate system is a coordinate system that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are often chosen such that one of the numbers represents a vertical position and two or three of the numbers represent a horizontal position; alternatively, a geographic position may be expressed in a combined three-dimensional Cartesian vector. A common choice of coordinates is latitude, longitude and elevation. To specify a location on a plane requires a map projection.

Circle of latitude Geographic notion

A circle of latitude on Earth is an abstract east–west circle connecting all locations around Earth at a given latitude.

Rhumb line arc crossing all meridians of longitude at the same angle

In navigation, a rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true or magnetic north.

Robinson projection compromise map projection defined via a look-up table of precomputed values

The Robinson projection is a map projection of a world map which shows the entire world at once. It was specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image.

Orthographic projection in cartography map projection of cartography

The use of orthographic projection in cartography dates back to antiquity. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective projection, in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic projection is at infinite distance. It depicts a hemisphere of the globe as it appears from outer space, where the horizon is a great circle. The shapes and areas are distorted, particularly near the edges.

Azimuthal equidistant projection azimuthal map projection

The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection.

Gnomonic projection map projection

A gnomonic map projection displays all great circles as straight lines, resulting in any straight line segment on a gnomonic map showing a geodesic, the shortest route between the segment's two endpoints. This is achieved by casting surface points of the sphere onto a tangent plane, each landing where a ray from the center of the sphere passes through the point on the surface and then on to the plane. No distortion occurs at the tangent point, but distortion increases rapidly away from it. Less than half of the sphere can be projected onto a finite map. Consequently, a rectilinear photographic lens, which is based on the gnomonic principle, cannot image more than 180 degrees.

The scale of a map is the ratio of a distance on the map to the corresponding distance on the ground. This simple concept is complicated by the curvature of the Earth's surface, which forces scale to vary across a map. Because of this variation, the concept of scale becomes meaningful in two distinct ways.

Sinusoidal projection pseudocylindrical equal-area map projection

The sinusoidal projection is a pseudocylindrical equal-area map projection, sometimes called the Sanson–Flamsteed or the Mercator equal-area projection. Jean Cossin of Dieppe was one of the first mapmakers to use the sinusoidal, appearing in a world map of 1570.

Lambert cylindrical equal-area projection

In cartography, the Lambert cylindrical equal-area projection, or Lambert cylindrical projection, is a cylindrical equal-area projection. This projection is undistorted along the equator, which is its standard parallel, but distortion increases rapidly towards the poles. Like any cylindrical projection, it stretches parallels increasingly away from the equator. The poles accrue infinite distortion, becoming lines instead of points.

Johannes Stabius (1450–1522) was an Austrian cartographer of Vienna who developed, around 1500, the heart-shape (cordiform) projection map later developed further by Johannes Werner. It is called the Werner map projection, but also the Stabius-Werner or the Stab-Werner projection.

Werner may refer to:

Cylindrical equal-area projection

In cartography, the cylindrical equal-area projection is a family of cylindrical, equal-area map projections.

Loximuthal projection

In cartography, the loximuthal projection is a map projection introduced by Karl Siemon in 1935, and independently in 1966 by Waldo R. Tobler, who named it. It is characterized by the fact that loxodromes from one chosen central point are shown straight lines, correct in azimuth from the center, and are "true to scale" in the sense that distances measured along such lines are proportional to lengths of the corresponding rhumb lines on the surface of the earth. It is neither an equal-area projection nor conformal.

References

  1. Snyder, John P (1993), Flattening the Earth: Two Thousand Years of Map Projections, pp. 60–2, ISBN   0-226-76747-7 .
  2. (1987), "Map Projections—A Working Manual", Professional Paper, United States Geological Survey, pp. 138–0.