Miller cylindrical projection
The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 4⁄5, projected according to Mercator, the result is multiplied by 5⁄4 to retain scale along the equator. Hence: x = λ y = 5 4 ln = 5 4 sinh − 1 or inversely, λ = x φ = 5 2 tan − 1 e 4 y 5 − 5 π 8 = 5 4 tan − 1 where λ is the longitude from the central meridian of the projection, φ is the latitude. Meridians are thus about 0.733 the length of the equator. In GIS applications, this projection is known as: "ESRI:54003 - World Miller Cylindrical"Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees. List of map projections Math formulae information Historical information Miller projection in proj4
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, its standard parallel, but distortion increases towards the poles. Like any cylindrical projection, it stretches parallels away from the equator; the poles accrue infinite distortion. The projection was invented by the Swiss mathematician Johann Heinrich Lambert and described in his 1772 treatise, Beiträge zum Gebrauche der Mathematik und deren Anwendung, part III, section 6: Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten, translated as, Notes and Comments on the Composition of Terrestrial and Celestial Maps. Lambert's projection is the basis for the cylindrical equal-area projection family. Lambert chose the equator as the parallel of no distortion. By multiplying the projection's height by some factor and dividing the width by the same factor, the regions of no distortion can be moved to any desired pair of parallels north and south of the equator.
These variations the Gall–Peters projection, are more encountered in maps than Lambert’s original projection due to their lower distortion overall. X = λ − λ 0 y = sin φ where φ is the latitude, λ is the longitude and λ0 is the central meridian. List of map projections Lambert azimuthal equal-area projection Lambert conformal conic projection Media related to Lambert cylindrical equal-area projection at Wikimedia Commons Table of examples and properties of all common projections, from radicalcartography.net An interactive Java Applet to study the metric deformations of the Lambert Cylindrical Equal-Area Projection
Equirectangular projection
The equirectangular projection is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100. The projection maps meridians to vertical straight lines of constant spacing, circles of latitude to horizontal straight lines of constant spacing; the projection is neither equal area nor conformal. Because of the distortions introduced by this projection, it has little use in navigation or cadastral mapping and finds its main use in thematic mapping. In particular, the plate carrée has become a standard for global raster datasets, such as Celestia and NASA World Wind, because of the simple relationship between the position of an image pixel on the map and its corresponding geographic location on Earth; the forward projection transforms. The reverse projection transforms from the plane back onto the sphere; the formulae presume a spherical model and use these definitions: λ is the longitude of the location to project. X = cos φ 1 y = The plate carrée, is the special case.
This projection maps x to be the value of the longitude and y to be the value of the latitude, therefore is sometimes called the latitude/longitude or lat/lon projection or is said to be “unprojected”. While a projection with spaced parallels is possible for an ellipsoidal model, it would no longer be equidistant because the distance between parallels on an ellipsoid is not constant. More complex formulae can be used to create an equidistant map whose parallels reflect the true spacing. Λ = x cos φ 1 + λ 0 φ = y + φ 1 List of map projections Cartography Cassini projection Gall–Peters projection with resolution regarding the use of rectangular world maps Mercator projection Spherical image projection Global MODIS based satellite map The blue marble: land surface, ocean color and sea ice. Table of examples and properties of all common projections, from radicalcartography.net. Panoramic Equirectangular Projection, PanoTools wiki. Equidistant Cylindrical in proj4
Lambert azimuthal equal-area projection
The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk. It represents area in all regions of the sphere, but it does not represent angles, it is named for the Swiss mathematician Johann Heinrich Lambert, who announced it in 1772. "Zenithal" being synonymous with "azimuthal", the projection is known as the Lambert zenithal equal-area projection. The Lambert azimuthal projection is used as a map projection in cartography. For example, the National Atlas of the US uses a Lambert azimuthal equal-area projection to display information in the online Map Maker application, the European Environment Agency recommends its usage for European mapping for statistical analysis and display, it is used in scientific disciplines such as geology for plotting the orientations of lines in three-dimensional space. This plotting is aided by a special kind of graph paper called a Schmidt net. To define the Lambert azimuthal projection, imagine a plane set tangent to the sphere at some point S on the sphere.
Let P be any point on the sphere other than the antipode of S. Let d be the distance between S and P in three-dimensional space; the projection sends P to a point P′ on the plane, a distance d from S. To make this more precise, there is a unique circle centered at S, passing through P, perpendicular to the plane, it intersects the plane in two points. This is the projected point. See the figure; the antipode of S is excluded from the projection. The case of S is degenerate. Explicit formulas are required for carrying out the projection on a computer. Consider the projection centered at S = on the unit sphere, the set of points in three-dimensional space R3 such that x2 + y2 + z2 = 1. In Cartesian coordinates on the sphere and on the plane, the projection and its inverse are described by =, =. In spherical coordinates on the sphere and polar coordinates on the disk, the map and its inverse are given by =, =. In cylindrical coordinates on the sphere and polar coordinates on the plane, the map and its inverse are given by =, = ( R 1 − R 2 4, Θ, − 1 + R 2 2
Lambert conformal conic projection
A Lambert conformal conic projection is a conic map projection used for aeronautical charts, portions of the State Plane Coordinate System, many national and regional mapping systems. It is one of seven projections introduced by Johann Heinrich Lambert in his 1772 publication Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten. Conceptually, the projection seats a cone over the sphere of the Earth and projects the surface conformally onto the cone; the cone is unrolled, the parallel, touching the sphere is assigned unit scale. That parallel is called standard parallel. By scaling the resulting map, two parallels can be assigned unit scale, with scale decreasing between the two parallels and increasing outside them; this gives the map two standard parallels. In this way, deviation from unit scale can be minimized within a region of interest that lies between the two standard parallels. Unlike other conic projections, no true secant form of the projection exists because using a secant cone does not yield the same scale along both standard parallels.
Pilots use aeronautical charts based on LCC because a straight line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints for typical flight distances. The US systems of VFR sectional charts and terminal area charts are drafted on the LCC with standard parallels at 33°N and 45°N; the European Environment Agency and the INSPIRE specification for coordinate systems recommends using this projection for conformal pan-European mapping at scales smaller or equal to 1:500,000. In Metropolitan France, the official projection is Lambert-93, a Lambert conic projection using RGF93 geodetic system and defined by references parallels that are 44°N and 49°N; the National Spatial Framework for India uses Datum WGS84 with a LCC projection and is a recommended NNRMS standard. Each state has its own set of reference parameters given in the standard; the U. S. National Geodetic Survey's "State Plane Coordinate System of 1983" uses the Lambert conformal conic projection to define the grid-coordinate systems used in several states those that are elongated west to east such as Tennessee.
The Lambert projection is easy to use: conversions from geodetic to State Plane Grid coordinates involve trigonometric equations that are straightforward and which can be solved on most scientific calculators programmable models. The projection as used in CCS83 yields maps in which scale errors are limited to 1 part in 10,000; the Lambert conformal conic is one of several map projection systems developed by Johann Heinrich Lambert, an 18th-century Swiss mathematician, physicist and astronomer. Coordinates from a spherical datum can be transformed into Lambert conformal conic projection coordinates with the following formulas, where λ is the longitude, λ0 the reference longitude, φ the latitude, φ0 the reference latitude, φ1 and φ2 the standard parallels: x = ρ sin y = ρ 0 − ρ cos where n = ln ln ρ = F cot n ρ 0 = F cot n ( 1 4 π + 1
James Gall
Rev James Gall was a Scottish clergyman who founded the Carrubbers Close Mission. A remarkable man, he was a cartographer, sculptor and author. In cartography he gives his name to three different map projections: Gall Stereographic, he was born on 27 September 1808, the son of James Gall, a printer who founded the printing company of Gall & Inglis in Edinburgh, which specialised in easy-access astronomy. His mother was Ann Collie, his uncle, John Gall, ran a coach-building business. He was baptised at St Cuthbert's Church, Edinburgh on 15 October 1808. James Gall lived with his family at Potterrow on the South Side of Edinburgh. James was educated at the High School close at the Trustees Academy, he was apprenticed as a printer in his father's firm from 1822 before studying at Edinburgh University. From 1838 he became a partner in his father's publishing firm. Late in life, in 1849, aged 41, he decided to retrain as a Free Church minister and studied at New College, Edinburgh graduating in 1855, his first role was in the establishment of a mission at Carrubbers Close on the Royal Mile.
At this time James was still a partner in Inglis. He was living at Myrtle Bank in Edinburgh. In 1858 he was chosen to minister at the new Free Church in the Canongate, holding the overspill from the growing mission work at Carrubbers Close; this held services in a hall at Moray House until a building was completed in 1862. This stood on Holyrood Road on the Site now occupied by the main Moray College building, it was named the Moray Free Church. He lived adjacent to the church at 10 St John Street, he resigned from the church in 1872 to concentrate on mission work. His place at the Moray Church was filled by Rev Walter Glendinning, he lost his manse at John Street as a result of this decision, lived for a while thereafter at a flat at 47 Forrest Road. He died at home, 35 Newington Road in Edinburgh on 7 February 1895, he is buried in the north-east section of Grange Cemetery in Edinburgh, nearby his father. His funeral was attended by over 600 of his many admirers. Most of Gall's work on religion was detailed in a book called The Stars and the Angels, in which he not only argues for the existence of other inhabited planets, but describes the view that Gabriel would have had on his way from heaven to earth to tell Mary that she would have a baby next Christmas.
A rare, but important, work by Gall is The Synagogue Not the Temple, the Germ and Model of the Christian Church, published in 1890. It discusses the foundation upon. Gall's main work as an astronomer was with the constellations; as part of this work he developed the Gall orthographic projection, a derivative of the Lambert cylindrical equal-area projection, to project the celestial sphere onto flat paper in a manner that avoided distorting the shapes of the constellations. He applied this technique to terrestrial mapmaking as a way to make a flat map of the round Earth. Gall Orthographic was re-invented by Arno Peters in 1967 and adopted by organisations such as UNESCO. In recognition of both men the form is now called the Gall-Peters projection. Gall himself was an advocate of accessible mapping for blind people. One format he suggested was to combine Braille printing with twine to indicate lines. An 1851 book included such a map by his partner Inglis, it used raised borders to indicate other features.
Easy Guide to the Constellations People's Atlas of the Stars Handbook to Astronomy Use of Cylindrical Projections for Geographical and Scientific Purposes Anthropology of the Bible The Science of Missions The Synagogue as the Model of the Christian Church Catechism of Christian Baptism Dipping not Baptism Evangelistic Baptism Good Friday: A Chronological Mistake Home Missions: The People's Work Revival of Pentecostal Christianity Where the Morisonians Are Wrong Gall's father, James Gall, designed a "triangular alphabet" used for embossed books for blind people and was instrumental.in founding the Royal Blind School in Edinburgh. He was the principal creator of the Scottish Sunday School system. In 1833 Gall married Mary Campbell from Belfast, their eldest son, James Gall became a businessman in Jamaica. Their daughter, Elizabeth Walkingshaw Gall, married Robert Inglis, the son of James Gall's business partner, who inherited the printing company of Gall & Inglis on James's death. Robert's son, James Gall Inglis FRSE was a keen astronomer and came to the firm in 1880.
He is buried with James Gall. Anna Gall died a spinster. Astronomical Publishing in Edinburgh in the 19th Century Carrubbers Close Mission History at carrubbers.org James P. Snyder, Map Projections—A Working Manual: U. S. Geological Survey Professional Paper 1395, Washington: Government Printing Office
Cartography
Cartography is the study and practice of making maps. Combining science and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively; the fundamental problems of traditional cartography are to: Set the map's agenda and select traits of the object to be mapped. This is the concern of map editing. Traits may be physical, such as roads or land masses, or may be abstract, such as toponyms or political boundaries. Represent the terrain of the mapped object on flat media; this is the concern of map projections. Eliminate characteristics of the mapped object that are not relevant to the map's purpose; this is the concern of generalization. Reduce the complexity of the characteristics that will be mapped; this is the concern of generalization. Orchestrate the elements of the map to best convey its message to its audience; this is the concern of map design. Modern cartography constitutes many theoretical and practical foundations of geographic information systems.
What is the earliest known map is a matter of some debate, both because the term "map" is not well-defined and because some artifacts that might be maps might be something else. A wall painting that might depict the ancient Anatolian city of Çatalhöyük has been dated to the late 7th millennium BCE. Among the prehistoric alpine rock carvings of Mount Bego and Valcamonica, dated to the 4th millennium BCE, geometric patterns consisting of dotted rectangles and lines are interpreted in archaeological literature as a depiction of cultivated plots. Other known maps of the ancient world include the Minoan "House of the Admiral" wall painting from c. 1600 BCE, showing a seaside community in an oblique perspective, an engraved map of the holy Babylonian city of Nippur, from the Kassite period. The oldest surviving world maps are from 9th century BCE Babylonia. One shows Babylon on the Euphrates, surrounded by Assyria and several cities, all, in turn, surrounded by a "bitter river". Another depicts Babylon as being north of the center of the world.
The ancient Greeks and Romans created maps from the time of Anaximander in the 6th century BCE. In the 2nd century CE, Ptolemy wrote his treatise on Geographia; this contained Ptolemy's world map – the world known to Western society. As early as the 8th century, Arab scholars were translating the works of the Greek geographers into Arabic. In ancient China, geographical literature dates to the 5th century BCE; the oldest extant Chinese maps come from the State of Qin, dated back to the 4th century BCE, during the Warring States period. In the book of the Xin Yi Xiang Fa Yao, published in 1092 by the Chinese scientist Su Song, a star map on the equidistant cylindrical projection. Although this method of charting seems to have existed in China before this publication and scientist, the greatest significance of the star maps by Su Song is that they represent the oldest existent star maps in printed form. Early forms of cartography of India included depictions of the pole star and surrounding constellations.
These charts may have been used for navigation. "Mappae mundi are the medieval European maps of the world. About 1,100 of these are known to have survived: of these, some 900 are found illustrating manuscripts and the remainder exist as stand-alone documents; the Arab geographer Muhammad al-Idrisi produced his medieval atlas Tabula Rogeriana in 1154. By combining the knowledge of Africa, the Indian Ocean and the Far East with the information he inherited from the classical geographers, he was able to write detailed descriptions of a multitude of countries. Along with the substantial text he had written, he created a world map influenced by the Ptolemaic conception of the world, but with significant influence from multiple Arab geographers, it remained the most accurate world map for the next three centuries. The map was divided with detailed descriptions of each zone; as part of this work, a smaller, circular map was made depicting the south on top and Arabia in the center. Al-Idrisi made an estimate of the circumference of the world, accurate to within 10%.
In the Age of Exploration, from the 15th century to the 17th century, European cartographers both copied earlier maps and drew their own, based on explorers' observations and new surveying techniques. The invention of the magnetic compass and sextant enabled increasing accuracy. In 1492, Martin Behaim, a German cartographer, made the oldest extant globe of the Earth. In 1507, Martin Waldseemüller produced a globular world map and a large 12-panel world wall map bearing the first use of the name "America". Portuguese cartographer Diego Ribero was the author of the first known planisphere with a graduated Equator. Italian cartographer Battista Agnese produced at least 71 manuscript atlases of sea charts. Johannes Werner promoted the Werner projection; this was an equal-area, heart-shaped world map projection, used in the 16th and 17th centuries. Over time, other iterations of this map type arose; the Werner projection places its standard parallel at the North Pole. In 1569, mapmaker Gerardus Mercato