|
Lee Conformal Projection
The Lee conformal world in a tetrahedron is a polyhedral, conformal map projection that projects the globe onto a tetrahedron using Dixon elliptic functions. It is conformal everywhere except for the four singularities at the vertices of the polyhedron. Because of the nature of polyhedra, this map projection can be tessellated infinitely in the plane. It was developed by L. P. Lee in 1965. Coordinates from a spherical datum can be transformed into Lee conformal projection coordinates with the following formulas, where is the longitude and the latitude: : 2 \operatornamew\,\operatornamew = 2^\exp(i\lambda) \tan\bigl(\tfrac14\pi - \tfrac12\phi\bigr) where : w = x + y i and sm and cm are Dixon elliptic functions. Since there is no elementary expression for these functions, Lee suggests using the 28th degree MacLaurin series. See also * List of map projections * AuthaGraph projection, another tetrahedral projection, 1999 * Dymaxion map, 1943 * Peirce quincuncial projecti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lee Conformal World In A Tetrahedron Projection
Lee may refer to: Name Given name * Lee (given name), a given name in English Surname * Chinese surnames romanized as Li or Lee: ** Li (surname 李) or Lee (Hanzi ), a common Chinese surname ** Li (surname 利) or Lee (Hanzi ), a Chinese surname *Lý (Vietnamese surname) or Lí (李), a common Vietnamese surname * Lee (Korean surname) or Rhee or Yi (Hanja , Hangul or ), a common Korean surname * Lee (English surname), a common English surname * List of people with surname Lee **List of people with surname Li ** List of people with the Korean family name Lee Geography United Kingdom * Lee, Devon * Lee, Hampshire * Lee, London * Lee, Mull, a location in Argyll and Bute * Lee, Northumberland, a location * Lee, Shropshire, a location * Lee-on-the-Solent, Hampshire * Lee District (Metropolis) * The Lee, Buckinghamshire, parish and village name, formally known as Lee * River Lee - alternative name for River Lea United States * Lee, California * Lee, Florida * Lee, Illinoi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lee Tetrahedral (triangular) With Tissot's Indicatrices Of Distortion
Lee may refer to: Name Given name * Lee (given name), a given name in English Surname * Chinese surnames romanized as Li or Lee: ** Li (surname 李) or Lee (Hanzi ), a common Chinese surname ** Li (surname 利) or Lee (Hanzi ), a Chinese surname * Lý (Vietnamese surname) or Lí (李), a common Vietnamese surname * Lee (Korean surname) or Rhee or Yi (Hanja , Hangul or ), a common Korean surname * Lee (English surname), a common English surname * List of people with surname Lee **List of people with surname Li ** List of people with the Korean family name Lee Geography United Kingdom * Lee, Devon * Lee, Hampshire * Lee, London * Lee, Mull, a location in Argyll and Bute * Lee, Northumberland, a location * Lee, Shropshire, a location * Lee-on-the-Solent, Hampshire * Lee District (Metropolis) * The Lee, Buckinghamshire, parish and village name, formally known as Lee * River Lee - alternative name for River Lea United States * Lee, California * Lee, Florida * Lee, Il ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lee Tetrahedral Projection Tessellated
Lee may refer to: Name Given name * Lee (given name), a given name in English Surname * Chinese surnames romanized as Li or Lee: ** Li (surname 李) or Lee (Hanzi ), a common Chinese surname ** Li (surname 利) or Lee (Hanzi ), a Chinese surname * Lý (Vietnamese surname) or Lí (李), a common Vietnamese surname * Lee (Korean surname) or Rhee or Yi (Hanja , Hangul or ), a common Korean surname * Lee (English surname), a common English surname * List of people with surname Lee **List of people with surname Li ** List of people with the Korean family name Lee Geography United Kingdom * Lee, Devon * Lee, Hampshire * Lee, London * Lee, Mull, a location in Argyll and Bute * Lee, Northumberland, a location * Lee, Shropshire, a location * Lee-on-the-Solent, Hampshire * Lee District (Metropolis) * The Lee, Buckinghamshire, parish and village name, formally known as Lee * River Lee - alternative name for River Lea United States * Lee, California * Lee, Florida * Lee, Il ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Map Projection
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections. More generally, projections are considered in several fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Map Projection
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections. More generally, projections are considered in several fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such nets. For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dixon Elliptic Functions
In mathematics, the Dixon elliptic functions sm and cm are two elliptic functions (doubly periodic meromorphic functions on the complex plane) that map from each regular hexagon in a hexagonal tiling to the whole complex plane. Because these functions satisfy the identity \operatorname^3 z + \operatorname^3 z = 1, as real functions they parametrize the cubic Fermat curve x^3 + y^3 = 1, just as the trigonometric functions sine and cosine parametrize the unit circle x^2 + y^2 = 1. They were named sm and cm by Alfred Dixon in 1890, by analogy to the trigonometric functions sine and cosine and the Jacobi elliptic functions sn and cn; Göran Dillner described them earlier in 1873. Definition The functions sm and cm can be defined as the solutions to the initial value problem: :\frac \operatorname z = -\operatorname^2 z,\ \frac \operatorname z = \operatorname^2 z,\ \operatorname(0) = 1,\ \operatorname(0) = 0 Or as the inverse of the Schwarz–Christoffel mapping from the complex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional spaces, higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include ''regular tilings'' with regular polygonal tiles all of the same shape, and ''semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An ''aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern. A ''tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Datum (geodesy)
A geodetic datum or geodetic system (also: geodetic reference datum, geodetic reference system, or geodetic reference frame) is a global datum reference or reference frame for precisely representing the position of locations on Earth or other planetary bodies by means of ''geodetic coordinates''. DatumsThe plural is not "data" in this case are crucial to any technology or technique based on spatial location, including geodesy, navigation, surveying, geographic information systems, remote sensing, and cartography. A horizontal datum is used to measure a location across the Earth's surface, in latitude and longitude or another coordinate system; a ''vertical datum'' is used to measure the elevation or depth relative to a standard origin, such as mean sea level (MSL). Since the rise of the global positioning system (GPS), the ellipsoid and datum WGS 84 it uses has supplanted most others in many applications. The WGS 84 is intended for global use, unlike most earlier datums. Before G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Map Projections
This is a summary of map projections that have articles of their own on Wikipedia or that are otherwise notable Notability is the property of being worthy of notice, having fame, or being considered to be of a high degree of interest, significance, or distinction. It also refers to the capacity to be such. Persons who are notable due to public responsibi .... Because there is no limit to the number of possible map projections, there can be no comprehensive list. Table of projections *The first known popularizer/user and not necessarily the creator. Key Type of projection ; Cylindrical: In standard presentation, these map regularly-spaced meridians to equally spaced vertical lines, and parallels to horizontal lines. ; Pseudocylindrical: In standard presentation, these map the central meridian and parallels as straight lines. Other meridians are curves (or possibly straight from pole to equator), regularly spaced along parallels. ; Conic: In standard presentation, conic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AuthaGraph Projection
AuthaGraph is an approximately equal-area world map projection invented by Japanese architect Hajime Narukawa in 1999. The map is made by equally dividing a spherical surface into 96 triangles, transferring it to a tetrahedron while maintaining area proportions, and unfolding it onto a rectangle: it is a polyhedral map projection. The map substantially preserves sizes and shapes of all continents and oceans while it reduces distortions of their shapes, as inspired by the Dymaxion map. The projection does not have some of the major distortions of the Mercator projection, like the expansion of countries in far northern latitudes, and allows for Antarctica to be displayed accurately and in whole. Triangular world maps are also possible using the same method. The name is derived from " authalic" and "graph". The method used to construct the projection ensures that the 96 regions of the sphere that are used to define the projection each have the correct area, but the projection does n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Tetrahedron")
