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Geographic Coordinate Conversion
In geodesy, conversion among different geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion is composed of a number of different types of conversion: format change of geographic coordinates, conversion of coordinate systems, or transformation to different geodetic datums. Geographic coordinate conversion has applications in cartography, surveying, navigation and geographic information systems. In geodesy, geographic coordinate ''conversion'' is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. A geographic coordinate ''transformation'' is a translation among different geodetic datums. Both geographic coordinate conversion and transformation will be considered in this article. This article assumes readers are already familiar with the content in the articles geographic coordinate system and geodetic datum. Chang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesy
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equivalent measurements for other planets (known as ''planetary geodesy''). Geodynamical phenomena, including crustal motion, tides and polar motion, can be studied by designing global and national control networks, applying space geodesy and terrestrial geodetic techniques and relying on datums and coordinate systems. The job title is geodesist or geodetic surveyor. History Definition The word geodesy comes from the Ancient Greek word ''geodaisia'' (literally, "division of Earth"). It is primarily concerned with positioning within the temporally varying gravitational field. Geodesy in the German-speaking world is divided into "higher geodesy" ( or ), which is concerned with measuring Earth on the global scale, and "practical geodes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semi-major Axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle. The length of the semi-major axis of an ellipse is related to the semi-minor axis's length through the eccentricity and the semi-latus rectum \ell, as follows: The semi-major axis of a hyperbola is, depending on the convention, plus or minus one half of the distance between the two branches. Thus it is the distance from the cente ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertical Direction
In astronomy, geography, and related sciences and contexts, a '' direction'' or '' plane'' passing by a given point is said to be vertical if it contains the local gravity direction at that point. Conversely, a direction or plane is said to be horizontal if it is perpendicular to the vertical direction. In general, something that is vertical can be drawn from up to down (or down to up), such as the y-axis in the Cartesian coordinate system. Historical definition The word ''horizontal'' is derived from the Latin , which derives from the Greek , meaning 'separating' or 'marking a boundary'. The word ''vertical'' is derived from the late Latin ', which is from the same root as ''vertex'', meaning 'highest point' or more literally the 'turning point' such as in a whirlpool. Girard Desargues defined the vertical to be perpendicular to the horizon in his 1636 book ''Perspective''. Geophysical definition The plumb line and spirit level In physics, engineering and construction, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geocentric Latitude
In geography, latitude is a coordinate that specifies the north–south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pole, with 0° at the Equator. Lines of constant latitude, or ''parallels'', run east–west as circles parallel to the equator. Latitude and ''longitude'' are used together as a coordinate pair to specify a location on the surface of the Earth. On its own, the term "latitude" normally refers to the ''geodetic latitude'' as defined below. Briefly, the geodetic latitude of a point is the angle formed between the vector perpendicular (or ''normal'') to the ellipsoidal surface from the point, and the plane of the equator. Background Two levels of abstraction are employed in the definitions of latitude and longitude. In the first step the physical surface is modeled by the geoid, a surface which approximates the mean sea level over the oceans ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodetic Latitude
Geodetic coordinates are a type of curvilinear orthogonal coordinate system used in geodesy based on a '' reference ellipsoid''. They include geodetic latitude (north/south) , ''longitude'' (east/west) , and ellipsoidal height (also known as geodetic height). The triad is also known as Earth ellipsoidal coordinates (not to be confused with '' ellipsoidal-harmonic coordinates''). Definitions Longitude measures the rotational angle between the zero meridian and the measured point. By convention for the Earth, Moon and Sun, it is expressed in degrees ranging from −180° to +180°. For other bodies a range of 0° to 360° is used. For this purpose, it is necessary to identify a ''zero meridian'', which for Earth is usually the Prime Meridian. For other bodies a fixed surface feature is usually referenced, which for Mars is the meridian passing through the crater Airy-0. It is possible for many different coordinate systems to be defined upon the same reference ellipsoid. Geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ENU And NED
ENU, also known as ''N''-ethyl-''N''-nitrosourea (chemical formula C3H7N3O2), is a highly potent mutagen. For a given gene in mice, ENU can induce 1 new mutation in every 700 loci. It is also toxic at high doses. The chemical is an alkylating agent, and acts by transferring the ethyl group of ENU to nucleobases (usually thymine) in nucleic acids. Its main targets are the spermatogonial stem cells, from which mature sperm are derived. Background of discovery of ENU as a mutagen Bill Russell (1951) created a landmark in the field of mouse genetics by creating a specifically designed mouse strain, the ''T'' (test) stock that was used in genetic screens for testing mutagens such as radiations and chemicals. The ''T''-stock mouse harbors 7 recessive, viable mutations affecting easily recognizable traits. At the Oak Ridge National Laboratory, Russell's initial goal was to determine the rate of inheritable gene mutations in the germ line induced by radiations. Thus he decided to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Tangent Plane
Local tangent plane coordinates (LTP), also known as local ellipsoidal system, local geodetic coordinate system, or local vertical, local horizontal coordinates (LVLH), are a spatial reference system based on the tangent plane defined by the local vertical direction and the Earth's axis of rotation. It consists of three coordinates: one represents the position along the northern axis, one along the local eastern axis, and one represents the vertical position. Two right-handed variants exist: east, north, up (ENU) coordinates and north, east, down (NED) coordinates. They serve for representing state vectors that are commonly used in aviation and marine cybernetics. Axes These frames are location dependent. For movements around the globe, like air or sea navigation, the frames are defined as tangent to the lines of geographical coordinates: *East-West tangent to parallels, *North-South tangent to meridians, and *Up-Down in the direction normal to the oblate spheroid used as Ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartic Equation
In mathematics, a quartic equation is one which can be expressed as a ''quartic function'' equaling zero. The general form of a quartic equation is :ax^4+bx^3+cx^2+dx+e=0 \, where ''a'' ≠ 0. The quartic is the highest order polynomial equation that can be solved by radicals in the general case (i.e., one in which the coefficients can take any value). History Lodovico Ferrari is attributed with the discovery of the solution to the quartic in 1540, but since this solution, like all algebraic solutions of the quartic, requires the solution of a cubic to be found, it couldn't be published immediately. The solution of the quartic was published together with that of the cubic by Ferrari's mentor Gerolamo Cardano in the book '' Ars Magna'' (1545). The proof that this was the highest order general polynomial for which such solutions could be found was first given in the Abel–Ruffini theorem in 1824, proving that all attempts at solving the higher order polynomials would ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton–Raphson
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function defined for a real variable , the function's derivative , and an initial guess for a root of . If the function satisfies sufficient assumptions and the initial guess is close, then :x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the intersection of the -axis and the tangent of the graph of at : that is, the improved guess is the unique root of the linear approximation at the initial point. The process is repeated as :x_ = x_n - \frac until a sufficiently precise value is reached. This algorithm is first in the class of Householder's methods, succeeded by Halley's method. The method can also be extended to complex functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triaxial Ellipsoidal Longitude
The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an ''oblate ellipsoid'', a slightly flattened sphere. A '' geodesic'' is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry . If the Earth is treated as a sphere, the geodesics are great circles (all of which are closed) and the problems reduce to ones in spherical trigonometry. However, showed that the effect of the rotation of the Earth results in its resembling a slightly oblate ellipsoid: in this case, the equator and the meridians are the only simple closed geodesics. Furthermore, the shortest path between two points on the equator does not necessarily run along the equator. Finally, if the ellipsoid is further perturbed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meridian Arc
In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. The purpose of measuring meridian arcs is to determine a figure of the Earth. One or more measurements of meridian arcs can be used to infer the shape of the reference ellipsoid that best approximates the geoid in the region of the measurements. Measurements of meridian arcs at several latitudes along many meridians around the world can be combined in order to approximate a ''geocentric ellipsoid'' intended to fit the entire world. The earliest determinations of the size of a spherical Earth required a single arc. Accurate survey work beginning in the 19th century required several arc measurements in the region the survey was to be conducted, leading to a proliferation of reference ellipsoids around the world. The latest determinations use astro-geodetic measurements and the method ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
