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Resection (surveying)
Position resection and intersection are methods for determining an unknown geographic position ( position finding) by measuring angles with respect to known positions. In ''resection'', the one point with unknown coordinates is occupied and sightings are taken to the known points; in ''intersection'', the two points with known coordinates are occupied and sightings are taken to the unknown point. Measurements can be made with a compass and topographic map (or nautical chart), theodolite or with a total station using known points of a geodetic network or landmarks of a map. Resection versus intersection Resection and its related method, ''intersection'', are used in surveying as well as in general land navigation (including inshore marine navigation using shore-based landmarks). Both methods involve taking azimuths or bearings to two or more objects, then drawing ''lines of position'' along those recorded bearings or azimuths. When intersecting, lines of position are used to fix t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geographic Position
A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude. It is the simplest, oldest, and most widely used type of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface. A full GCS specification, such as those listed in the EPSG and ISO 19111 standards, also includes a choice of geodetic datum (including an Earth ellipsoid), as different datums will yield different latitude and longitude values for the same location. History The invention of a geographic coordinate system is generally credited to Eratosthenes of Cyrene, who composed his now-lost ''Geography'' at the Library of Alexandria in the 3rd century&nbs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Collins (mathematician)
John Collins Fellow of the Royal Society, FRS (25 March 1625 – 10 November 1683) was an English mathematician. He is most known for his extensive correspondence with leading scientists and mathematicians such as Giovanni Alfonso Borelli, Gottfried Leibniz, Isaac Newton, and John Wallis. His correspondence provides details of many of the discoveries and developments made in his time, and shows his role in making some of these discoveries available to a wider audience. He was called "English Marin Mersenne, Mersenne" for his extensive collecting and diffusing of scientific information. Life He was the son of a nonconformist minister, and was born at Woodeaton, Wood Eaton in Oxfordshire, 5 March 1625. Apprenticed at the age of sixteen to Thomas Allam, a bookseller, living outside the Turl Gate of Oxford, he was driven to quit the trade by the troubles of the time, and accepted a clerkship in the employment of John Marr, clerk of the kitchen to the Charles II of England, Prince of W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Position Line
A position line or line of position (LOP) is a line (or, on the surface of the Earth, a curve) that can be both identified on a chart (nautical chart or aeronautical chart) and translated to the surface of the Earth. The intersection of a minimum of two position lines is a fix that is used in position fixing to identify a navigator's location. There are several types of position line: * Compass bearing – the angle between north and the line passing through the compass and the point of interest * Transit – a line passing through the observer and two other reference points * Leading line – the line passing through two marks indicating a safe channel * Leading lights – the line passing through two beacons indicating a safe channel * Sector lights – the lines created by masked colored lights that indicate a safe channel See also * Coordinate line * Intersection (aeronautics) * Navigation * Position circle * Sight reduction In astronavigation, sight reduction is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orienteering Compass
A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with North magnetic pole, magnetic north. Other methods may be used, including gyroscopes, magnetometers, and GPS receivers. Compasses often show angles in degrees: north corresponds to 0°, and the angles increase clockwise, so east is 90°, south is 180°, and west is 270°. These numbers allow the compass to show azimuths or bearing (angle), bearings which are commonly stated in degrees. If local magnetic declination, variation between magnetic north and true north is known, then direction of magnetic north also gives direction of true north. Among the Four Great Inventions, the magnetic compass was first invented as a device for divination as early as the history of science and technology in China, Chinese Han dynasty (since c. 206 BC),#Li, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orienteering
Orienteering is a group of sports that involve using a map and compass to navigation, navigate from point to point in diverse and usually unfamiliar terrain whilst moving at speed. Participants are given a topographical map, usually a specially prepared orienteering map, which they use to find Control point (orienteering), control points. Originally a training exercise in Land navigation (military), land navigation for military officers, orienteering has developed many variations. Among these, the oldest and the most popular is foot orienteering. For the purposes of this article, foot orienteering serves as a point of departure for discussion of all other variations, but almost any sport that involves racing against a clock and requires navigation with a map is a type of orienteering. Orienteering is included in the programs of world sporting events including the World Games (see Orienteering at the World Games) and World Police and Fire Games. History The history of ori ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection (aeronautics)
In aviation, an intersection is a virtual navigational fix that helps aircraft maintain their flight plan. It is usually defined as the intersection (in the geometrical sense) of two VOR (VHF Omnidirectional Range) radials. They are usually identified as major airway intersections where aircraft, operating under instrument flight rules, often change direction of flight while ''en route''. According to the Federal Aviation Regulations, some intersections are designated as mandatory reporting points for pilots who are not in radar contact with air traffic control. Intersections also play an important role in departure and approach procedures. All intersections have an alphabetical or alphanumeric designation. Near major airports, the intersection designation code typically consists of three letters followed by the runway number. Most other intersection designations consist of five-letter combinations that are either pronounceable or chosen for their mnemonic value, since either a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hansen's Problem
In trigonometry, Hansen's problem is a problem in planar surveying, named after the astronomer Peter Andreas Hansen (1795–1874), who worked on the geodetic survey of Denmark. There are two known points , and two unknown points . From and an observer measures the angles made by the lines of sight to each of the other three points. The problem is to find the positions of and . See figure; the angles measured are . Since it involves observations of angles made at unknown points, the problem is an example of resection (as opposed to intersection). Solution method overview Define the following angles: \begin \gamma &= \angle P_1 AP_2, &\quad \delta &= \angle P_1BP_2, \\ pt \phi &= \angle P_2 AB, &\quad \psi &= \angle P_1 BA. \end As a first step we will solve for and . The sum of these two unknown angles is equal to the sum of and , yielding the equation \phi + \psi = \beta_1 + \beta_2. A second equation can be found more laboriously, as follows. The law of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hand Compass
A hand compass (also hand bearing compass or sighting compass) is a compact magnetic compass capable of one-hand use and fitted with a sighting device to record a precise bearing or azimuth to a given target or to determine a location. Hand or sighting compasses include instruments with simple notch-and-post alignment ("gunsights"), prismatic sights, direct or lensatic sights, and mirror/vee (reflected-image) sights. With the additional precision offered by the sighting arrangement, and depending upon construction, sighting compasses provide increased accuracy when measuring precise bearings to an objective. The term ''hand compass'' is used by some in the forestry and surveying professions to refer to a certain type of hand compass optimized for use in those fields, also known as a forester or cruiser compass. A ''hand compass'' may also include the various one-hand or 'pocket' versions of the surveyor's or geologist's transit. History and use While small portable compas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection Variation
Projection or projections may refer to: Physics * Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction * The display of images by a projector Optics, graphics, and cartography * Map projection, reducing the surface of a three-dimensional planet to a flat map * Graphical projection, the production of a two-dimensional image of a three-dimensional object Chemistry * Fischer projection, a two-dimensional representation of a three-dimensional organic molecule * Haworth projection, a way of writing a structural formula to represent the cyclic structure of monosaccharides * Natta projection, a way to depict molecules with complete stereochemistry in two dimensions in a skeletal formula * Newman projection, a visual representation of a chemical bond from front to back Mathematics * Projection (mathematics), any of several different types of geometrical mappings ** Projection (linear algebra), a line ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Excess
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook ''Spherical trigonometry for the use of colleges and Schools''. Since then, significant developments have been the application of vector methods, quaternion methods, and the use of numerical methods. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesy
Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional space, 3D. It is called planetary geodesy when studying other astronomical body, astronomical bodies, such as planets or Natural satellite, circumplanetary systems. Geodynamics, Geodynamical phenomena, including crust (geology), crustal motion, tides, and polar motion, can be studied by designing global and national Geodetic control network, control networks, applying space geodesy and terrestrial geodetic techniques, and relying on Geodetic datum, datums and coordinate systems. Geodetic job titles include geodesist and geodetic surveyor. History Geodesy began in pre-scientific Classical antiquity, antiquity, so the very word geodesy comes from the Ancient Greek word or ''geodaisia'' (literally, "division of Earth"). Early ideas about t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Snellius–Pothenot Problem
In trigonometry, the Snellius–Pothenot problem is a problem first described in the context of planar surveying. Given three known points , an observer at an unknown point observes that the line segment subtends an angle and the segment subtends an angle ; the problem is to determine the position of the point . (See figure; the point denoted is between and as seen from ). Since it involves the observation of known points from an unknown point, the problem is an example of resection. Historically it was first studied by Snellius, who found a solution around 1615. Formulating the equations First equation Denoting the (unknown) angles as and as gives: x+y = 2 \pi - \alpha - \beta - C by using the sum of the angles formula for the quadrilateral . The variable represents the (known) internal angle in this quadrilateral at point . (Note that in the case where the points and are on the same side of the line , the angle will be greater than ). Second equation Applyi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
