About measurement by the use of triangles In trigonometry and geometry , triangulation is the process ... then be fixed as the third point of a triangle with one known side and two known angles. Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation .... Points inside the triangles can all then be accurately located with reference to it. Such triangulation ... Image Distance by triangulation.svg thumb 310px Triangulation can be used to calculate the coordinate ... d . Image Triangulation .jpg right 200px Triangulation The coordinate s and distance ... of 1726 Image G F triangulation.jpg thumb right Gemma Frisius s 1533 proposal to use triangulation for mapmaking Image L Triangulierung.png thumb right Nineteenth century triangulation network for the triangulation of Rhineland Hesse Triangulation today is used for many purposes, including surveying ... Forschungsinstitut, Oberwolfach, Germany. ISBN 3515082239. ref In the field, triangulation ... 0 87548 422 0. pp. 119 122 ref Abu Rayhan Biruni d. 1048 also introduced triangulation techniques ... is dated 1296. Gemma Frisius and triangulation for mapmaking On land, the Dutch cartographer Gemma Frisius proposed using triangulation to accurately position far away places for map making in his .... The astronomer Tycho Brahe applied the method in Scandinavia, completing a detailed triangulation ... been suggested that Christopher Saxton may have used rough and ready triangulation to place ... Saxton s Hampshire Surveying , University of Portsmouth ref Willebrord Snell and modern triangulation networks The modern systematic use of triangulation networks stems from the work of the Dutch ... son C sar Fran ois Cassini de Thury C sar Cassini undertook the first triangulation of the whole ... map of France constructed on rigorous principles. Triangulation methods were by now well established ... began to establish detailed triangulation network surveys to map whole countries. The Principal Triangulation ... more details
Wiktionary triangulationTriangulation surveying refers to measurement by using triangles. Triangulation may also refer to Mathematics and computer science Subdivisions of spaces into triangles or higher dimensional simplices triangulation geometry , division of the Euclidean plane into triangles and of Euclidean spaces into simplices polygon triangulation , division of a polygon into triangles point set triangulation , division of the convex hull of a point set into triangles using only that set as triangle vertices triangulation topology , generalizations to topological spaces other than R sup d sup In graph theory Maximal planar graph s are sometimes called triangulations, and a maximal planar supergraph of a graph G may be called a triangulation of G . Chordal graph s are sometimes called triangulated graphs. As in the planar case, if a graph G is a subgraph of a chordal graph H , H may be called a triangulation of G . A triangulated category is a category defined by a set of axioms involving triangles of arrows. Triangulation computer vision is the computation of a 3D point given its projection onto two, or more, images. In linear algebra , triangulation is a process of finding an upper triangular matrix similar to given a matrix. See Schur triangulation . Mobile phone tracking uses triangulation , actually, trilateration , to calculate the location of the handset. Other fields Triangulation actuary , a model that actuaries use to predict future costs of past and current claims obligations. Triangulation chess , a maneuver in which one player moves a piece often a king in a triangular pattern in order to force the opponent to make a weakening move Triangulation psychology .... Triangulation politics , the act of a candidate presenting his or her ideology as above and between the left and right side of the political spectrum Triangulation social science , the use of multiple cross checked sources and methodology disambig cs Triangulace rozcestn k de Triangulation pl Triangulacja ... more details
Image Pitteway.svg thumb 360px Left A Pitteway triangulation. Every interior Delaunay edge black crosses .... Right A Delaunay triangulation that is not a Pitteway triangulation the red interior Delaunay ... have the bottom vertex as their nearest neighbor. In computational geometry , a Pitteway triangulation is a point set triangulation in which the Nearest neighbor search nearest neighbor of any point p within the triangulation is one of the vertices of the triangle containing p . Alternatively, it is a Delaunay triangulation in which each internal edge crosses its Dual graph dual Voronoi diagram ... point set supports a Pitteway triangulation. When such a triangulation exists it is a special case of the Delaunay triangulation , and consists of the union of the Gabriel graph and convex hull . History The concept of a Pitteway triangulation was introduced by harvtxt Pitteway 1973 . See also harvtxt .... The name Pitteway triangulation was given by harvtxt Okabe Boots Chiu Sugihara 2000 . Counterexamples harvtxt Gold 1978 points out that not every point set supports a Pitteway triangulation. For instance, any triangulation of a regular pentagon includes a central isosceles triangle such that a point .... Relation to other geometric graphs When a Pitteway triangulation exists, the midpoint of each edge interior to the triangulation must have the two edge endpoints as its nearest neighbors, for any other .... Thus, a circle having that edge as diameter must be empty of vertices, so the Pitteway triangulation ... the Gabriel graph and convex hull together form a triangulation, it is a Pitteway triangulation. Since all Gabriel graph and convex hull edges are part of the Delaunay triangulation , a Pitteway triangulation ... triangulation. However point sets with no Pitteway triangulation will still have a Delaunay triangulation. In the Pitteway triangulation, each edge pq either belongs to the convex hull or crosses the edge ... is used to define a Pitteway triangulation, as a Delaunay triangulation in which all internal ... more details
dablink Related topics include Point set triangulation and Polygon triangulation . In advanced geometry , in the most general meaning, triangulation is a subdivision of a geometric object into simplex simplices . In particular, in the plane it is a subdivision into triangle geometry triangle s, hence the name. Different branches of geometry use slightly differing definitions of the term. A triangulation T of math mathbb R n 1 math is a subdivision of math mathbb R n 1 math into n 1 dimensional simplex simplices such that any two simplices in T intersect in a common face or not at all any bounded set in math mathbb R n 1 math intersects only finite set finite ly many simplices in T . A point set triangulation , i.e., a triangulation of a discrete space discrete set of points math P subset mathbb R n 1 math is a subdivision of the convex hull of the points into simplices such that any two simplices intersect in a common face or not at all and the set of points that are vertices of the subdividing simplices coincides with math P math . The Delaunay triangulation is a famous triangulation of a set of points where the circum hypersphere of each simplex contains none of the points. See also Pseudotriangulation Simplicial complex Delaunay triangulation External links mathworld urlname SimplicialComplex title Simplicial complex mathworld urlname Triangulation title Triangulation Category Geometry geometry stub he pl Triangulacja matematyka ... more details
Image Delaunay circumcircles.png right thumb 280px A Delaunay triangulation in the plane with circumcircles shown In mathematics and computational geometry , a Delaunay triangulation for a set P of points in the plane is a triangulation geometry triangulation DT P such that no point in P is inside the Circumcircle ... triangulations maximize the minimum angle of all the angles of the triangles in the triangulation they tend to avoid skinny triangles. The triangulation was invented by Boris Delaunay in 1934 ... triangulation the notion of triangulation is degenerate for this case . For four points on the same circle e.g., the vertices of a rectangle the Delaunay triangulation is not unique the two ... circumscribed spheres, the notion of Delaunay triangulation extends to three and higher dimensions ... triangulation is not guaranteed to exist or be unique. Relationship with the Voronoi diagram The Delaunay triangulation geometry triangulation of a discrete space discrete point set P in general position ... centers.png The Delaunay triangulation with all the circumcircles and their centers in red . Image Delaunay ... P of points in the d dimensional Euclidean space , a Delaunay triangulation is a Triangulation geometry triangulation DT P such that no point in P is inside the circumcircle circum hypersphere of any simplex in DT P . It is known ref name deBerg that there exists a unique Delaunay triangulation ... of finding the Delaunay triangulation of a set of points in d dimensional Euclidean space can ... hull is unique, so is the triangulation, assuming all facets of the convex hull are simplex ... and d the number of dimensions. The union of all simplices in the triangulation is the convex hull of the points. The Delaunay triangulation contains at most O n sup d 2 sup simplices ... d 2 , if there are b vertices on the convex hull, then any triangulation of the points has at most ... triangulation maximizes the minimum angle. Compared to any other triangulation of the points, the smallest ... more details
For other uses of triangulation in mathematics Triangulation disambiguation In mathematics , topology generalizes the notion of triangulation geometry triangulation in a natural way as follows A triangulation of a topological space math X math is a simplicial complex K , homeomorphic to X , together with a homeomorphism h K math to math X . Triangulation is useful in determining the properties of a topological space. For example, one can compute Homology mathematics homology and cohomology groups of a triangulated space using simplicial homology and cohomology theories instead of more complicated homology and cohomology theories. Piecewise linear structures For topological manifold s, there is a slightly stronger notion of triangulation a piecewise linear triangulation sometimes just called a triangulation is a triangulation with the extra property that the link of any simplex is a piecewise linear sphere. The link of a simplex s in a simplicial complex K is a subcomplex of K consisting ... to the n sphere with a triangulation that is not piecewise linear it has a simplex whose ... and Robert Hardt admit a piecewise linear triangulation. Topological manifold s of dimensions 2 and 3 are always triangulable by an Hauptvermutung essentially unique triangulation up to piecewise linear ... 4, however, the E8 manifold does not admit a triangulation, and some compact 4 manifolds ... Hauptvermutung . Explicit methods of triangulation An important special case of topological triangulation ..., this finite set of triangles can be used iteratively to construct a triangulation. Another ... sup m sup , subdivide a cubical lattice in R sup m sup into simplices to give a triangulation of R ... many of the vertices, the triangulation will be in general position with respect to X thus no simplices ... wholly inside the tubular neighbourhood. The triangulation is given by the projection of this simplicial complex onto X . Graphs on surfaces A Whitney triangulation or clean triangulation of a surface ... more details
Optical Triangulation Sensors are commonly used to provide door mounted safety detection on swinging automatic doors. In North America , these types of sensors are very common and manufactured in very high volumes. When automatic swinging doors open and close, it is important that they do not come into contact with pedestrians passing through the door. Sensors used in the automatic door industry typically fall into four categories Microwave Sensors used to detect motion of a person as they approach an automatic door, Reflective Optical Sensors that are mounted on the door header and detect the presence of a person in the door path Camera based sensors that are also mounted on the door header and detect presence a competing technology to Reflective Optical Sensors and Triangulation sensors which are mounted on the door and move with the door to provide safety. Reflective and Camera technologies do not perform well on moving swing doors, because they typically depend upon detection of changes in the background. A sensor mounted on a swing door system is constantly in motion, so the background i.e. floor beneath the door changes continuously. To overcome this problem, a triangulation sensor provides an innovative solution. Triangulation Sensor Functionality In most cases an optical triangulation sensor is mounted near the top of the swinging door frame, inside a long extruded aluminum tube with an optical window facing the floor. An 880nm LED light source emits a collimated light beam that is emitted from the sensor, bounces off the floor and is received by a photodiode positioned adjacent to the LED source. A second photodiode or a linear array of photodiodes is positioned farther along the length of the sensor. When the emitted beam bounces off the floor, the reflected energy is almost exclusively concentrated on the first adjacent photodiode. When a human or object moves ... and providing safety. Triangulation sensors are found on a number of door brands and manufactured ... more details
cleanup date July 2009 Wireless triangulation is a method of determining the location of wireless nodes using IEEE 802.11 standards. ref cite web url http www.interlinknetworks.com graphics news wireless detection and tracking.pdf title A Practical Approach to Identifying and Tracking Unauthorized 802.11 Cards and Access Points accessdate 2009 07 08 ref It is normally implemented by measuring the RSSI signals strength. ref cite web url http www.techonline.com learning techpaper 216200021 title Wireless Triangulation Using RSSI Signals accessdate 2009 07 08 ref See also Location awareness Real time locating standards Wireless Local Area Network Wireless Personal Area Network references Category Radio frequency identification Category Radio navigation Category Tracking Category Wireless locating ... more details
Cleanup date July 2007 Triangulation is most commonly used to express a situation in which one family member will not communicate directly with another family member, but will communicate with a third family member, which can lead to the third family member becoming part of the triangle. The concept originated in the study of dysfunctional family systems, but can describe behaviors in other systems as well, including work. Triangulation can also be used as a label for a form of splitting in which one person plays the third family member against one that he or she is upset about. This is playing the two people against each other, but usually the person doing the splitting, will also engage in character assassination , only with both parties. Triangulation in psychology In the field of psychology, triangulations are necessary steps in the child s development when a two party relationship is opened up by a third party into a new form of relationship. So the child gains new mental abilities. The concept was introduced in 1971, by the Swiss psychiatrist Dr. Ernest L. Abelin, especially as early triangulation , to describe the transitions in psychoanalytic object relations theory and parent child relationship in the age of 18 months. In this presentation, the mother is the early caregiver with a nearly symbiotic relationship to the child, and the father lures the child away to the outside ... an http www.organizer model.org organizer and triangulation model , in which he based the whole human mental and psychic development on several steps of triangulation. Some earlier related work .... Child, 18 307 324. ref Family triangulation In family therapy , the term triangulation is most closely ... 478 ref In the family triangulation system the third person can either be used as a substitute for the direct .... Internat. J. Psycho Anal. 56 293 302 Ernst Abelin 1980 Triangulation, the Role of the Father and the Origins ... Triangulation. Von der Psychologie zur Psychoanalyse. In Das Vaterbild in Kontinuit t und Wandel ... more details
chess notation Triangulation is a chess tactics tactic used in chess to put one s opponent in zugzwang . That is, it gets to the same position with the other player to move, when it is a disadvantage for that player to move, e.g. he has to give up a blockade and let the other player penetrate his position. Triangulation is also called losing a tempo chess tempo or losing a move . Triangulation occurs most commonly in Chess endgame endgames with only king chess kings and pawn chess pawns when one king can maneuver on three adjacent squares in the shape of a triangle and maintain the basic position while the opposing king only has two such squares. Thus, if one king triangulates by using three ... Tempo chess tempo and reached the same position with the other player to move. Triangulation can ... Chess diagram tright Triangulation pd kd pl pl kl xw xw White to move. White needs it to be Black s move in this position, so he triangulates. The dots indicate triangulation squares for the white ... chess promoting the b pawn 2. Kd4 Kd7 3. Kd5 and now the triangulation is complete and we have the same ... to win after his third move. Other pieces For an example of triangulation with a Queen chess queen ..., but a knight chess knight cannot Harvcol M ller Pajeken 2008 pp 40, 175, 189 . Triangulation with the king ... Black s 64th move Triangulation can occur in endgames other than king and pawn endgames, such as this game ... if it were his move. Black achieves this through triangulation 64... Kd2 65. Re4 Kc3 66. Rh4 ... p 62 . clear Triangulation with a rook Chess diagram tright Topalov vs. Karpov, 2002 kl xw pl kd xw ... king and triangulation gains the opposition chess opposition , putting the opponent in zugzwang ... November title Endgame Lab Triangulation journal Chess Life volume issue pages 48 49 doi id url format accessdate External links http www.chessvideos.tv endgame training basic king triangulation 10.php Interactive King Triangulation Endgame vs Chess Computer Category Chess terminology Category ... more details
triangulation . Morris advocated a set of policies that were different from the traditional ... and balanced budgets . One of the most widely cited capstones of Clinton s triangulation strategy ... date 2010 01 29 accessdate 2010 05 26 ref Recent use Politicians alleged to have used triangulation ... triangulation. ref ref name bbc cite news url http news.bbc.co.uk 2 hi programmes world news ... Party United States U.S. Democratic Party , in particular the left, insist that triangulation is dead. They cite the attempted uses of triangulation by Democrats in the 2000 and 2004 U.S. presidential ... of triangulation by John Kerry in the United States presidential election, 2004 2004 presidential ... that he would remain with his agenda in the face of criticism, rather than resort to triangulation. ref name nyt However, the campaign of President Barack Obama made expert use of triangulation ... win support from soft adherents of the opposing camp. The term triangulation is often used as a pejorative ... that triangulation has led to multiple electoral defeats and eroded the principles of those who use ... more details
Unreferenced date December 2009 Stellar triangulation is a method of geodesy which uses cosmic instead of terrestrial targets. It was first done by the Finnish geodesist Yrj V is l V is l in 1959, who made astrometric photograph s of the sky at two stations together with a balloon probe between them. Even this first step showed the potential of the method, because V is l got the azimuth between Helsinki and Turku a distance of 150 km with an accuracy of 1 . Soon the method was successfully tested by External ballistics ballistic rockets and for some special satellites. Adequate computer program s were written for the astrometric reduction of the photographic plates, the Intersection set theory intersection of the observation planes containing the stations and the targets, and the adjustment of stellar terrestric networks with Data redundancy redundancy . The advantage of stellar triangulation is the possibility to cross far distances terrestrial observations are restricted to approx. 30 km, and even in high mountains to 60 km , and the independency of the Earth s gravity field. The results are azimuth s between the stations in the stellar inertial system , despite of no direct Line of sight propagation line of sight . In 1960 the first appropriate space probe was launched the 30 m diameter balloon satellite Project Echo . By then the whole of Western Europe could be linked together geodetically with accuracies 2 10 times better than by classical triangulation . During the late 1960s a global project was begun by H.H. Schmid Switzerland to connect 45 stations all over the continents, with distances of 3000 5000 km. It was finished in 1974 by precise ... of the Earth Triangulation Trilateration Satellite geodesy PAGEOS satellite fundamental station Satellite ... Schn delbach et al. Western European Satellite Triangulation Programme WEST , 2nd Experimental ... Triangulation Category Geodesy Category Astrometry ... more details
In computational geometry , polygon triangulation is the decomposition of a polygonal area simple polygon P into a set of triangles , ref name bkos Citation author Mark de Berg , Marc van Kreveld , Mark Overmars , and Otfried Schwarzkopf year 2000 title Computational Geometry publisher Springer Verlag edition 2nd revised isbn 3 540 65620 0 Chapter 3 Polygon Triangulation pp.45 61. ref i.e., finding the set of triangles with pairwise non intersecting interiors whose union is P . In the strict sense, these triangles may have vertices only at the vertices of P . In a less strict sense, points can be added anywhere on or inside the polygon to serve as vertices of triangles. In addition, the cases of triangulation of a simple polygon and of a polygonal area with polygonal holes are treated separately. Triangulations may be viewed as special cases of planar straight line graph s. When there are no holes or added points, triangulations form outerplanar graph maximal outerplanar graphs . Polygon triangulation without extra vertices Over time a number of algorithms have been proposed to triangulate a polygon. Special cases A convex polygon is trivial to triangulate in linear time , by adding ... inside it and with an extra property unimportant for triangulation . ref Meisters, G. H., Polygons have ... Robert E. Tarjan discovered an O n log log n algorithm for triangulation. Simple ... for Delaunay triangulation publisher Tomsk State University journal Geoinformatics. Theory and practice ... Skvortsov The time complexity of triangulation of a polygon with holes has an n log n lower bound . ref name bkos See also Catalan number Point set triangulation Delaunay triangulation Minimum weight triangulation , for a point set and for a simple polygon References reflist Citation ... swf , A Sweep Line algorithm. DEFAULTSORT Polygon Triangulation Category Geometric algorithms ar fa fr Triangulation d un polygone ... more details
orphan date April 2008 unreferenced date August 2008 Triangulation is a Trading strategy strategy whereby a Trader finance trader exploits the relationship between 3 Currency currencies , as 3 pairs. For example, Euro EUR Swiss franc CHF EUR United States dollar USD and USD CHF. EUR USD and USD CHF are USD opposites except for pip value , so if USD is moving, EUR USD and USD CHF should move opposite, but they do not. They move in same direction, but not in appropriate, proportional amount of price . Category Finance Category foreign exchange market ... more details
Naldrett to encourage people to visit triangulation pillars as part of countryside hikes. The Trigpoint ... for hikers. Spain In Spain there are 11000 triangulation stations, concrete buildings which typically ... John Image Beeston Bump 4th November 2007 7 .JPG Triangulation pillar on the Summit of Beeston ... Alban near Nice , France Image U.S. Coast & Geodetic Survey Triangulation Station.jpg U.S. Coast & Geodetic Survey Triangulation Station Image Gorc znak pomiarowy.JPG Trig point in Gorce mountains ... of trig points in New Zealand DEFAULTSORT Triangulation Station Category Surveying Category Geography ... more details
wiktionarypar aeroAero is a Greek prefix relating to flight, and air. It British English it is used as an adjective related to flight as a shortened substitute for aeroplane , as in aero engine Aero may also refer to In aeronautics .aero , the internet top level domain Aeroplane Aerospace engineering Aero Contractors Nigeria , a scheduled airline from Nigeria Aero Contractors US , private charter ... Intelligence Agency. Aero, a United States aircraft manufacturer, later became Aero Design and Engineering Company, and later the Aero Commander division of Rockwell International . Aero Polish airline Aero , a Polish airline founded in 1925 which later was merged into LOT Aero Ltd , a Polish aircraft company A ropostale aviation , a French aviation company Aero Vodochody , a Czech aircraft company Aero Airlines , an Estonian airline owned by Finnair Aero O Y , the name of Finnair until 1953. Aeroflot Russian Airlines Aero makes up the first part of many Latin America n airlines including Aeroper literally translated as Air Peru Aerom xico Aerocondor Aero Condor Peru Aerol neas Argentinas ... Fuso Aero Bus series Hyundai Aero , a bus built by the Hyundai Motor Company Aero automobile , a Czechoslovak automobile Aero Minor , a Czechoslovak automobile SSC Aero , a mid engine sports car ... bridges In computing Windows Aero , a user interface in Windows Vista and Windows 7 Dell Aero , the first smartphone from Dell Nokia Aero , concept phone by Nokia Compaq Aero , a Personal digital assistant In fiction Aero comics , A comic book character associated with the New X Men Aero the Acro Bat , a game by Iguana Entertainment In geography r , an island in Denmark Aero, British Columbia ... Aerodynamic song , by Daft Punk Aerosmith AERO , a 2004 album by Jean Michel Jarre List of Jean Michel Jarre concerts Aero Tribute to the Wind Aero Tribute to the Wind , a 2002 concert by Jean Michel ... founded in 1989 to advance learner centered approaches to education. Akron Aeros Aero chocolate ... more details
Infobox Top level domain name aero background FCC image Image Dotaero.png .aero the domain of aviation ... SITA SC a Dot Aero Council was formed to take input from community various industry associations ... www.icann.org tlds agreements aero ICANN registry agreement disputepolicy UDRP , http www.icann.org ... Procedure CEDRP website http www.information.aero information.aero .aero derived from aeronautics ... sponsored top level domain based on a single industrial theme. The tt aero tt domain is reserved for companies .... It was created in 2002 and is operated by SITA . SITA created and operates the Dot Aero Council . Two letter codes under tt .aero tt are reserved for airlines according to the IATA Airline Designators ... http information.aero news 2008 11 04 08 ref The tt aero tt top level domain was initially approved ... www.icann.org tlds agreements aero sponsorship amendment2 17may07.pdf ref and continued to be renewed ... aero sponsorship amendment6 08dec08.htm.pdf ref In 2009, SITA and ICANN completed a new 10 year sponsorship agreement for the operation of tt aero tt . ref cite web title New .aero sponsorship agreement ... ref References Reflist External links http www.iana.org root whois aero.htm IANA .aero WHOIS info ... registrars List of .aero accredited registrars http www.information.aero index.php?id 11 Dot Aero Council http www.icann.org tlds renewals aero renewal proposal 16dec05.pdf SITA s proposal for renewal of its agreement with ICANN for .aero http forum.icann.org lists aero renewal Public comments on the .aero renewal proposal http information.aero news 2007 10 24 04 Meet the .aero domain name registrars http www.namesbeyond.aero NamesBeyond .aero accredited registrar http www.domainregistry.aero Secura .aero accredited registrar GTLD DEFAULTSORT Aero Category Council of European National Top Level Domain Registries members Category Sponsored top level domains compu domain stub bs .aero ca .aero cs .aero da .aero es .aero fa .aero fr .aero it .aero hu .aero mzn .aero nl .aero ja .aero ... more details
For other uses Aero disambiguation Infobox Album See Wikipedia WikiProject Albums Name AERO Type compilation Artist Jean Michel Jarre Cover AERO album cover.jpg Released September 2004 Recorded 2004 at Croissy Studio Genre Electronica , New Age Length 73 42 Label Warner Music Producer Jean Michel Jarre Reviews Release Music Magazine 7 10 http www.releasemagazine.net Onrecord orjeanmicheljarrea.htm link Last album Geometry of Love br 2003 This album AERO br 2004 Next album Jarre in China br 2005 AERO Anthology of Electronic Revisited Originals is a 2004 album of electronic music by Jean Michel Jarre . It is composed of previously released tracks re recorded in 5.1 surround sound plus three new tracks and a bonus live track. All tracks are sewn together through surround sound scenes . The album .... On the release of AERO , Jarre commented that he had always envisioned his music in surround with the advent ... AERO website. ref However, DVD Audio discs are normally authored to provide surround sound compatible ... are part of the adjacent tracks on the CD. CD Aero Opening 0 50 Oxygene 2 7 41 Aero 3 09 Equinoxe ... bonus track, live version, featuring Safri Duo , recorded at the 2002 AERO concert 7 34 DVD Aero Opening 0 16 Scene 1 0 33 Oxyg ne 2 7 12 Scene 2 0 31 Aero 3 09 Equinoxe 8 1 26 Oxygene 4 4 16 Scene 3 ... Rendez Vous 4 bonus track, live version, featuring Safri Duo , recorded at the 2002 AERO concert 7 35 References reflist External links http www.jeanmicheljarre.com Official AERO website this is now the website for Oxygene 3D http www.jarreuk.com aeroalbum.htm AERO at http www.jarreuk.com Jarre UK http magneticfields.dk kunstnere aero.htm AERO at http magneticfields.dk Magnetic Fields in Danish Jean Michel Jarre DEFAULTSORT Aero Category 2004 compilation albums Category Jean Michel Jarre albums Category Concept albums Category 2004 video albums Category Music video compilation albums es Aero bg AERO fr AERO it AERO ka AERO hu AERO album pl AERO pt A.E.R.O. sv AERO tr AERO ... more details
A S Aero was a Norway Norwegian airline company founded by Tancred Ibsen in January 1920. The company was financed by Tancred Ibsen s uncle, businessman Einar Bj rnson, and two shipowners. Despite the A S for private company limited by shares in its name, A S Aero was never formally registered as a limited company. The company purchased one Hansa Brandenburg W.29 and four Friedrichshafen FF.49 aircraft from Germany in February. This deal was probably illegal as the Triple Entente Entente prohibited the export of German surplus aircraft, but Ibsen nevertheless got permission from the Norwegian Ministry of Defence to import the five German aircraft. During the summer of 1920 A S Aero successly operated demonstration, advertising, and limited mail flights from the Bestumkilen bay in Oslo, with Tancred Ibsen as the head pilot. The company also chartered out airplanes to serve the Det Norske Luftfartrederi routes in southern Norway. Tancred Ibsen soon got tired of his career as a pilot, and the activity of A S Aero ended, with the company becoming part of the aircraft factory in T nsberg , A S Norske Aeroplanfabrik . External links http www.europeanairlines.no ?p 239 Tancred Ibsen and A S Aero Category Defunct airlines of Norway Category Airlines established in 1920 Category Airlines disestablished in 1920 ... more details
Unreferenced date December 2009 A triangulation of a set of points P in the plane geometry plane is a Polygon triangulationtriangulation of the convex hull of P , with all points from P being among the vertices of the triangulation. Triangulations are special cases of planar straight line graph s. There are special triangulations like the Delaunay triangulation which is the Dual polytope geometric dual of the Voronoi diagram . Subsets of the Delaunay triangulation are the Gabriel graph , nearest neighbor graph and the minimal spanning tree . Triangulations have a number of applications, and there is an interest to find a good triangulation for a given point set under some criteria. One of them is a minimum weight triangulation . Sometimes it is desirable to have a triangulation with special properties, e.g., in which all triangles have large angles long and narrow splinter triangles are avoided . Given a set of edges that connect some pairs of the points, the problem to determine whether they contain a triangulation is NP complete Lloyd, 1977 . ref E. L. Lloyd. On triangulations of a set of points in the plane. Proceedings of the 18th Annual IEEE Symposium on Foundations of Computer Science, Providence, Rhode Island, pp. 228 240, 1977. ref Triangulation and convex hull A triangulation of the set of points S in general position may be derived from of the convex hull of a set of points S sub 1 sub in the space of dimension larger by 1 which are the projections of the original point set onto the paraboloid surface math x n 1 x 1 2 cdots x n 2 math . One has to construct the convex hull of the set S sub 1 sub and project it back onto the space of S . If points are not in general position, additional effort is required to triangulate the non tetrahedral facet geometry facet s. See also Polygon triangulation References reflist DEFAULTSORT Point Set Triangulation Category Discrete geometry Category Geometric algorithms de Triangulation Punktemenge fr Triangulation d un ensemble ... more details
for other uses of triangulation to lugag alo disambiguation In the social sciences , triangulation is often used to indicate that more than two methods are used in a study with a view to double or triple checking results. This is also called cross examination . ref Cheng, Liying 2005 . Changing language teaching through language testing a washback study. Cambridge University Press. p. 72. ref The idea is that one can be more confident with a result if different methods lead to the same result. If an investigator uses only one method, the temptation is strong to believe in the findings. If an investigator uses two methods, the results may well clash. By using three methods to get at the answer ..., or both. Triangulation in research Triangulation is a powerful technique that facilitates ... The purpose of triangulation in qualitative research is to increase the credibility and validity of the results. Several scholars have aimed to define triangulation throughout the years.This is considered to be Triangulation Cohen and Manion 1986 define triangulation as an attempt to map out, or explain ... edition . ref Altrichter et al. 2008 contend that triangulation gives a more detailed and balanced ... edition . ref According to O Donoghue and Punch 2003 , triangulation is a method of cross checking ... Types Denzin 1978 identified four basic types of triangulation ref Denzin, N. 2006 . Sociological Methods A Sourcebook. Aldine Transaction. ISBN 9780 202308401. 5th edition . ref Data triangulation involves time, space, and persons Investigator triangulation involves multiple researchers in an investigation Theory triangulation involves using more than one theoretical scheme in the interpretation of the phenomenon Methodological triangulation involves using more than one method to gather data, such as interviews ... www.referenceworld.com sage socialscience triangulation.pdf Types of Triangulation Category Social sciences methodology Category Evaluation methods Link GA de cs Triangulace metodologie de Triangulation ... more details
File 3foottheodoliteramsden.jpg thumb right Three foot Theodolite used in the triangulation The Principal Triangulation of Britain was a triangulation project carried out between 1783 and about 1853 at the instigation of the Director of the Ordnance Survey General William Roy 1726 1790 . In 1782, General Roy had commissioned the building of the Ramsden theodolite from leading instrument maker Jesse Ramsden . The Ramsden theodolite for the first time divided angular scales accurately to within a arcsecond second of arc . General Roy and his team used it to accurately triangulate the distance between the London and Paris observatories. The baseline for this triangulation was established in 1784 between Hampton, London Hampton Poor House and King s Arbour on Hounslow Heath , a distance of just over 27,400 feet. ref http www.remuseum.org.uk biography rem bio roy.htm Major General William Roy biography , Royal Engineers Museum ref ref Michael Knowles, http www.brlsi.org proceedvol7 Astronomy200301.htm THE FRENCH CONNEXION BETWEEN ENGLISH AND FRENCH MAP SURVEYS , Proceedings of the BRLSI Volume 7 2003 ref The triangulation was completed in 1787. The baseline derived during that work, together with the new theodolite, served as the basis for the planning and execution of the subsequent work on the Principal Triangulation. Around 1791, shortly after his death, Roy s team began the field work, using the specially built Ramsden theodolite. In 1794 a seven mile long baseline of verification ... Club Journal Volume 2 Number 5 ref Eventually the triangulation extended to cover the whole of the British ... for accurate land taxing. The Principal Triangulation was subsequently superseded by the Retriangulation ... million. Corrections During subsequent triangulation errors due to atmospheric diffraction, deflection ... and its links to Britain http www.trigtools.co.uk Information and Maps on many aspects of Triangulation & Levelling in Great Britain DEFAULTSORT Principal Triangulation Of Great Britain Category Geography ... more details
In computational geometry and computer science , the minimum weight triangulation MWT problem is the problem of finding a triangulation geometry triangulation of minimal weight. Of particular interest is the problem of finding a minimum weight point set triangulation . Minimum weight triangulation for a finite planar point set The weight of a triangulation of a set of points in the Euclidean plane is defined as the sum of lengths of its edges. The computational complexity of the problem of finding an MWT for a planar point set used to be one of the long standing open problems listed in the seminal book Computers and Intractability by Garey and Johnson. Its decision variant , i.e., the problem of deciding whether there exists a triangulation of weight less than a given weight, was proven to be NP hard in 2006 by W. Mulzer and G. Rote. Their proof is by Reduction complexity reduction from the PLANAR 1 IN 3 SAT ref PLANAR 1 in 3 SAT is a special case of the Boolean satisfiability problem , in which a 3 CNF whose graph is planar graph planar is accepted if there are variable values which satisfy exactly one clause in each literal, see One in three 3SAT . ref problem. ref name mulzer Wolfgang Mulzer, G nter Rote, Minimum Weight Triangulation Is NP Hard , In Proceedings of the 22nd Annual Symposium on Computational Geometry , Sedona, June 5&ndash 7, 2006, http dx.doi.org 10.1145 1137856.1137859 pp. 1&ndash 10 final version in Journal of the ACM , Vol. 55, No. 2, http dx.doi.org 10.1145 1346330.1346336 article 11 , 2008. ref It is not known whether it is NP complete , since this depends on the known open problem whether the sum of radicals may be computed in polynomial time. Mulzer and Rote remark that the problem is NP complete if the edge weights are the rounded lengths. Their result also implies the NP hardness of finding an approximate solution with relative approximation error at most O 1 n sup 2 sup . Minimum weight triangulation for a planar polygon A polygon triangulation ... more details
In computational geometry , a constrained Delaunay triangulation is a generalization of the Delaunay triangulation that forces certain required segments into the triangulation ref cite conference first1 L. Paul last1 Chew title Constrained Delaunay Triangulations booktitle Proceedings of the Third Annual Symposium on Computational Geometry year 1987 ref ref cite journal first1 Jonathan R. last1 Shewchuk title General Dimensional Constrained Delaunay and Constrained Regular Triangulations, I Combinatorial Properties booktitle Discrete & Computational Geometry year 2008 volume 39 issue 1 3 pages 580 637 ref . See Also Chew s second algorithm References Reflist Category Discrete geometry Category Geometric algorithms Category Triangles Category Geometric graphs comp sci theory stub ... more details
Otheruses Triangulation disambiguation In computer vision triangulation refers to the process of determining a point in 3D space given its projections onto two, or more, images. In order to solve this problem it is necessary to know the parameters of the camera projection function from 3D to 2D for the cameras involved, in the simplest case represented by the camera matrix camera matrices . Triangulation is sometimes also referred to as reconstruction . The triangulation problem is in theory trivial ... is involved. Introduction In the following, it is assumed that triangulation is made on corresponding ... for the triangulation. The corresponding projection lines blue do not, in general, intersect in 3D space ... have to be used to recover the true one. The image points used for triangulation are often found ... lines do not intersect. This observation leads to the problem which is solved in triangulation ... methods for computing x sub est sub presented in the literature are briefly described. All triangulation .... Properties of triangulation methods A triangulation method can be described in terms of a function ... triangulation method is chosen for a particular problem depends to some extent on these characteristics ... , mathbf C 1 , mathbf C 2 math . A point in this subset is then a singularity of the triangulation method .... Invariance In some applications, it is desirable that the triangulation is independent of the coordinate system used to represent 3D points if the triangulation problem is formulated in one coordinate ... in the same way. This property is commonly referred to as invariance . Not every triangulation method ... image coordinates math mathbf y k sim mathbf bar C k , mathbf bar x mathbf C k , mathbf x math If the triangulation ... y 2 math For each triangulation method, it can be determined if this last relation is valid. If it is, it may ... of the operations involved may vary between the different methods. Some triangulation methods found ... main Direct linear transformation Via the essential matrix Optimal triangulation References ... more details
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