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# Topic: Triangulation

###### In the News (Fri 19 Jul 19)

 Triangulation - Wikipedia, the free encyclopedia In trigonometry and elementary geometry, triangulation is the process of finding a distance to a point by calculating the length of one side of a triangle, given measurements of angles and sides of the triangle formed by that point and two other reference points. The sum of the angles of a triangle is Ï€ rad or 180 degrees. Triangulation is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision and gun direction of weapons. en.wikipedia.org /wiki/Triangulation   (272 words)

 Triangulation (social science) - Wikipedia, the free encyclopedia In the social sciences, triangulation is often used to indicate that more than one method is used in a study with a view to double (or triple) checking results. Another definition of "triangulation" which is commonly used in the social sciences is the description of when a person, either intentionally or unintentionally pits two others against each other to achieve a desired result or outcome. Triangulation is also used in instances where goods and services are traded from one nation to another, using an intermediate nation. en.wikipedia.org /wiki/Triangulation_(social_science)   (375 words)

 Delaunay triangulation - Wikipedia, the free encyclopedia In mathematics, and computational geometry, the Delaunay triangulation or Delone triangularization for a set P of points in the plane is the triangulation DT(P) of P such that no point in P is inside the circumcircle of any triangle in DT(P). The triangulation was invented by Boris Delaunay in 1934 [1]. Delaunay triangulations are often used to build meshes for the finite element method, because of the angle guarantee and the fact that we know fast triangulation algorithms. en.wikipedia.org /wiki/Delaunay_triangulation   (1126 words)

 Define triangulation - a Whatis.com definition Triangulation is a process by which the location of a radio transmitter can be determined by measuring either the radial distance, or the direction, of the received signal from two or three different points. Triangulation is sometimes used in cellular communications to pinpoint the geographic position of a user. Triangulation apparatus can be confused by the reflection of signals from objects such as large steel-frame buildings, water towers, communications towers, and other obstructions. searchnetworking.techtarget.com /sDefinition/0,,sid7_gci753924,00.html   (302 words)

 When Index Equals Content A triangulation of a polygon D is a division of D into a finite number of triangles so that each edge on the boundary of D belongs to just one triangle of the subdivision, and each edge in the interior of D is shared by exactly two triangles of the subdivision. Triangulate it in any way and label the vertices of the triangulation with the three labels A, B, and C. A triangle in a triangulation is called complete iff its three vertices all received different labels. The vertices of the original triangle are labeled with three different letters A, B, and C. Vertices of the triangulation that lie on the side AB are labeled either A or B. A similar condition holds for the vertices on sides BC and AC. www.cut-the-knot.org /do_you_know/poincare.shtml   (1359 words)

 An Unshellable Triangulation A triangulation is a tessellation of a simply connected polygon by triangles such that no vertex of a triangle lies in the interior of an edge of another triangle. In the plane a triangulation can always be built by starting with one triangle and then adding one triangle at a time so that at every step one has a set of triangles whose union forms a polygon that can be continuously deformed into a square (i.e., it's homeomorphic to a square). A triangulation that can be built by adding one simplex (tetrahedron) at a time such that at every step you have a collection of tetrahedra whose union is homeomorphic to a cube is called shellable. www.math.utah.edu /~alfeld/Rudin.html   (536 words)

 FQS 2(1) Udo Kelle: Sociological Explanations between Micro and Macro and the Integration of Qualitative and ... Thereby it will be shown that an understanding of triangulation in its original trigonometrical sense (although it cannot be considered as a methodological model suitable for all aspects of method integration) may be helpful in gaining a deeper insight into theoretical aspects of method integration in sociology. Hence two meanings of triangulation have emerged in these debates: triangulation as a process of cumulative validation or triangulation as a means to produce a more complete picture of the investigated phenomena. Consequently, the trigonometrical interpretation of triangulation (which may be considered as a strict version of the complementarity approach) seems to provide the most adequate metaphor for the integration of research methods and results concerning the industrial mechanicsÅ½ educational behaviour. qualitative-research.net /fqs-texte/1-01/1-01kelle-e.htm   (7879 words)

 Polygon Triangulation Computing the triangulation of a polygon is a fundamental algorithm in computational geometry. In computer graphics, polygon triangulation algorithms are widely used for tessellating curved geometries, as are described by splines [Kumar and Manocha 1994]. A monotone polygon can be triangulated in linear time by using a simple greedy algorithm which repeatedly cuts off the convex corners of the polygon [Fournier and Montuno 1984]. www.cs.unc.edu /~dm/CODE/GEM/chapter.html   (837 words)

 Transform - Triangulation A triangulation of a point set treats the points as nodes in a network and draws links between them that divides the region between the points into triangular tiles. The Delaunay triangulation is closely related to the Voronoi tiling of a region, as can be seen from the following illustration that shows both a Voronoi tiling as well as a triangulation. The triangulation operators except will transfer column data from source to target (created) objects using whatever transfer rules are in force for the data attribute columns. exchange.manifold.net /manifold/manuals/5_userman/mfd50Transform__Triangulation.htm   (791 words)

 Triangulation, Good Politics -- Bad For The Country: - John Hawkins   (Site not responding. Last check: 2007-10-05) For all intents and purposes, triangulation is the art of trying to be all things to all voters, or at least getting as close as possible. In short, triangulation is political akido that allows you to defeat your opponent by replacing your principles and ideology with polling data. Triangulation is why Bill Clinton, a do-nothing President who couldn't keep his pants up and got caught lying more times than Pinocchio, spent two terms in the White House and was very popular. www.americandaily.com /article/2242   (1002 words)

 ELEPHANT RACING Tech Topic, Triangulation Triangulation allows a chassis to be rigid and lightweight at the same time. Triangulation does not provide rigidity to forces that are applied to structural members mid-span. A visible example of triangulation put to practice on a Porsche 911 is the Elephant Racing Triangulated Strut Brace. www.elephantracing.com /techtopic/triangulation.htm   (439 words)

 Isomorphic Triangulation of Simple Polygons Triangulation of simple polygons is a common problem in Computational Geometry and has applications in many different sciences. In Figure 1, triangle(a, c, d) in P does not map to a triangle in the triangulation of Q, and thus the shown triangulations of P and Q are not isomorphic under the given vertex mapping. Figure 2: A new triangulation of Q such that the triangulations are isomorphic under the given mapping. www.cim.mcgill.ca /~dianag/cgweb   (476 words)

 How to Triangulate With Your Compass Triangulation is a big word for finding the point where two bearings, taken from two different locations, intersect. Another variation on triangulation would be a clue that tells you which direction your two landmarks should be from the letterbox (i.e. Triangulation is a powerful tool for providing precise directions to an otherwise non-descript location and is an easy skill to learn with a bit of practice. www.atlasquest.com /tutorials/compass/triangulation.html   (439 words)

 SDI : Fast & Fully Dynamic Constrained Delaunay Triangulation Library by David Kornmann   (Site not responding. Last check: 2007-10-05) Usually, other triangulation libraries that you will find will require their own data formats, forcing you to have to deal with multiple databases basically representing the same thing. With SDI, it is possible to share the same triangulation database between SDI for the geometry update, the rendering part of your application, and other specific computations, saving them a lot of memory. The memory management is static, which means that all the memory needed for the triangulation sessions is allocated at once when the user defined data is connected to the triangulator. www.dlc.fi /~dkpa   (1359 words)

 Triangulation   (Site not responding. Last check: 2007-10-05) Programs for the Delaunay triangulation of a point set, either in the plane or in higher dimensions, are listed on the pages about convex hull and low-dimensional Voronoi diagrams (since the computations are equivalent!). Programs for the triangulation or trapezoidation of a polygon or a set of line segments in the plane are on the polygon page and on the page about constrained Delaunany triangulation. In GIS, a triangulation of a function (known as a height field), is known as a TIN. www.geom.uiuc.edu /software/cglist/tri.html   (224 words)

 Triangulate   (Site not responding. Last check: 2007-10-05) Triangulation involves creating from the sample points a set of non-overlapping triangularly bounded facets, the vertices of the triangles are the input sample points. There are a number of triangulation algorithms that may be advocated, the more popular algorithms are the radial sweep method and the Watson algorithm which implement Delaunay triangulation. Triangulation based methods honor this situation by giving a large number of triangles and hence more detail to the highly sampled regions and large triangles, less detail, to the regions with a few samples. astronomy.swin.edu.au /~pbourke/terrain/triangulate   (1877 words)

 Applications of 3D Delaunay triangulation algorithms in geoscientific modelling. In this research, Delaunay triangulation procedures have been used in the reconstruction of 3D geometric figures where the complexity of the problem is much greater than the 2D case. Similarly we can obtain a triangulation for higher dimensions, for example in three dimensions if we connect all pairs of points sharing a common facet in the Voronoi diagram, the result is a set of tetrahedra filling the entire domain. The Delaunay triangulation for a set of points is defined only if the points are distinct, so the uniqueness of the points in the given set is treated as a prerequisite for the applicability of this algorithm. www.ncgia.ucsb.edu /conf/SANTA_FE_CD-ROM/sf_papers/lattuada_roberto/paper.html   (3508 words)

 TOOLS, November 2005; Internet Prospector Triangulation is a process used by navigators to determine a location by forming a triangle of the unknown point and two known points. In addition to helping with triangulation, the address look-up is a nice way to find others who might be part of your prospect's personal or corporate network. Triangulation can be useful in identifying prospects, but it does have its limits. www.internet-prospector.org /tool1105.htm   (756 words)

 Triangulation   (Site not responding. Last check: 2007-10-05) The simplest way to triangulate them would be to add to the convex hull diagonals from the first point to all of the others. Higher-dimensional Delaunay triangulations are a special case of higher-dimensional convex hulls, and Qhull [BDH97] appears to be the convex hull code of choice for general dimensions (i.e. Linear-time algorithms for triangulating monotone polygons have been long known [GJPT78] and are the basis of algorithms for triangulating simple polygons. www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE186.HTM   (1143 words)

 Collision detection between moving objects using uniform space subdivision In the third chapter, triangulation of particular VRML shape nodes is described. The bottom is triangulated in the same way as the circular top or bottom of a cylinder. The operation is similar to triangulation of the curved face of a cylinder, but note that the top and the bottom side of the region between the neighbouring parallels are not of the same size. www.cescg.org /CESCG-2001/SSinjur   (4138 words)

 Computing Papers on Triangulation   (Site not responding. Last check: 2007-10-05) Delaunay triangulation when the dual graph is drawn with straight lines, it produces a planar triangulation, D(P), of the Voronoi sites P (if no four sites are cocircular). Theorem 5.5.5- A minimum spanning tree is a subset of the Delaunay triangulation: c. The triangulations are made for correlatable units including the Reef Package and the J-M Reef; the hanging-wall peridotite/dunite buckshot olivine unit; the footwall mafic unit which is made up of norites, melano-norites and bronzite cumulates; several anorthosite units; and mafic dikes. computing.breinestorm.net /triangulation   (639 words)

 Triangulation in Research   (Site not responding. Last check: 2007-10-05) What - Triangulation is the application and combination of several research methodologies in the study of the same phenomenon. Triangulation is the application and combination of several research methodologies in the study of the same phenomenon. Triangulation method is preferred line in the social sciences due to its strengthens to combining multiple observers, theories, methods, and empirical materials in which Sociologists hope to overcome the weakness or intrinsic biases and the problems that come from single method, single-observer, single-theory studies. www.tele.sunyit.edu /traingulation.htm   (1839 words)

 Teacher Research: Trianguating your evidence   (Site not responding. Last check: 2007-10-05) Triangulation: multiple forms of overlapping, diverse pieces of evidence and perspectives. Triangulation is a key tenant of the anthropological approach to data gathering (and therefore, teacher research). As opposed to relying on one single form of evidence or perspective as the basis for findings, multiple forms of diverse and redundant types of evidence are used to check the validity and reliability of the findings (Jacob, 1990; O'Malley & Valdez Pierce, 1996; Maxwell, 1996; Wiggins, 1998). gse.gmu.edu /research/tr/TRtriangulation.shtml   (278 words)

 Triangulation   (Site not responding. Last check: 2007-10-05) Even when we consider only surface triangulations, there are still an exponential number of valid triangulations that all fit the data. We propose selecting a triangulation based on its consistency with this set of images of the object. A typical naive triangulation is obtained by performing a 2D Delaunay triangulation in one of the images and projecting onto 3D. www.cs.cmu.edu /~ddmorris/triangulation   (219 words)

 qdelaunay -- Delaunay triangulation The Delaunay triangulation is the triangulation with empty circumspheres. Each region of the Delaunay triangulation corresponds to a facet of the lower half of the convex hull. To avoid non-simplicial regions either triangulate the output ('Qt') or joggle the input ('QJ'). www.qhull.org /html/qdelaun.htm   (1835 words)

 Triangulation Algorithm   (Site not responding. Last check: 2007-10-05) This section provides an explanation of the Triangulation Algorithm function and how it can be successfully applied in different circumstances. Choose Triangulation algorithm from the Triangulate menu and select new algorithm with transforms.This is the default setting that is suitable for most data sets. Due to the nature of triangulation algorithms it is sometimes possible for the object to have the minimum surface area but display an unacceptable geometry. www.surpac.com /refman/default/tutorials/solids/togglestitchalgorithm.htm   (546 words)

 Graphics Archive - Delaunay triangulation with Qhull by Brad Barber   (Site not responding. Last check: 2007-10-05) The Delaunay triangulation is the triangulation with empty circumcircles for each triangle. The dual of the Delaunay triangulation is the Voronoi diagram. To compute the Delaunay triangulation, project the points to a paraboloid by summing the squares of their coordinates. www.geom.uiuc.edu /graphics/pix/Special_Topics/Computational_Geometry/delaunay.html   (250 words)

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