Relevant bibliographies by topics / Triangulation

Academic literature on the topic 'Triangulation'

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Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Triangulation"

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Mitchell, Scott A. "Finding a Covering Triangulation Whose Maximum Angle is Provably Small." International Journal of Computational Geometry & Applications 07, no. 01n02 (February 1997): 5–20. http://dx.doi.org/10.1142/s021819599700003x.

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We consider the following problem: given a planar straight-line graph, find a covering triangulation whose maximum angle is as small as possible. A covering triangulation is a triangulation whose vertex set contains the input vertex set and whose edge set contains the input edge set. The covering triangulation problem differs from the usual Steiner triangulation problem in that we may not add a vertex on any input edge. Covering triangulations provide a convenient method for triangulating multiple regions sharing a common boundary, as each region can be triangulated independently. We give an explicit lower bound γopt on the maximum angle in any covering triangulation of a particular input graph in terms of its local geometry. Our algorithm produces a covering triangulation whose maximum angle γ is provably close to γopt. Specifically, we show that [Formula: see text], i.e., our γ is not much closer to π than is γopt. To our knowledge, this result represents the first nontrivial bound on a covering triangulation's maximum angle. Our algorithm adds O(n) Steiner points and runs in time O(n log n), where n is the number of vertices of the input. We have implemented an O(n2) time version of our algorithm.
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Wu, Bai Chao, Ai Ping Tang, and Lian Fa Wang. "A Constrained Delaunay Triangulation Algorithm Based on Incremental Points." Applied Mechanics and Materials 90-93 (September 2011): 3277–82. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.3277.

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The foundation ofdelaunay triangulationandconstrained delaunay triangulationis the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generatingconstrained delaunay triangulationin two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures related to constrained edges and polygons. In order to maintain the delaunay criterion largely，some new incremental points are added onto the constrained ones. After the data set is preprocessed, the foundation ofconstrained delaunay triangulationis showed as follows: firstly, the constrained edges and polygons generate initial triangulations，then the remained points completes the triangulation . Some pseudo-codes involved in the algorithm are provided. Finally, some conclusions and further studies are given.
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Keil, J. Mark, and Tzvetalin S. Vassilev. "Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints." Serdica Journal of Computing 4, no. 3 (October 21, 2010): 321–34. http://dx.doi.org/10.55630/sjc.2010.4.321-334.

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We consider sets of points in the two-dimensional Euclidean plane. For a planar point set in general position, i.e. no three points collinear, a triangulation is a maximal set of non-intersecting straight line segments with vertices in the given points. These segments, called edges, subdivide the convex hull of the set into triangular regions called faces or simply triangles. We study two triangulations that optimize the area of the individual triangles: MaxMin and MinMax area triangulation. MaxMin area triangulation is the triangulation that maximizes the area of the smallest area triangle in the triangulation over all possible triangulations of the given point set. Similarly, MinMax area triangulation is the one that minimizes the area of the largest area triangle over all possible triangulations of the point set. For a point set in convex position there are O(n^2 log n) time and O(n^2) space algorithms that compute these two optimal area triangulations. No polynomial time algorithm is known for the general case. In this paper we present an approach to approximation of the MaxMin and MinMax area triangulations of a general point set. The algorithm, based on angular constraints and perfect matchings between triangulations, runs in O(n^3) time and O(n^2) space. We determine the approximation factors as functions of the minimal angles inthe optimal (unknown) triangulation and the approximating one.
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Levcopoulos, Christos, and Drago Krznaric. "Quasi-Greedy Triangulations Approximating the Minimum Weight Triangulation." Journal of Algorithms 27, no. 2 (May 1998): 303–38. http://dx.doi.org/10.1006/jagm.1997.0918.

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 Stanchev, Bozhidar Angelov, and Hristo Ivanov Paraskevov. "CONSTRAINING TRIANGULATION TO LINE SEGMENTS: A FAST METHOD FOR CONSTRUCTING CONSTRAINED DELAUNAY TRIANGULATION." Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application 12, no. 1-2 (2020): 164–78. http://dx.doi.org/10.56082/annalsarscimath.2020.1-2.164.

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"In this paper we present an edge swapping approach for incorporating line segments into triangulation. If the initial triangulation is Delaunay, the algorithm tends to produce optimal Constrained Delaunay triangulation by improving the triangles’ aspect ratios from the local area being constrained. There are two types of methods for constructing Constrained Delaunay Triangulation: straight-forward ones which take both points and line segments as source data and produce constrained triangulation from them at once; and post-processing ones which take an already constructed triangulation and incorporate line segments into it. While most of the existing post-processing approaches clear the triangle’s edges intersected by the line segment being incorporated and fill the opened hole (cavity) by re-triangulating it, the only processing that our algorithm does is to change the triangulation connectivity and to improve the triangles’ aspect ratios through edge swapping. Hereof, it is less expensive in terms of both operating and memory costs. The motivation behind our approach is that most of the existing straight-forward triangulators are too slow and not stable enough. The idea is to use pure Delaunay triangulator to produce an initial Delaunay triangulation and later on to constrain it to the line segments (in other words, to split the processing into two steps, each of which is stable enough and the combination of them works much faster). The algorithm also minimizes the number of the newly introduced triangulation points - new points are added only if any of the line segment’s endpoints does not match an existing triangulation point."
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Cavicchioli, Maddalena. "Acute Triangulations of Trapezoids and Pentagons." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/747128.

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An acute triangulation of a polygon is a triangulation whose triangles have all their angles less than . The number of triangles in a triangulation is called the size of it. In this paper, we investigate acute triangulations of trapezoids and convex pentagons and prove new results about such triangulations with minimum size. This completes and improves in some cases the results obtained in two papers of Yuan (2010).
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Mirzoev, Tigran, and Tzvetalin S. Vassilev. "Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons." Serdica Journal of Computing 4, no. 3 (October 21, 2010): 335–48. http://dx.doi.org/10.55630/sjc.2010.4.335-348.

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We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area triangulations of convex polygons in two dimensions and their algorithmic implications. We improve the algorithm’s running time to quadratic for large classes of convex polygons. We also present experimental results on MaxMin area triangulation.
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BURTON, BENJAMIN A. "FACE PAIRING GRAPHS AND 3-MANIFOLD ENUMERATION." Journal of Knot Theory and Its Ramifications 13, no. 08 (December 2004): 1057–101. http://dx.doi.org/10.1142/s0218216504003627.

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The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal ℙ2-irreducible triangulation. In addition we present constraints upon the combinatorial structure of such a triangulation that can be deduced from its face pairing graph. These results are then applied to the enumeration of closed minimal ℙ2-irreducible 3-manifold triangulations, leading to a significant improvement in the performance of the enumeration algorithm. Results are offered for both orientable and non-orientable triangulations.
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Ramprogus, Vince. "Triangulation." Nurse Researcher 12, no. 4 (April 2005): 4–6. http://dx.doi.org/10.7748/nr2005.04.12.4.4.c5954.

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Singh, Surinder. "Triangulation." London Journal of Primary Care 2, no. 1 (June 2009): 86–87. http://dx.doi.org/10.1080/17571472.2009.11493257.

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Dissertations / Theses on the topic "Triangulation"

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Below, Alexander. "Complexity of triangulation /." [S.l.] : [s.n.], 2002. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=14672.

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Pihlström, Max. "Visual representation by triangulation." Thesis, Uppsala universitet, Institutionen för informationsteknologi, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-264109.

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n this thesis the triangulation is treated as a general-purpose visual representation by investigation of various domain-specific methods such as triangulation interpolation, mesh flows, vertex neighborhood feature measures and re-triangulation for spatial transformations. Suggested new methods include an effective cost for image interpolation based on work by Sederberg et al. and a ridge-edge measure related to the Harris edge detector.
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Trisiripisal, Phichet. "Image Approximation using Triangulation." Thesis, Virginia Tech, 2003. http://hdl.handle.net/10919/33337.

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An image is a set of quantized intensity values that are sampled at a finite set of sample points on a two-dimensional plane. Images are crucial to many application areas, such as computer graphics and pattern recognition, because they discretely represent the information that the human eyes interpret. This thesis considers the use of triangular meshes for approximating intensity images. With the help of the wavelet-based analysis, triangular meshes can be efficiently constructed to approximate the image data. In this thesis, this study will focus on local image enhancement and mesh simplification operations, which try to minimize the total error of the reconstructed image as well as the number of triangles used to represent the image. The study will also present an optimal procedure for selecting triangle types used to represent the intensity image. Besides its applications to image and video compression, this triangular representation is potentially very useful for data storage and retrieval, and for processing such as image segmentation and object recognition.
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Mankiewicz, Piotr, Carsten Schuett, and schuett@math uni-kiel de. "On the Delone Triangulation Numbers." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi952.ps.

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Benderius, Björn. "Laser Triangulation Using Spacetime Analysis." Thesis, Linköping University, Department of Electrical Engineering, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-10522.

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In this thesis spacetime analysis is applied to laser triangulation in an attempt to eliminate certain artifacts caused mainly by reflectance variations of the surface being measured. It is shown that spacetime analysis do eliminate these artifacts almost completely, it is also shown that the shape of the laser beam used no longer is critical thanks to the spacetime analysis, and that in some cases the laser probably even could be exchanged for a non-coherent light source. Furthermore experiments of running the derived algorithm on a GPU (Graphics Processing Unit) are conducted with very promising results.

The thesis starts by deriving the theory needed for doing spacetime analysis in a laser triangulation setup taking perspective distortions into account, then several experiments evaluating the method is conducted.

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Kyle, Stephen Alexander. "Triangulation methods in engineering measurement." Thesis, University College London (University of London), 1988. http://discovery.ucl.ac.uk/1318061/.

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Industrial surveying and photogrammetry are being increasingly applied to the measurement of engineering objects which have typical dimensions in the range 2-100 metres. Both techniques are examples of the principle of triangulation. By applying photocrammetric concepts to surveying methods and vice-versa, a general approach is established which has a number of advantages. In particular. alternative strategies for constructing and analysing measurement networks are developed. These should help to strengthen the geometry and simplify the analysis. The primary results concern the use of non-levelled theodolites, which have applications on board floating objects, and three new suggestions for controlling and computing relative orientations in photogrammetry. These involve reciprocal observations with theodolites. the photographing of linear scales defined by three target points and employing cameras which have been levelled. As a secondary result, some consideration Is given to automation, and instrument design. It is suggested that polarimetry could be successfully applied to improve the transfer of orientation in confined situations, such as in mining. In addition, the potential use of electronic cameras as photo-theodolites is discussed.
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Jaw, Jen-Jer. "Control surface in aerial triangulation /." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu148818889444039.

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Potter, John R. "Pseudo-triangulations on closed surfaces." Worcester, Mass. : Worcester Polytechnic Institute, 2008. http://www.wpi.edu/Pubs/ETD/Available/etd-021408-102227/.

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Pelegris, Gerasimos. "A triangulation method for passive ranging." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1994. http://handle.dtic.mil/100.2/ADA284180.

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Thesis (M.S. in Electrical Engineering and M.S. in Applied Physics)--Naval Postgraduate School, June 1994.
Thesis advisor(s): Pieper, Ron J. ; Cooper, Wlfred W. "June 1994." Includes bibliographical references. Also available online.
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Lemaire, Christophe. "Triangulation de Delaunay et arbres multidimensionnels." Phd thesis, Ecole Nationale Supérieure des Mines de Saint-Etienne, 1997. http://tel.archives-ouvertes.fr/tel-00850521.

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Les travaux effectués lors de cette thèse concernent principalement la triangulation de Delaunay. On montre que la complexité en moyenne - en termes de sites inachevés - du processus de fusion multidimensionnelle dans l'hypothèse de distribution quasi-uniforme dans un hypercube est linéaire en moyenne. Ce résultat général est appliqué au cas du plan et permet d'analyser de nouveaux algorithmes de triangulation de Delaunay plus performants que ceux connus à ce jour. Le principe sous-jacent est de diviser le domaine selon des arbres bidimensionnels (quadtree, 2d-tree, bucket-tree. . . ) puis de fusionner les cellules obtenues selon deux directions. On étudie actuellement la prise en compte de contraintes directement pendant la phase de triangulation avec des algorithmes de ce type. De nouveaux algorithmes pratiques de localisation dans une triangulation sont proposés, basés sur la randomisation à partir d'un arbre binaire de recherche dynamique de type AVL, dont l'un est plus rapide que l'algorithme optimal de Kirkpatrick, au moins jusqu'à 12 millions de sites K Nous travaillons actuellement sur l'analyse rigoureuse de leur complexité en moyenne. Ce nouvel algorithme est utilisé pour construire " en-ligne " une triangulation de Delaunay qui est parmi les plus performantes des méthodes " en-ligne " connues à ce jour.
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Books on the topic "Triangulation"

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Whitaker, Phil. Triangulation. New York: Picador USA, 1999.

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Amoretti, Maria Cristina, and Gerhard Preyer, eds. Triangulation. Berlin, Boston: DE GRUYTER, 2011. http://dx.doi.org/10.1515/9783110326833.

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Flick, Uwe. Triangulation. Wiesbaden: VS Verlag für Sozialwissenschaften, 2008. http://dx.doi.org/10.1007/978-3-531-91976-8.

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Flick, Uwe. Triangulation. Wiesbaden: VS Verlag für Sozialwissenschaften, 2004. http://dx.doi.org/10.1007/978-3-322-97512-6.

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Flick, Uwe. Triangulation. Wiesbaden: VS Verlag für Sozialwissenschaften, 2011. http://dx.doi.org/10.1007/978-3-531-92864-7.

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Wolfgang, Kühnel. Tight polyhedral submanifolds and tight triangulations. New York: Springer-Verlag, 1995.

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Lüdemann, Jasmin, and Ariane Otto, eds. Triangulation und Mixed-Methods. Wiesbaden: Springer Fachmedien Wiesbaden, 2019. http://dx.doi.org/10.1007/978-3-658-24225-1.

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Skvortsov, Alexey V. Delaunay triangulation and its applications. Tomsk: Tomsk state university, 2002. http://dx.doi.org/10.17273/book.2002.1.

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Alber, Ina, Birgit Griese, and Martina Schiebel, eds. Biografieforschung als Praxis der Triangulation. Wiesbaden: Springer Fachmedien Wiesbaden, 2018. http://dx.doi.org/10.1007/978-3-658-18861-0.

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Anagnostou, Efthymios. Progress in minimum weight triangulation. Toronto: University of Toronto, Dept. of Computer Science, 1990.

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Book chapters on the topic "Triangulation"

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Flick, Uwe. "Einleitung." In Triangulation, 7–10. Wiesbaden: VS Verlag für Sozialwissenschaften, 2004. http://dx.doi.org/10.1007/978-3-322-97512-6_1.

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Flick, Uwe. "Geschichte und Theorie der Triangulation." In Triangulation, 11–26. Wiesbaden: VS Verlag für Sozialwissenschaften, 2004. http://dx.doi.org/10.1007/978-3-322-97512-6_2.

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Flick, Uwe. "Methoden-Triangulation in der qualitativen Forschung." In Triangulation, 27–49. Wiesbaden: VS Verlag für Sozialwissenschaften, 2004. http://dx.doi.org/10.1007/978-3-322-97512-6_3.

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Flick, Uwe. "Triangulation in der Ethnographie." In Triangulation, 51–66. Wiesbaden: VS Verlag für Sozialwissenschaften, 2004. http://dx.doi.org/10.1007/978-3-322-97512-6_4.

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Flick, Uwe. "Triangulation qualitativer und quantitativer Forschung." In Triangulation, 67–85. Wiesbaden: VS Verlag für Sozialwissenschaften, 2004. http://dx.doi.org/10.1007/978-3-322-97512-6_5.

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Flick, Uwe. "Planung und Durchführung einer Triangulationsstudie." In Triangulation, 87–102. Wiesbaden: VS Verlag für Sozialwissenschaften, 2004. http://dx.doi.org/10.1007/978-3-322-97512-6_6.

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Flick, Uwe. "Einleitung." In Triangulation, 7–10. Wiesbaden: VS Verlag für Sozialwissenschaften, 2011. http://dx.doi.org/10.1007/978-3-531-92864-7_1.

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Flick, Uwe. "Geschichte und Theorie der Triangulation." In Triangulation, 11–26. Wiesbaden: VS Verlag für Sozialwissenschaften, 2011. http://dx.doi.org/10.1007/978-3-531-92864-7_2.

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Flick, Uwe. "Methoden-Triangulation in der qualitativen Forschung." In Triangulation, 27–50. Wiesbaden: VS Verlag für Sozialwissenschaften, 2011. http://dx.doi.org/10.1007/978-3-531-92864-7_3.

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Flick, Uwe. "Triangulation in der Ethnographie." In Triangulation, 51–74. Wiesbaden: VS Verlag für Sozialwissenschaften, 2011. http://dx.doi.org/10.1007/978-3-531-92864-7_4.

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Conference papers on the topic "Triangulation"

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Saalfeld, A. "Joint triangulations and triangulation maps." In the third annual symposium. New York, New York, USA: ACM Press, 1987. http://dx.doi.org/10.1145/41958.41979.

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Herrmann, Michael, Shany Christian Islam, and René Beigang. "THz Triangulation." In Optical Terahertz Science and Technology. Washington, D.C.: OSA, 2007. http://dx.doi.org/10.1364/otst.2007.me7.

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Soltanaghaei, Elahe, Avinash Kalyanaraman, and Kamin Whitehouse. "Multipath Triangulation." In MobiSys '18: The 16th Annual International Conference on Mobile Systems, Applications, and Services. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3210240.3210347.

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Opitz, Felix, and Guy Kouemou. "Triangulation and Deghosting." In 2006 International Radar Symposium. IEEE, 2006. http://dx.doi.org/10.1109/irs.2006.4338143.

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Kukelova, Zuzana, and Viktor Larsson. "Radial Distortion Triangulation." In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2019. http://dx.doi.org/10.1109/cvpr.2019.00991.

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Hu, Xiaocheng, Yufei Tao, and Chin-Wan Chung. "Massive graph triangulation." In the 2013 international conference. New York, New York, USA: ACM Press, 2013. http://dx.doi.org/10.1145/2463676.2463704.

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Pantelyuk, P. A. "Triangulation error prediction." In X All-Russian Scientific Conference "System Synthesis and Applied Synergetics". Southern Federal University, 2021. http://dx.doi.org/10.18522/syssyn-2021-48.

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Hammersley, Richard, and Hong-Qian (Karen) Lu. "Decremental Delaunay triangulation." In ACM SIGGRAPH 99 Conference abstracts and applications. New York, New York, USA: ACM Press, 1999. http://dx.doi.org/10.1145/311625.312128.

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Lindstrom, Peter. "Triangulation made easy." In 2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2010. http://dx.doi.org/10.1109/cvpr.2010.5539785.

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Mayfield, James, and Paul McNamee. "Triangulation without translation." In the 27th annual international conference. New York, New York, USA: ACM Press, 2004. http://dx.doi.org/10.1145/1008992.1009085.

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Reports on the topic "Triangulation"

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Edelsbrunner, H., Ho-Lun Cheng, T. K. Dey, and J. Sullivan. Dynamic Skin Triangulation. Fort Belvoir, VA: Defense Technical Information Center, January 2001. http://dx.doi.org/10.21236/ada410934.

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Engel, Daniel, and Matthew J. O'Brien. Surface Triangulation for CSG in Mercury. Office of Scientific and Technical Information (OSTI), August 2015. http://dx.doi.org/10.2172/1236744.

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D`Azevedo, E. F., C. H. Romine, and J. M. Donato. Coefficient adaptive triangulation for strongly anisotropic problems. Office of Scientific and Technical Information (OSTI), January 1996. http://dx.doi.org/10.2172/221032.

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Bernal, J., and C. Witzgall. Triangulation-based L1-fitting of terrain surfaces. Gaithersburg, MD: National Institute of Standards and Technology, 1999. http://dx.doi.org/10.6028/nist.ir.6346.

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Nguyen, Hoa G., and Michael R. Blackburn. A Simple Method for Range Finding via Laser Triangulation. Fort Belvoir, VA: Defense Technical Information Center, January 1995. http://dx.doi.org/10.21236/ada292529.

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Whiteside, T. S. A Triangulation Method for Identifying Hydrostratigraphic Locations of Well Screens. Office of Scientific and Technical Information (OSTI), January 2015. http://dx.doi.org/10.2172/1171996.

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Hardwick, Jonathan C. Implementation and Evaluation of an Efficient 2D Parallel Delaunay Triangulation Algorithm,. Fort Belvoir, VA: Defense Technical Information Center, April 1997. http://dx.doi.org/10.21236/ada328005.

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Turner, Daniel Z. An overview of the stereo correlation and triangulation formulations used in DICe. Office of Scientific and Technical Information (OSTI), February 2017. http://dx.doi.org/10.2172/1367484.

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Chaconas, Karen. Range from triangulation using an inverse perspective method to determine relative camera pose. Gaithersburg, MD: National Institute of Standards and Technology, 1990. http://dx.doi.org/10.6028/nist.ir.4385.

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Bruce, W. A., D. J. Romer, D. M. Barborak, and D. Yapp. PR-185-9316-R01 Development of a Laser-Based System for Mapping External Corrosion Damage on Pipeline. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), May 1995. http://dx.doi.org/10.55274/r0011926.

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Describes a simple laser-based system that can be used in the field to accurately and efficiently measure corrosion damage on the external surface of an exposed pipeline. The system that was developed uses a laser-based range sensor that projects a stripe of laser light on the pipe surface then uses optical triangulation to construct three-dimensional contour maps of corroded areas. Software that incorporates the RSTRENG method was developed for use in assessing corroded areas in these contour maps.
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