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Relevant bibliographies by topics / Delaunay triangle

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Academic literature on the topic 'Delaunay triangle'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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Journal articles on the topic "Delaunay triangle"

1

zhou, Longquan, Hongjuan Wang, Xinming Lu, Wei Zhang, and Xingli Zhang. "Algorithm for Curved Surface Mesh Generation Based on Delaunay Refinement." International Journal of Pattern Recognition and Artificial Intelligence 34, no. 04 (July 29, 2019): 2050007. http://dx.doi.org/10.1142/s021800142050007x.

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Curved surface mesh generation is a key step for many areas. Here, a mesh generation algorithm for closed curved surface based on Delaunay refinement is proposed. We focus on improving the shape quality of the meshes generated and making them conform to 2-manifold. The Delaunay tetrahedralization of initial sample is generated first, the initial surface mesh which is a subset of the Delaunay tetrahedralization can be achieved. A triangle is refined by inserting a new point if it is large or of bad quality. For each sample, we also check the triangles that adjoin it whether from a topological disk. If not, the largest triangle will be refined. Finally, the surface mesh is updated after a new point is inserted into the sample. The definition of mesh size function for surface mesh generation is also put in this paper. Meshing experiments of some models demonstrate that the new algorithm is advantageous in generating high quality surface mesh, the count of mesh is suitable and can well approximate the curved surface. The presented method can be used for a wide range of problems including computer graphics, computer vision and finite element method.

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Kreslin, Rok, Pilar M. Calvo, Luis G. Corzo, and Peter Peer. "Linear Chromatic Adaptation Transform Based on Delaunay Triangulation." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/760123.

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Computer vision algorithms that use color information require color constant images to operate correctly. Color constancy of the images is usually achieved in two steps: first the illuminant is detected and then image is transformed with the chromatic adaptation transform (CAT). Existing CAT methods use a single transformation matrix for all the colors of the input image. The method proposed in this paper requires multiple corresponding color pairs between source and target illuminants given by patches of the Macbeth color checker. It uses Delaunay triangulation to divide the color gamut of the input image into small triangles. Each color of the input image is associated with the triangle containing the color point and transformed with a full linear model associated with the triangle. Full linear model is used because diagonal models are known to be inaccurate if channel color matching functions do not have narrow peaks. Objective evaluation showed that the proposed method outperforms existing CAT methods by more than 21%; that is, it performs statistically significantly better than other existing methods.

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Liu, Yong, and Yanwei Zheng. "Accurate Volume Calculation Driven by Delaunay Triangulation for Coal Measurement." Scientific Programming 2021 (April 16, 2021): 1–10. http://dx.doi.org/10.1155/2021/6613264.

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Volume calculation from 3D point cloud is widely used in engineering and applications. The existing methods either have large errors or are time-consuming. This paper focuses on the coal measurement. Based on the triangular mesh generated from the point cloud, each triangle is projected downward to the base plane to form a voxel. We derive the calculation formula of voxel by an integral method, which is more efficient than the method of decomposing voxel into tetrahedrons and more accurate than slicing methods. Furthermore, this paper proposes a Delaunay triangulation-driven volume calculation (DTVC) method. DTVC does not preserve the Delaunay triangles but directly calculates the volume in the process of triangulation. It saves memory and running time. Experimental results show that DTVC has achieved a good balance between error and efficiency.

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Morrison, Paul, and Ju Jia Zou. "Triangle refinement in a constrained Delaunay triangulation skeleton." Pattern Recognition 40, no. 10 (October 2007): 2754–65. http://dx.doi.org/10.1016/j.patcog.2006.12.021.

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MURPHY, MICHAEL, DAVID M. MOUNT, and CARL W. GABLE. "A POINT-PLACEMENT STRATEGY FOR CONFORMING DELAUNAY TETRAHEDRALIZATION." International Journal of Computational Geometry & Applications 11, no. 06 (December 2001): 669–82. http://dx.doi.org/10.1142/s0218195901000699.

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A strategy is presented to find a set of points that yields a Conforming Delaunay tetrahedralization of a three-dimensional Piecewise-Linear complex (PLC). This algorithm is novel because it imposes no angle restrictions on the input PLC. In the process, an algorithm is described that computes a planar conforming Delaunay triangulation of a Planar Straight-Line Graph (PSLG) such that each triangle has a bounded circumradius, which may be of independent interest.

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Dym, Nadav, Raz Slutsky, and Yaron Lipman. "Linear variational principle for Riemann mappings and discrete conformality." Proceedings of the National Academy of Sciences 116, no. 3 (December 28, 2018): 732–37. http://dx.doi.org/10.1073/pnas.1809731116.

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We consider Riemann mappings from bounded Lipschitz domains in the plane to a triangle. We show that in this case the Riemann mapping has a linear variational principle: It is the minimizer of the Dirichlet energy over an appropriate affine space. By discretizing the variational principle in a natural way we obtain discrete conformal maps which can be computed by solving a sparse linear system. We show that these discrete conformal maps converge to the Riemann mapping in H1, even for non-Delaunay triangulations. Additionally, for Delaunay triangulations the discrete conformal maps converge uniformly and are known to be bijective. As a consequence we show that the Riemann mapping between two bounded Lipschitz domains can be uniformly approximated by composing the discrete Riemann mappings between each Lipschitz domain and the triangle.

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Dereudre, David, and Hans-Otto Georgii. "Variational Characterisation of Gibbs Measures with Delaunay Triangle Interaction." Electronic Journal of Probability 14 (2009): 2438–62. http://dx.doi.org/10.1214/ejp.v14-713.

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Zhang, Zi Xian, Ichiro Hagiwara, Maria Savchenko, Yi Xiong Feng, and Junichi Shinoda. "A Novel Tetrahedral Mesh Generation Algorithm for Finite Element Analysis." Advanced Materials Research 189-193 (February 2011): 545–48. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.545.

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In this paper, a robust tetrahedral mesh generation method based on Advancing Front technique is proposed. The proposed method inherits advantages of Delaunay method and Advancing Front method, such as efficiency of Delaunay method and maintaining the given boundary triangle mesh exactly of advancing front method. Tetrahedral mesh is generated from the given triangle surface mesh. This method mainly includes three stages. Firstly, the minimum container box of the triangular surface mesh is calculated and points are inserted into the box. Then the proper point is selected out to generate tetrahedron’s layers from surface to the interior volume of the model, so g the surface mesh can be maintained. The operation is simplified, and calculation efficiency is also higher than common Advancing Front method. At last, triangle intersection is examined. This technique allows generating the tetrahedral mesh with high quality elements with surface mesh preservation. A shoes model with both convex and concave surface is chosen for the experiment. The result clarified the robust and high efficiency of the proposed algorithm.

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Xi, Jian Hui, and Shan Chao Zuo. "An Improved Algorithm Based on Incremental Insertion in Delaunay Triangulation." Applied Mechanics and Materials 397-400 (September 2013): 1691–94. http://dx.doi.org/10.4028/www.scientific.net/amm.397-400.1691.

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Target position is a critical step in the process of constructing Delaunay triangulation. This paper establishes an improved incremental insertion method which realizes fast location based on moving center of gravity along the search direction. It is effective to solve unstable searching path problem usually occurring in some special cases, such as the line from target point to current center of gravity passes through a vertex of a triangle or coincides with a triangle edge. Simulation results show that there exists only location path using this method and the constructing efficiency is increased.

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FORTUNE, STEVEN. "NUMERICAL STABILITY OF ALGORITHMS FOR 2D DELAUNAY TRIANGULATIONS." International Journal of Computational Geometry & Applications 05, no. 01n02 (March 1995): 193–213. http://dx.doi.org/10.1142/s0218195995000118.

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We consider the correctness of 2-d Delaunay triangulation algorithms implemented using floating-point arithmetic. The α-pseudocircle through points a, b, c consists of three circular arcs connecting ab, bc, and ac, each arc inside the circumcircle of a, b, c and forming angle α with the circumcircle; a triangulation is α-empty if the α-pseudocircle through the vertices of each triangle is empty. We show that a simple Delaunay triangulation algorithm—the flipping algorithm—can be implemented to produce O(n∈)-empty triangulations, where n is the number of point sites and ∈ is the relative error of floating-point arithmetic; its worst-case running time is O(n2). We also discuss floating-point implementation of other 2-d Delaunay triangulation algorithms.

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Dissertations / Theses on the topic "Delaunay triangle"

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Choung, Yunjae. "Extraction of blufflines from 2.5 dimensional Delaunay triangle mesh using LiDAR data." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1251138890.

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Satonobu, Kuniko. "Cercle, triangle, carré : analyse des formes élémentaires et des procédés dans l'oeuvre abstraite de Sonia Delaunay." Paris 1, 1992. http://www.theses.fr/1992PA010502.

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Cette étude sur Sonia Delaunay est essentiellement une tentative d'interprétation de son œuvre abstraite (la période 1930-79). En se limitant aux recherches sur les formes élémentaires de ses compositions et les procédés inhérents à celles-ci, je voudrais expliciter la méthode de travail de Sonia. Dans ce but, nous remontons aux années dix pour déceler la genèse des formes élémentaires et nous poursuivons nos recherches sur sa création des années vingt dans le domaine de l'art appliqué. Partie I : je montre comment le cercle, le triangle et le carré apparaissent dans l'œuvre des années dix. Partie II : je mets en évidence l'évolution de ces formes à travers ses activités des années vingt dans le domaine de la mode, de la danse et des costumes. Partie III : j'analyse sa création sur tissu, les formes élémentaires et les procédés (décaler, tourner, inverser, agrandir, étendre). Partie IV : après avoir donné un aperçu chronologique de l'évolution générale de l'œuvre abstraite de 1930 à 1979, j'examine d'abord les œuvres avec d'un seul motif et puis celles de deux ou de trois motifs; dans cet combinaison de motifs, les méthodes employées dans la création sur tissu joue un rôle essentiel
Sonia delaunay's late work (1930-1979) is the main subject of this analysis which wants to show (1) how she composes her abstract works of that period and (2) how her works are related to her earlier experiences. We find that it is deaply rooted in her activities as a designer of fashion and patterns for textile fabrics in the 1920s and in her early achievements in painting as well as the common research on the concepts of simultaneity with her husband robert. In her works as a fashion and textil designer she invented and applied extensively her basic vocabulary of mainly geometric forms and her workingmethods (manipulating a motif by turning, reversing stretching, splitting) which she used later in her abstract work. For example, in her famous series of the sixties combinig three motifs (triptych) and indifferently called "rythme couleur", she practices clearly these methods to unite the different parts harmoniously. We can conclude that her way of creating abstract works is based on her activity in the field of the applied arts

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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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Hung, Chen-Ming, and 陳明宏. "Precision Analysis of Digitized Cadastral Map Using Delaunay Triangle Coordinate Transformation." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/62920201056806336955.

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碩士
國立成功大學
地球科學系專班
96
Applying the cadastral maps drawed during the Japanese colonial period in the current land survey correction could be distracting due to inconsistent of coordinate systems. Accuracy of land survey correction results seems to be somehow controvertible for general land owners. In the reservation of cadastral maps, maps usually could not be jointed with whole areas but only reluctantly jointed partially. This study is based on Taiwan digital cadastral map from the ministry of the interior, using third-class satellite control points, reliable state points from land survey correction of land offices, and road central piles as the common points to build up Delaunay triangulation for affine transformations. Transforming old cadastral maps from TWD67 system to the new framework of TWD97 coordinate system to proceed common boundary point positioning, land parcel length, and area accuracy analysis. The result of this research showing that, coordinate transformation result is better while using third-class satellite control points with reliable state points to construct Delaunay triangulation from the testing densely area of urban constructions, with point positioning root mean square deviation of RMS(εN）±19.5cm and RMS(εE）of ±21.9 cm. When increasing reliable state point as conditions, acute angle in Delaunay triangulation should be avoided. The mistakes from old cadastral maps are caused by historical causes, and current corrections still can not recover 100% of its original states. The quality of surveyors, current actual land usage, disputions and other factors could all effect the coordinate transformation result of Delaunay triangulation. Even though it can not fully satisfy the accuracy of urban boundary surveying numerical method, but it can still be provided as the references for lead process of land survey correction. How to apply digital cadastral map results and improve land survey correction accuracy in order to accord with current regulations and practical needs will remain as the arduously goal.

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Tu, Xi. "Image representation with explicit discontinuities using triangle meshes." Thesis, 2012. http://hdl.handle.net/1828/4264.

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Triangle meshes can provide an effective geometric representation of images. Although many mesh generation methods have been proposed to date, many of them do not explicitly take image discontinuities into consideration. In this thesis, a new mesh model for images, which explicitly represents discontinuities (i.e., image edges), is proposed along with two corresponding mesh-generation methods that determine the mesh-model parameters for a given input image. The mesh model is based on constrained Delaunay triangulations (DTs), where the constrained edges correspond to image edges. One of the proposed methods is named explicitly-represented discontinuities-with error diffusion (ERDED), and is fast and easy to implement. In the ERDED method, the error diffusion (ED) scheme is employed to select a subset of sample points that are not on the constrained edges. The other proposed method is called ERDGPI. In the ERDGPI method, a constrained DT is first constructed with a set of prespecified constrained edges. Then, the greedy point insertion (GPI) scheme is employed to insert one point into the constrained DT in each iteration until a certain number of points is reached. The ERDED and ERDGPI methods involve several parameters which must be provided as input. These parameters can affect the quality of the resulting image approximations, and are discussed in detail. We also evaluate the performance of our proposed ERDED and ERDGPI methods by comparing them with the highly effective ED and GPI schemes. Our proposed methods are demonstrated to be capable of producing image approximations of higher quality both in terms of PSNR and subjective quality than those generated by other schemes. For example, the reconstructed images produced by the proposed ERDED method are often about 3.77 dB higher in PSNR than those produced by the ED scheme, and our proposed ERDGPI scheme produces image approximations of about 1.08 dB higher PSNR than those generated by the GPI approach.
Graduate

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EL, Marzouki Badr Eddine. "An improved incremental/decremental delaunay mesh-generation strategy for image representation." Thesis, 2016. http://hdl.handle.net/1828/7670.

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Two highly effective content-adaptive methods for generating Delaunay mesh models of images, known as IID1 and IID2, are proposed. The methods repeatedly alternate between mesh simplification and refinement, based on the incremental/decremental mesh-generation framework of Adams, which has several free parameters. The effect of different choices of the framework's free parameters is studied, and the results are used to derive two mesh-generation methods that differ in computational complexity. The higher complexity IID2 method generates mesh models of superior reconstruction quality, while the lower complexity IID1 method trades mesh quality in return for a decrease in computational cost. Some of the contributions of our work include the recommendation of a better choice for the growth-schedule parameter of the framework, as well as the use of Floyd-Steinberg error diffusion for the initial-mesh selection. As part of our work, we evaluated the performance of the proposed methods using a data set of 50 images varying in type (e.g., photographic, computer generated, and medical), size and bit depth with multiple target mesh densities ranging from 0.125% to 4%. The experimental results show that our proposed methods perform extremely well, yielding high-quality image approximations in terms of peak-signal-to-noise ratio (PSNR) and subjective visual quality, at an equivalent or lower computational cost compared to other well known approaches such as the ID1, ID2, and IDDT methods of Adams, and the greedy point removal (GPR) scheme of Demaret and Iske. More specifically, the IID2 method outperforms the GPR scheme in terms of mesh quality by 0.2-1.0 dB with a 62-93% decrease in computational cost. Furthermore, the IID2 method yields meshes of similar quality to the ID2 method at a computational cost that is lower by 9-41%. The IID1 method provides improvements in mesh quality in 93% of the test cases by margins of 0.04-1.31 dB compared to the IDDT scheme, while having a similar complexity. Moreover, reductions in execution time of 4-59% are achieved compared to the ID1 method in 86% of the test cases.
Graduate
0544, 0984, 0537
marzouki@uvic.ca

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Tsai, Chien-Chang, and 蔡建彰. "Using Delaunay Triangle to emplement framework of Coordinate Transformation within an integrated geo-spatial information system." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/57246884789892856879.

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碩士
國立成功大學
地球科學系專班
94
Abstract The cadastral maps currently used in Taiwan are the mounted duplicates of maps drawn during the 7-year period after the Japanese dispatched surveyors to Taiwan in 1894. The originals were destroyed in the bombing raids of Allied forces near the end of World War Two. Although the cadastral map renewal procedure started in 1975 using TWD67 2TM coordinates, it is still far from being a complete or effective update. From a judicial viewpoint, although old cadastral maps are in extremely poor condition, they are still legally valid. After Chi-Chi earthquake in 1999, the new TWD97 2TM coordinates and TWVD2000 vertical reference system were deployed over all islands as basis for Taiwan spatial data infrastructure (TSDI). Regardless of what cutting-edge surveying technology is used, it is very difficult in practice to integrate a seamless digital cadastral map solely based on these maps. Creating an integrated and automated coordinates transformation process model within a spatial information system for various application schemes remains an imperative task. To this day, now that GPS is providing a promising solution, a densification of 3rd order control points upto every 2 km interval. This study investigates the framework of multiple affine transformations between TWD67 and TWD97 with these control points in Tainan county SDI using the algorithm of Delaunay triangle. The proposed process not only provides reliable scale and angle deformation, but also preseves the spatial topology of cadastral parcels. The test shows this method is accurate, convenient and consistent. A numical example is included.

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Luo, Jun. "Effective techniques for generating Delaunay mesh models of single- and multi-component images." Thesis, 2018. https://dspace.library.uvic.ca//handle/1828/10436.

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In this thesis, we propose a general computational framework for generating mesh models of single-component (e.g., grayscale) and multi-component (e.g., RGB color) images. This framework builds on ideas from the previously-proposed GPRFSED method for single-component images to produce a framework that can handle images with any arbitrary number of components. The key ideas embodied in our framework are Floyd-Steinberg error diffusion and greedy-point removal. Our framework has several free parameters and the effect of the choices of these parameters is studied. Based on experimentation, we recommend two specific sets of parameter choices, yielding two highly effective single/multi-component mesh-generation methods, known as MED and MGPRFS. These two methods make different trade offs between mesh quality and computational cost. The MGPRFS method is able to produce high quality meshes at a reasonable computational cost, while the MED method trades off some mesh quality for a reduction in computational cost relative to the MGPRFS method. To evaluate the performance of our proposed methods, we compared them to three highly-effective previously-proposed single-component mesh generators for both grayscale and color images. In particular, our evaluation considered the following previously-proposed methods: the error diffusion (ED) method of Yang et al., the greedy-point-removal from-subset (GPRFSED) method of Adams, and the greedy-point removal (GPR) method of Demaret and Iske. Since these methods cannot directly handle color images, color images were handled through conversion to grayscale as a preprocessing step, and then as a postprocessing step after mesh generation, the grayscale sample values in the generated mesh were replaced by their corresponding color values. These color-capable versions of ED, GPRFSED, and GPR are henceforth referred to as CED, CGPRFSED, and CGPR, respectively. Experimental results show that our MGPRFS method yields meshes of higher quality than the CGPRFSED and GPRFSED methods by up to 7.05 dB and 2.88 dB respectively, with nearly the same computational cost. Moreover, the MGPRFS method outperforms the CGPR and GPR methods in mesh quality by up to 7.08 dB and 0.42 dB respectively, with about 5 to 40 times less computational cost. Lastly, our MED method yields meshes of higher quality than the CED and ED methods by up to 7.08 and 4.72 dB respectively, where all three of these methods have a similar computational cost.
Graduate

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Feng, Xiao. "A Novel Progressive Lossy-to-Lossless Coding Method for Mesh Models of Images." Thesis, 2015. http://hdl.handle.net/1828/6395.

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A novel progressive lossy-to-lossless coding method is proposed for mesh models of images whose underlying triangulations have arbitrary connectivity. For a triangulation T of a set P of points, our proposed method represents the connectivity of T as a sequence of edge flips that maps a uniquely-determined Delaunay triangulation (i.e., preferred-directions Delaunay triangulation) of P to T. The coding efficiency of our method is highest when the underlying triangulation connectivity is close to Delaunay, and slowly degrades as connectivity moves away from being Delaunay. Through experimental results, we show that our proposed coding method is able to significantly outperform a simple baseline coding scheme. Furthermore, our proposed method can outperform traditional connectivity coding methods for meshes that do not deviate too far from Delaunay connectivity. This result is of practical significance since, in many applications, mesh connectivity is often not so far from being Delaunay, due to the good approximation properties of Delaunay triangulations.
Graduate

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Nicholls, Gareth Michael. "Location inaccuracies in WSAN placement algorithms." Diss., 2010. http://hdl.handle.net/2263/26682.

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The random deployment of Wireless Sensor and Actuator Network (WSAN) nodes in areas often inaccessible, results in so-called coverage holes – i.e. areas in the network that are not adequately covered by nodes to suit the requirements of the network. Various coverage protocol algorithms have been designed to reduce or eliminate coverage holes within WSANs by indicating how to move the nodes. The effectiveness of such coverage protocols could be jeopardised by inaccuracy in the initial node location data that is broadcast by the respective nodes. This study examines the effects of location inaccuracies on five sensor deployment and reconfiguration algorithms – They include two algorithms which assume that mobile nodes are deployed (referred to as the VEC and VOR algorithms); two that assume static nodes are deployed (referred to as the CNPSS and OGDC algorithms); and a single algorithm (based on a bidding protocol) that assumes a hybrid scenario in which both static and mobile nodes are deployed. Two variations of this latter algorithm are studied. A location simulation tool was built using the GE Smallworld GIS application and the Magik programming language. The simulation results are based on three above-mentioned deployment scenarios; mobile, hybrid and static. The simulation results suggest the VOR algorithm is reasonably robust if the location inaccuracies are somewhat lower than the sensing distance and also if a high degree of inaccuracy is limited to a relatively small percentage of the nodes. The VEC algorithm is considerably less robust, but prevents nodes from drifting beyond the boundaries in the case of large inaccuracies. The bidding protocol used by the hybrid algorithm appears to be robust only when the static nodes are accurate and there is a low degree of inaccuracy within the mobile nodes. Finally the static algorithms are shown to be the most robust; the CPNSS algorithm appears to be immune to location inaccuracies whilst the OGDC algorithm was shown to reduce the number of active nodes in the network to a better extent than that of the CPNSS algorithm. Copyright
Dissertation (MSc)--University of Pretoria, 2010.
Computer Science
unrestricted

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Book chapters on the topic "Delaunay triangle"

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Bærentzen, Jakob Andreas, Jens Gravesen, François Anton, and Henrik Aanæs. "Triangle Mesh Generation: Delaunay Triangulation." In Guide to Computational Geometry Processing, 241–61. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-4075-7_14.

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Yang, Wencheng, Jiankun Hu, Song Wang, and Jucheng Yang. "Cancelable Fingerprint Templates with Delaunay Triangle-Based Local Structures." In Cyberspace Safety and Security, 81–91. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-03584-0_7.

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Shewchuk, Jonathan Richard. "Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator." In Applied Computational Geometry Towards Geometric Engineering, 203–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0014497.

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Deng, Huimin, and Qiang Huo. "Minutiae Matching Based Fingerprint Verification Using Delaunay Triangulation and Aligned-Edge-Guided Triangle Matching." In Lecture Notes in Computer Science, 270–78. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11527923_28.

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Lee, Dong Hoon, and Soon Ki Jung. "Delaunay Triangles Model for Image-Based Motion Retargeting." In Deformable Avatars, 158–68. Boston, MA: Springer US, 2001. http://dx.doi.org/10.1007/978-0-306-47002-8_14.

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Rivara, Maria-Cecilia, and Pedro A. Rodriguez-Moreno. "Tuned Terminal Triangles Centroid Delaunay Algorithm for Quality Triangulation." In Lecture Notes in Computational Science and Engineering, 211–28. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-13992-6_12.

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"An Efficient Delaunay Triangle Network Construction Algorithm." In International Conference on Electronics, Information and Communication Engineering (EICE 2012), 619–22. ASME Press, 2012. http://dx.doi.org/10.1115/1.859971.paper128.

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Conference papers on the topic "Delaunay triangle"

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Xuefeng Liang. "Distorted Fingerprint Indexing Using Minutia Detail and Delaunay Triangle." In 2006 3rd International Symposium on Voronoi Diagrams in Science and Engineering. IEEE, 2006. http://dx.doi.org/10.1109/isvd.2006.42.

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Yang, Wencheng, Jiankun Hu, and Song Wang. "A Delaunay Triangle-Based Fuzzy Extractor for Fingerprint Authentication." In 2012 IEEE 11th International Conference on Trust, Security and Privacy in Computing and Communications (TrustCom). IEEE, 2012. http://dx.doi.org/10.1109/trustcom.2012.23.

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Yang, Wencheng, Jiankun Hu, and Song Wang. "A Delaunay triangle group based fuzzy vault with cancellability." In 2013 6th International Congress on Image and Signal Processing (CISP). IEEE, 2013. http://dx.doi.org/10.1109/cisp.2013.6743946.

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Yin, Mei-Ling, Jianxun Chen, and Ziruo He. "Algorithm of drawing isoline based on improved Delaunay triangle net." In 2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA). IEEE, 2017. http://dx.doi.org/10.1109/iciea.2017.8282989.

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Yu-ze, Nie, Cheng Ying-lei, Qiu Lang-bo, He Man-yun, Zhao Zi-hao, and Pu Lei. "An algorithm of LiDAR building outline extraction by Delaunay triangle." In Eighth International Conference on Digital Image Processing (ICDIP 2016), edited by Charles M. Falco and Xudong Jiang. SPIE, 2016. http://dx.doi.org/10.1117/12.2245279.

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Xiang, Chuan-Jie, and Yunde Jia. "Practical algorithm of building Delaunay triangle mesh for terrain modeling." In Second International Conference on Image and Graphics, edited by Wei Sui. SPIE, 2002. http://dx.doi.org/10.1117/12.477107.

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Zhang, Hong, Lei Wang, and Ruiming Jia. "Scale-invariant global sparse image matching method based on Delaunay triangle." In Sixth International Symposium on Multispectral Image Processing and Pattern Recognition, edited by Tianxu Zhang, Bruce Hirsch, Zhiguo Cao, and Hanqing Lu. SPIE, 2009. http://dx.doi.org/10.1117/12.832804.

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Löffler, Maarten, and Wolfgang Mulzer. "Triangulating the Square and Squaring the Triangle: Quadtrees and Delaunay Triangulations are Equivalent." In Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2011. http://dx.doi.org/10.1137/1.9781611973082.135.

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Shults, Roman, Asset Urazaliev, Andriy Annenkov, Olena Nesterenko, Oksana Kucherenko, and Kateryna Kim. "Different Approaches to Coordinate Transformation Parameters Determination of Nonhomogeneous Coordinate Systems." In 11th International Conference “Environmental Engineering”. VGTU Technika, 2020. http://dx.doi.org/10.3846/enviro.2020.687.

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Abstract:

During reconstruction and restoration of city geodetic networks, there is quite a common problem that is related to the nonhomogeneity of existing geodetic networks. In any city, local authorities operate with their coordinate systems. Such conditions lead to inconsistency between data of different services. There is only one way how to overcome the problem that lies in the creation and deployment of the new common coordinate system for the whole city. But such an approach has a lack connected with the necessity of transformation parameters acquisition for the latest and old coordinate systems. Insofar as old coordinate systems had been created with different accuracy, using various equipment, and measuring technologies, it is not possible to consider them as homogeneous. It means that we cannot use a classical conformal Helmert transformation to link different coordinate systems. In the presented paper were studied the different approaches for transformation parameters acquisition. A case study of the Almaty city coordinate system was researched and compared the following methods: Helmert transformation, bilinear transformation, the second and third-order regression transformation, and the fourth-order conformal polynomial transformation. It was found out that neither of the considered methods maintains the necessary transformation accuracy (>5 cm). That is why the creation of the transformation field using the finite element method (FEM) was suggested. The whole city was divided into triangles using Delaunay triangulation. For each triangle, the transformation parameters were found using affine transformation with the necessary accuracy.

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Chen, Yifan, and Basavaraj Tonshal. "High Performance Dirichlet Parametrization Through Triangular Be´zier Surface Interpolation for Deformation of CAE Meshes." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34285.

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Abstract:

We present a method that extends the physics-based Dirichlet parametrization for applications concerning deformation of CAE meshes. Developed for a geometric surface feature framework called Direct Surface Manipulation, Dirichlet parametrization offers a number of operational flexibilities, such as its ability to use a single polynomial blending function to control deformation of a surface region subject to multiple user-specified displacement conditions. Dirichlet parametrization considers the domain of deformation as 2D steady-state conductive heat flow and solves for unique temperature distribution over the deformation domain using the finite element analysis (FEA) method. The result is used for evaluation of the polynomial blending function during surface deformation. The original Dirichlet parametrization, however, suffers from two limitations. First, because the 2D FEA mesh required for solving the steady-state heat transfer problem is obtained by directly projecting the affected 3D mesh onto a plane (deformation domain), both parameterization quality and performance depend on the structural characteristics of the projected 2D mesh (type of elements, node density, etc.) rather than geometrical characteristics of the deformation domain. Second, projecting a 3D mesh to create a 2D FEA mesh can be problematic when multiple areas of a 3D mesh are projected on the plane and overlap each other. Improvement techniques are presented in this paper. Instead of projecting the 3D mesh onto the plane to form the 2D FEA mesh, an auxiliary mesh is created based on geometric characteristics of the deformation domain, such as its size and boundary shape. Delaunay triangulation with an area constraint is applied in meshing the deformation region. The result is used as the 2D FEA mesh for solving the steady-state heat flow problem using the finite element method. Temperature of an affected node of the 3D mesh is obtained by interpolation in two steps. First, the node is projected onto the 2D FEA mesh, and the intersecting triangle is found. Second, the temperature at the intersection is obtained by interpolating the temperatures at the three vertices of the triangle using the cubic, triangular Be´zier interpolant. The result is equated to the temperature of the node. The use of an auxiliary mesh eliminated mesh-dependency for Dirichlet parametrization. The use of triangular cubic Be´zier interpolant results in better continuity condition of the interpolating surface between adjacent elements than linear interpolation. This allows us to employ a moderate size FEA mesh for computational efficiency. Implementation of the method is discussed and results are demonstrated.

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