Journal articles: 'Delaunay triangle'

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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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Walko, Robert L., and Roni Avissar. "A Direct Method for Constructing Refined Regions in Unstructured Conforming Triangular–Hexagonal Computational Grids: Application to OLAM." Monthly Weather Review 139, no. 12 (December 1, 2011): 3923–37. http://dx.doi.org/10.1175/mwr-d-11-00021.1.

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Abstract A scheme is presented for constructing refined regions of 2D unstructured computational meshes composed of triangular cells. The method preserves the conforming property of the original unrefined mesh and does not produce hanging nodes. The procedure consists of 1) doubling the resolution of triangles inside a specified closed region by adding three edges inside each triangle that connect the midpoints of its three edges; and 2) constructing one or more transition rows immediately outside the refined area by removing and adding edges in order to maintain the conforming property, to regulate the abruptness of the change in resolution, and to keep triangle shapes as close as possible to equilateral. The latter requirement is met partly by restricting the number of edges that meet at any vertex to values of 5, 6, or 7. The method for constructing the transition rows is the main new contribution of this work. Two variants of the construction are described, and for one variant, the number of transition rows is varied from 1 to 5. All construction is noniterative and is therefore extremely rapid, making the method suitable for dynamic mesh refinement. Final adjustment of gridcell shapes is performed iteratively, but this can be limited to only the transition rows and then converges very rapidly. A suitable constraint on triangle shapes that is applied in the adjustment process and satisfies the criterion for a Delaunay mesh naturally extends the mesh refinement algorithm to its dual-Voronoi diagram, which is composed primarily of hexagons plus a few pentagons and heptagons. The refinement method is tested on both Delaunay and Voronoi meshes in the Ocean–Land–Atmosphere Model (OLAM) using shallow-water test case 5. A choice of two or three transition rows is found to be optimal, although using five can increase accuracy slightly.

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BERN, MARSHALL, DAVID EPPSTEIN, and FRANCES YAO. "THE EXPECTED EXTREMES IN A DELAUNAY TRIANGULATION." International Journal of Computational Geometry & Applications 01, no. 01 (March 1991): 79–91. http://dx.doi.org/10.1142/s0218195991000074.

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We give an expected-case analysis of Delaunay triangulations. To avoid edge effects we consider a unit-intensity Poisson process in Euclidean d-space, and then limit attention to the portion of the triangulation within a cube of side n1/d. For d equal to two, we calculate the expected maximum edge length, the expected minimum and maximum angles, and the average aspect ratio of a triangle. We also show that in any fixed dimension the expected maximum vertex degree is Θ( log n/ log log n). Altogether our results provide some measure of the suitability of the Delaunay triangulation for certain applications, such as interpolation and mesh generation.

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Chen, Jian, Dan Zeng, Chen Kang, and Zhi Jiang Zhang. "A Triangle Division Based Point Matching for Image Registration." Advanced Materials Research 765-767 (September 2013): 726–29. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.726.

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One basic requirement of image registration is the high precision of point matching. In this paper, we present a simple and robust method to get more accurate matching points by using the structural information of divided triangles. The method initially construct triangles using Delaunay Triangulation which considering rough matched points as vertices, and then iteratively removes outliers until obtain the consensus topology structure. An algorithm called K-Nearest Neighbor Dis-ratio is also presented to avoiding mismatches. Compared with RANSAC and GTM, Our proposed method acquires more inliers and demonstrates higher matching accuracy.

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Sandhya, Mulagala, Munaga V. N. K. Prasad, and Raghavendra Rao Chillarige. "Generating cancellable fingerprint templates based on Delaunay triangle feature set construction." IET Biometrics 5, no. 2 (June 1, 2016): 131–39. http://dx.doi.org/10.1049/iet-bmt.2015.0034.

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Zhao, Pengcheng, Qingwu Hu, Zhixiong Tang, and Mingyao Ai. "A Smooth Transition Algorithm for Adjacent Panoramic Viewpoints Using Matched Delaunay Triangular Patches." ISPRS International Journal of Geo-Information 9, no. 10 (October 10, 2020): 596. http://dx.doi.org/10.3390/ijgi9100596.

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The unnatural panoramic image transition between two adjacent viewpoints reduces the immersion and interactive experiences of 360° panoramic walkthrough systems. In this paper, a dynamic panoramic image rendering and smooth transition algorithm for adjacent viewpoints is proposed. First, the feature points of adjacent view images are extracted, a robust matching algorithm is used to establish adjacent point pairs, and the matching triangles are formed by using the homonymous points. Then, a dynamic transition model is formed by the simultaneous linear transitions of shape and texture for each control triangle. Finally, the smooth transition between adjacent viewpoints is implemented by overlaying the dynamic transition model with the 360° panoramic walkthrough scene. Experimental results show that this method has obvious advantages in visual representation with distinct visual movement. It can realize the smooth transition between two indoor panoramic stations with arbitrary station spacing, and its execution efficiency is up to 50 frames per second. It effectively enhances the interactivity and immersion of 360° panoramic walkthrough systems.

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MILLER, GARY L., STEVEN E. PAV, and NOEL J. WALKINGTON. "WHEN AND WHY DELAUNAY REFINEMENT ALGORITHMS WORK." International Journal of Computational Geometry & Applications 15, no. 01 (February 2005): 25–54. http://dx.doi.org/10.1142/s0218195905001592.

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An "adaptive" variant of Ruppert's Algorithm for producing quality triangular planar meshes is introduced. The algorithm terminates for arbitrary Planar Straight Line Graph (PSLG) input. The algorithm outputs a Delaunay mesh where no triangle has minimum angle smaller than about 26.45° except "across" from small angles of the input. No angle of the output mesh is smaller than arctan [(sin θ*)/(2-cos θ*)] where θ* is the minimum input angle. Moreover no angle of the mesh is larger than about 137°, independent of small input angles. The adaptive variant is unnecessary when θ* is larger than 36.53°, and thus Ruppert's Algorithm (with concentric shell splitting) can accept input with minimum angle as small as 36.53°. An argument is made for why Ruppert's Algorithm can terminate when the minimum output angle is as large as 30°.

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Ma, Ji, Hsi-Yung Feng, and Lihui Wang. "Normal Vector Estimation for Point Clouds via Local Delaunay Triangle Mesh Matching." Computer-Aided Design and Applications 10, no. 3 (January 2013): 399–411. http://dx.doi.org/10.3722/cadaps.2013.399-411.

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J.S., Praveen, and Shibu V.S. "Structural Representation of Colon Tissue using Delaunay Triangle for Cancer Detection and Grading." International Journal of Computer Applications 128, no. 13 (October 15, 2015): 12–15. http://dx.doi.org/10.5120/ijca2015906718.

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Löffler, Maarten, and Wolfgang Mulzer. "Triangulating the Square and Squaring the Triangle: Quadtrees and Delaunay Triangulations are Equivalent." SIAM Journal on Computing 41, no. 4 (January 2012): 941–74. http://dx.doi.org/10.1137/110825698.

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Xiu, Yao Yao, and Sen Liang. "Topology Optimization and Digital Manufacturing of Stress-Constrained Structure Based on Level Set Method." Applied Mechanics and Materials 556-562 (May 2014): 4202–5. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.4202.

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A theoretical model of stress-constrained topology optimization is established via level set method, a novel sensitivity analysis for the mean compliance with the stress constraint of the global measure of von Mises stress is derived by the material derivative. The triangle plane method and the Delaunay triangulation are explored to extract and sort the boundary point-cloud data, respectively. Digital manufacturing of optimization result is accomplished by automatically programming technique and wire electrical-discharge machining. Numerical examples of two-dimensional cantilever beam structure show the validity of the proposed method of this present work.

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Jiang, San, Wanshou Jiang, Lelin Li, Lizhe Wang, and Wei Huang. "Reliable and Efficient UAV Image Matching via Geometric Constraints Structured by Delaunay Triangulation." Remote Sensing 12, no. 20 (October 16, 2020): 3390. http://dx.doi.org/10.3390/rs12203390.

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Outlier removal is a crucial step in local feature-based unmanned aerial vehicle (UAV) image matching. Inspired by our previous work, this paper proposes a method for reliable and efficient outlier removal in UAV image matching. The inputs of the method are only two images without any other auxiliary data. The core idea is to design local geometric constraints within the neighboring structure via the Delaunay triangulation and use a two-stage method for outlier removal and match refinement. In the filter stage, initial matches are first organized as the Delaunay triangulation (DT) and its corresponding graph, and their dissimilarity scores are computed from the affine-invariant spatial angular order (SAO), which is used to achieve hierarchical outlier removal. In addition, by using the triangle constraint between the refined Delaunay triangulation and its corresponding graph, missed inliers are resumed from match expansion. In the verification stage, retained matches are refined using the RANSAC-based global geometric constraint. Therefore, the two-stage algorithm is termed DTSAO-RANSAC. Finally, using four datasets, DTSAO-RANSAC is comprehensively analyzed and compared with other methods in feature matching and image orientation tests. The experimental results demonstrate that compared with the LO-RANSAC algorithm, DTSAO-RANSAC can achieve efficient outlier removal with speedup ratios ranging from 4 to 16 and, it can provide reliable matching results for image orientation of UAV datasets.

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Liu, Haijian, and Changshan Wu. "Developing a Scene-Based Triangulated Irregular Network (TIN) Technique for Individual Tree Crown Reconstruction with LiDAR Data." Forests 11, no. 1 (December 23, 2019): 28. http://dx.doi.org/10.3390/f11010028.

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LiDAR (Light Detection and Ranging)-based individual tree crown reconstruction is a challenge task due to the variable canopy morphologies and the penetrating properties of LiDAR to tree crown surfaces. Traditional methods, including LiDAR-derived rasterization, low-pass filtering smooth algorithm, and original triangular irregular network (TIN) model, have difficulties in balancing morphological accuracy and model smoothness. To address this issue, a scene-based TIN was generated with three steps based on the local scene principle. First, local Delaunay triangles were formed through connecting neighboring point sets. Second, key control points within each local Delaunay triangle, including steeple, inverted tip, ridge, saddle, and horseshoe shape control points, were extracted by analyzing multiple local scenes. These key points were derived to determine the fluctuations of forest canopies. Third, the scene-based TIN model was generated using the control points as nodes. Visual analysis indicates the new model can accurately reconstruct different canopy shapes with a relatively smooth surface, and statistical analysis of individual trees confirms that the overall error of the new model is smaller than others. Especially, the scene-based TIN derived raster reduced the average error to 0.18 m, with a standard deviation of 0.41, while the average errors of LiDAR-derived raster, low-pass filtered smooth raster, and original TIN derived raster have average errors of 0.96, 2.05, and 1.00 m, respectively. The local scene-based control point extraction also reduces data storage due to the elimination of redundant points, and furthermore the different point densities on different objects are beneficial for canopy segmentation.

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Wang, Xiang-yang, Li-xian Jiao, Xue-bing Wang, Hong-ying Yang, and Pan-pan Niu. "Copy-move forgery detection based on compact color content descriptor and Delaunay triangle matching." Multimedia Tools and Applications 78, no. 2 (July 7, 2018): 2311–44. http://dx.doi.org/10.1007/s11042-018-6354-1.

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Karim, Samsul Ariffin Bin Abdul, and Azizan Saaban. "Visualization Terrain Data Using Cubic Ball Triangular Patches." MATEC Web of Conferences 225 (2018): 06023. http://dx.doi.org/10.1051/matecconf/201822506023.

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Scattered data technique is important to visualize the geometrical images of the surface data especially for terrain, earthquake, geochemical distribution, rainfall etc. The main objective of this study is to visualize the terrain data by using cubic Ball triangular patches. First step, the terrain data is triangulated by using Delaunay triangulation. Then partial derivative will be estimated at the data points. Sufficient condition for C1 continuity will be derived for each triangle. Finally, a convex combination comprising three rational local scheme is used to construct the surface. The scheme is tested to visualize the terrain data collected at central region of Malaysia.

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Deniz, I., and H. Ozener. "Estimation of strain accumulation of densification network in Northern Marmara Region, Turkey." Natural Hazards and Earth System Sciences 10, no. 10 (October 8, 2010): 2135–43. http://dx.doi.org/10.5194/nhess-10-2135-2010.

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Abstract. Strain analysis is one of the methods for the kinematic analysis of the repeated geodetic measurements. In order to derive strain accumulation in Marmara Region, different institutions carried out several Global Positioning System (GPS) campaigns in 1999 and 2006. The GPS campaigns were performed on the geodetic network which cover the provinces: Kirklareli, Tekirdag, Bursa, Bilecik and Adapazari. Then, the displacements of the network stations were estimated by means of analysing the GPS space geodetic measurements. For the assessment of the datum differences between 1999 and 2006 on the station coordinates, 3-D Helmert transformation was applied to the coordinates of each 1999 and 2006 datum. Then, a global test was introduced to determine the significant deformation which occurred in the geodetic GPS network. Strain accumulation with a finite element model was then computed. First, triangles were constructed for the whole network with the Delaunay method. Hereafter, strain parameters were calculated for each triangle. Maximum values of strain accumulation were found around the surroundings of Marmara Ereglisi and Izmit, whereas minimum values are around Istanbul.

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Ortigoza Capetillo, Gerardo Mario, Alberto Pedro Lorandi Medina, and Alfonso Cuauhtemoc García Reynoso. "Reordering edges and elements in unstructured meshes to reduce execution time in Finite Element Computations." Nova Scientia 10, no. 20 (May 25, 2018): 263–79. http://dx.doi.org/10.21640/ns.v10i20.1317.

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Reverse Cuthill McKee (RCM) reordering can be applied to either edges or elements of unstructured meshes (triangular/tetrahedral) , in accordance to the respective finite element formulation, to reduce the bandwidth of stiffness matrices . Grid generators are mainly designed for nodal based finite elements. Their output is a list of nodes (2d or 3d) and an array describing element connectivity, be it triangles or tetrahedra. However, for edge-defined finite element formulations a numbering of the edges is required. Observations are reported for Triangle/Tetgen Delaunay grid generators and for the sparse structure of the assembled matrices in both edge- and element-defined formulations. The RCM is a renumbering algorithm traditionally applied to the nodal graph of the mesh. Thus, in order to apply this renumbering to either the edges or the elements of the respective finite element formulation, graphs of the mesh were generated. Significant bandwidth reduction was obtained. This translates to reduction in the execution effort of the sparse-matrix-times-vector product. Compressed Sparse Row format was adopted and the matrix-times-vector product was implemented in an OpenMp parallel routine.

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Li, Chengming, Yong Yin, Pengda Wu, and Wei Wu. "Skeleton Line Extraction Method in Areas with Dense Junctions Considering Stroke Features." ISPRS International Journal of Geo-Information 8, no. 7 (July 16, 2019): 303. http://dx.doi.org/10.3390/ijgi8070303.

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Extraction of the skeleton line of complex polygons is difficult, and a hot topic in map generalization study. Due to the irregularity and complexity of junctions, it is difficult for traditional methods to maintain main structure and extension characteristics when dealing with dense junction areas, so a skeleton line extraction method considering stroke features has been proposed in this paper. Firstly, we put forward a long-edge adaptive node densification algorithm, which is used to construct boundary-constrained Delaunay triangulation to uniformly divide the polygon and extract the initial skeleton line. Secondly, we defined the triangles with three adjacent triangles (Type III) as the basic unit of junctions, then obtained the segmented areas with dense junctions on the basis of local width characteristics and correlation relationships of each Type III triangle. Finally, we concatenated the segments into strokes and corrected the initial skeleton lines based on the extension direction features of each stroke. The actual water network data of Jiangsu Province in China were used to verify the method. Experimental results show that the proposed method can better identify the areas with dense junctions and that the extracted skeleton line is naturally smooth and well-connected, which accurately reflects the main structure and extension characteristics of these areas.

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Huo, Li, Bo Jiang, and Tao Ning. "A New Algorithm for Solving TSP and its Applications." Applied Mechanics and Materials 713-715 (January 2015): 1504–8. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.1504.

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A new algorithm for TSP which is an improved ACO combined with MMAS and CSDT is proposed. MMAS can prevent the search from local optimum and search stagnation. We use candidate set strategy based on the Delaunay triangle (CSDT) in order to reduce serch space and accelerate the speed of the algorithm. Additionally, pheromone update and parameter optimization are detailed in this paper. The comparison analysis of the new algorithm, basic ant colony algorithm and MMAS algorithm is also given by using TSPLIB experimental data. Finally, we give an actual TSP case and compute the optimum solution by our new algorithm.The results show that the new algorithm is validity and effectively.

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Luo, Junhai, Yijun Cai, and Changping Zhong. "A Data Forwarding Scheme Based on Delaunay Triangulation for Cyber-Physical Systems." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/465369.

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Cyber-physical system (CPS) cooperates with physical processes, computing, communication, and control (3C) into multiple levels of information processing and operation management to streamline and fortify the operation of physical systems. Due to the unique characteristics, such as unpredictable node mobility, low node density, lack of global information and network intermittent connectivity, an algorithm for data forwarding in CPS is a considerably difficult and challenging problem, and there is no good solution to it in existing works. In this paper, we propose a fully-fledged data forwarding algorithm tailored to the CPS environment. The proposed protocol, called data forwarding based on Delaunay triangulation (DFDT), takes into account the computational geometry based on Delaunay triangulation to form a few triangle communities according to nodes’ connectivity. Data in a community are forwarded to other nodes once a node comes into this community to increase the data delivery ratio. DFDT achieves a good performance by data gathering and sending data to other nodes with higher probability of meeting the link. An extensive simulation has been performed to validate the analytical results and to show the effectiveness of our approach compared with the three existing popular data forwarding algorithms.

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Meng, Jinjun, Jiaqi Wu, Linlin Lu, Qingting Li, Qiang Zhang, Suyun Feng, and Jun Yan. "A Full-Spectrum Registration Method for Zhuhai-1 Satellite Hyperspectral Imagery." Sensors 20, no. 21 (November 5, 2020): 6298. http://dx.doi.org/10.3390/s20216298.

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Accurate registration is an essential prerequisite for analysis and applications involving remote sensing imagery. It is usually difficult to extract enough matching points for inter-band registration in hyperspectral imagery due to the different spectral responses for land features in different image bands. This is especially true for non-adjacent bands. The inconsistency in geometric distortion caused by topographic relief also makes it inappropriate to use a single affine transformation relationship for the geometric transformation of the entire image. Currently, accurate registration between spectral bands of Zhuhai-1 satellite hyperspectral imagery remains challenging. In this paper, a full-spectrum registration method was proposed to address this problem. The method combines the transfer strategy based on the affine transformation relationship between adjacent spectrums with the differential correction from dense Delaunay triangulation. Firstly, the scale-invariant feature transform (SIFT) extraction method was used to extract and match feature points of adjacent bands. The RANdom SAmple Consensus (RANSAC) algorithm and the least square method is then used to eliminate mismatching point pairs to obtain fine matching point pairs. Secondly, a dense Delaunay triangulation was constructed based on fine matching point pairs. The affine transformation relation for non-adjacent bands was established for each triangle using the affine transformation relation transfer strategy. Finally, the affine transformation relation was used to perform differential correction for each triangle. Three Zhuhai-1 satellite hyperspectral images covering different terrains were used as experiment data. The evaluation results showed that the adjacent band registration accuracy ranged from 0.2 to 0.6 pixels. The structural similarity measure and cosine similarity measure between non-adjacent bands were both greater than 0.80. Moreover, the full-spectrum registration accuracy was less than 1 pixel. These registration results can meet the needs of Zhuhai-1 hyperspectral imagery applications in various fields.

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OH, KWANG-MAN, JEONG-DAN CHOI, CHAN-SU LEE, CHAN-JONG PARK, and EE-TAEK LEE. "AN EFFICIENT AND SIMPLE QUAD EDGE CONVERSION OF POLYGONAL MAINFOLD OBJECTS." International Journal of Image and Graphics 01, no. 02 (April 2001): 251–71. http://dx.doi.org/10.1142/s0219467801000165.

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This paper presents an efficient and simple quad edge conversion method of polygonal (manifold) objects. In a wide variety of applications such as scientific visualization, virtual reality and computer aided geometric design, polygonal objects are expected to be visualized and manipulated within a given time constraint. To achieve these expectations, it is necessary to introduce an efficient data structure as well as high performance graphics hardware and real-time processing techniques such as simplification and level of details. The quad edge data structure is very efficient for handling polygonal objects even though it was originally designed to handle the subdivisions of manifold objects such as Delaunay triangulations and Voronoi diagrams. It, however, has not been used widely because there is no efficient algorithm for quad edge conversion of conventional polygonal objects. In this paper, we propose a new incremental quad edge conversion algorithm that processes the triangles one by one. Since quad edge has only the splice as a topological operator, the quad edge conversion of each triangle is done by applying three splice operations, a splice per vertex. As an applicaion for the quad edge, a simplification of conventional polygonal objects is implemented. It includes the removing, moving, replacing, and inserting of vertices and edges.

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Cui, Ji Wen, Jiu Bin Tan, and Q. Shi. "Measurement Method for Micro-Cavity Based on Improved MAP Algorithm." Key Engineering Materials 381-382 (June 2008): 191–94. http://dx.doi.org/10.4028/www.scientific.net/kem.381-382.191.

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In order to improve the measurement precision, an improved MAP algorithm is proposed to increase the edge aiming precision in this paper. The algorithm breaks the limitation of degenerated model, takes two actual factors into account, one is the distortion caused by motion, which solved by Huber-Markov random filed in the improved MAP algorithm, and the other is curvature of field, which solved by Delaunay triangle method. The algorithm can restore the high-frequency information of image, keep the edge character of image, and increase the aiming precision of the edge during the measurement. The experiments show that the uncertainty of location for the image captured in the measurement can be improved three folds, and the repeatability uncertain is less then 0.8µm when the diameter of φ0.2mm hole is measured using the proposed MAP algorithm and length-measuring interferometer together.

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Xi, Xu, Xinchang Zhang, Weidong Liang, Qinchuan Xin, and Pengcheng Zhang. "Dual Zero-Watermarking Scheme for Two-Dimensional Vector Map Based on Delaunay Triangle Mesh and Singular Value Decomposition." Applied Sciences 9, no. 4 (February 14, 2019): 642. http://dx.doi.org/10.3390/app9040642.

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Digital watermarking is important for the copyright protection of electronic data, but embedding watermarks into vector maps could easily lead to changes in map precision. Zero-watermarking, a method that does not embed watermarks into maps, could avoid altering vector maps but often lack of robustness. This study proposes a dual zero-watermarking scheme that improves watermark robustness for two-dimensional (2D) vector maps. The proposed scheme first extracts the feature vertices and non-feature vertices of the vector map with the Douglas-Peucker algorithm and subsequently constructs the Delaunay Triangulation Mesh (DTM) to form a topological feature sequence of feature vertices as well as the Singular Value Decomposition (SVD) matrix to form intrinsic feature sequence of non-feature vertices. Next, zero-watermarks are obtained by executing exclusive disjunction (XOR) with the encrypted watermark image under the Arnold scramble algorithm. The experimental results show that the scheme that synthesizes both the feature and non-feature information improves the watermark capacity. Making use of complementary information between feature and non-feature vertices considerably improves the overall robustness of the watermarking scheme. The proposed dual zero-watermarking scheme combines the advantages of individual watermarking schemes and is robust against such attacks as geometric attacks, vertex attacks and object attacks.

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BLANDFORD, DANIEL K., GUY E. BLELLOCH, DAVID E. CARDOZE, and CLEMENS KADOW. "COMPACT REPRESENTATIONS OF SIMPLICIAL MESHES IN TWO AND THREE DIMENSIONS." International Journal of Computational Geometry & Applications 15, no. 01 (February 2005): 3–24. http://dx.doi.org/10.1142/s0218195905001580.

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We describe data structures for representing simplicial meshes compactly while supporting online queries and updates efficiently. Our data structure requires about a factor of five less memory than the most efficient standard data structures for triangular or tetrahedral meshes, while efficiently supporting traversal among simplices, storing data on simplices, and insertion and deletion of simplices. Our implementation of the data structures uses about 5 bytes/triangle in two dimensions (2D) and 7.5 bytes/tetrahedron in three dimensions (3D). We use the data structures to implement 2D and 3D incremental algorithms for generating a Delaunay mesh. The 3D algorithm can generate 100 Million tetrahedra with 1 Gbyte of memory, including the space for the coordinates and all data used by the algorithm. The runtime of the algorithm is as fast as Shewchuk's Pyramid code, the most efficient we know of, and uses a factor of 3.5 less memory overall.

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Wang, Chao, Aiye Shi, Xin Wang, Fengchen Huang, and Hui Liu. "A novel registration method for high resolution remote sensing images based on JSEG and NMI." Computer Science and Information Systems 12, no. 1 (2015): 289–306. http://dx.doi.org/10.2298/csis140505089w.

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When traditional multi-scale analysis tools are applied to high resolution remote sensing image registration, difficulties and limitations are common in selection of directional sub-bands and distribution optimization of control point pairs etc. Aiming at this issue, a novel registration method based on JSEG and NMI is proposed in this paper. It is the method that incorporates the multi-scale segmentation method (JSEG) into image registration for the first time and proposes an adaptive feature point extraction method on the basis of blocking strategy. Then, NMI is adopted to obtain a set of control point pairs. Finally, the image registration is realized by virtue of Delaunay triangle local transform mapping functions. In accordance with experiments on high resolution remote sensing images collected by different sensors, it is found that the method can not only extract feature points accurately but also ensure reasonable distribution of control point pairs. Meanwhile, compared with traditional multi-scale tools-based methods, the method has relatively high accuracy and robustness.

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Andrews, Lawrence C., Herbert J. Bernstein, and Nicholas K. Sauter. "A space for lattice representation and clustering." Acta Crystallographica Section A Foundations and Advances 75, no. 3 (April 30, 2019): 593–99. http://dx.doi.org/10.1107/s2053273319002729.

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Algorithms for quantifying the differences between two lattices are used for Bravais lattice determination, database lookup for unit cells to select candidates for molecular replacement, and recently for clustering to group together images from serial crystallography. It is particularly desirable for the differences between lattices to be computed as a perturbation-stable metric, i.e. as distances that satisfy the triangle inequality, so that standard tree-based nearest-neighbor algorithms can be used, and for which small changes in the lattices involved produce small changes in the distances computed. A perturbation-stable metric space related to the reduction algorithm of Selling and to the Bravais lattice determination methods of Delone is described. Two ways of representing the space, as six-dimensional real vectors or equivalently as three-dimensional complex vectors, are presented and applications of these metrics are discussed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)

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Liu, Yaqiong, Seah Hock Soon, Ying He, Juncong Lin, and Jiazhi Xia. "Sketch Based Image Deformation and Editing with Guaranteed Feature Correspondence." International Journal of Virtual Reality 11, no. 1 (January 1, 2012): 25–32. http://dx.doi.org/10.20870/ijvr.2012.11.1.2834.

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The establishment of a good correspondence mapping is a key issue in planar animations such as image morphing and deformation. In this paper, we present a novel mapping framework for animation of complex shapes. We firstly let the user extract the outlines of the interested object and target interested area from the input images and specify some optional feature lines, and then we generate a sparse delaunay triangulation mesh taking the outlines and the feature lines of the source shape as constraints. Then we copy the topology from the source shape to the target shape to construct a valid triangulation in the target shape. After that, each triangle of this triangular mesh is further segmented into a dense mesh patch. Each mesh patch is parameterized onto a unit circle domain. With such parametrization, we can easily construct a correspondence mapping between the source patches and the corresponding target patches. Our framework can work well for various applications such as shape deformation and morphing. Pleasing results generated by our framework show that the framework works well.

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Batrakova, A., Y. Dorozhko, and V. Yemets. "FEATURES OF CONSTRUCTION OF DIGITAL RELIEF MODEL ACCORDING TO THE RESULTS OF GEODESIC SURVEYING LOCATIONS." Municipal economy of cities 1, no. 161 (March 26, 2021): 104–8. http://dx.doi.org/10.33042/2522-1809-2021-1-161-104-108.

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Topographic maps in digital and electronic forms are created on the basis of available paper topographic maps or on the basis of primary materials of geodetic surveys. Geodetic surveys are performed both by ground methods, without the use of photogrammetric materials, and on the basis of materials obtained as a result of ground phototheodolite or aerial photography. The construction of a digital terrain model is a multi-stage process, which consists of a significant number of interconnected operations performed at the stage of in-house processing of the results of geodetic measurements carried out during engineering and geodetic surveys. The quality of the final result of modeling depends on the quality of each stage of construction of a digital terrain model, so it is extremely important to pay attention to all technological processes of model construction. The digital relief model is considered as an ordered set of triangular faces constructed by the Delaunay algorithm. The main condition of this type of triangulation is that in the middle of the circle described around any triangle can not be the vertex of another triangle. Construction of a digital terrain model based on the results of geodetic surveying of the area in the general case can be divided into several stages. At the beginning, an automated construction of triangulation is performed on the basis of the results of geodetic measurements, which carry information about three-dimensional coordinates of survey points. Allotments adjust the display of horizontals. Regardless of the selected surface display style, the surface model is a grid of triangles. At the next stage of construction of the digital model of a relief carry out visual control of the created model and if necessary carry out editing of elements of a surface and change of position of edges of triangulation for change of position of horizontals. The last stage of building a digital terrain model based on the results of geodetic surveying of the area is the design of modeling results, the application of individual styles of reflection for individual areas of the surface and the creation of mountain strokes and signatures of horizontals.

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Barnhart, Katherine R., Eric W. H. Hutton, Gregory E. Tucker, Nicole M. Gasparini, Erkan Istanbulluoglu, Daniel E. J. Hobley, Nathan J. Lyons, et al. "Short communication: Landlab v2.0: a software package for Earth surface dynamics." Earth Surface Dynamics 8, no. 2 (May 26, 2020): 379–97. http://dx.doi.org/10.5194/esurf-8-379-2020.

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Abstract. Numerical simulation of the form and characteristics of Earth's surface provides insight into its evolution. Landlab is an open-source Python package that contains modularized elements of numerical models for Earth's surface, thus reducing time required for researchers to create new or reimplement existing models. Landlab contains a gridding engine which represents the model domain as a dual graph of structured quadrilaterals (e.g., raster) or irregular Voronoi polygon–Delaunay triangle mesh (e.g., regular hexagons, radially symmetric meshes, and fully irregular meshes). Landlab also contains components – modular implementations of single physical processes – and a suite of utilities that support numerical methods, input/output, and visualization. This contribution describes package development since version 1.0 and backward-compatibility-breaking changes that necessitate the new major release, version 2.0. Substantial changes include refactoring the grid, improving the component standard interface, dropping Python 2 support, and creating 31 new components – for a total of 58 components in the Landlab package. We describe reasons why many changes were made in order to provide insight for designers of future packages. We conclude by discussing lessons about the dynamics of scientific software development gained from the experience of using, developing, maintaining, and teaching with Landlab.

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Huang, Caiyun, and Changhua Yin. "DEEP LEARNING SURVIVAL PREDICTION FOR LUNG CANCER PATIENTS." Biomedical Engineering: Applications, Basis and Communications 33, no. 04 (May 4, 2021): 2150031. http://dx.doi.org/10.4015/s1016237221500319.

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Lung cancer is one of the most common cancers; lung cancer is a malignant tumor that seriously threatens the lives of patients. Improving survival prediction performance is meaningful for making the treatment plans and improving the survival rates of lung cancer patients. In this paper, an approach for predicting the survival of lung cancer patients is proposed based on pathological images. First, the deep learning method is used to automatically detect lung cancer cells in pathological pictures, and features of the detected lung cancer cells are extracted. In feature selection, an extraction method of topological features is given, it reflects the relationship and distribution characteristics of lung cancer cells, and the extracted topological features are used as predictive factors for survival analysis. In this paper, the extraction methods of global topological features are mainly studied; for example, the overall association, location relationship and distribution of cells, and the global topological features of lung cancer cells are extracted through the Voronoi diagram, Delaunay triangle, and minimum spanning tree methods. Finally, the Cox–LASSO method was used to predict the survival of lung cancer patients. Experimental results show that this method can improve the efficiency and accuracy of cell detection, and there is a higher ability to predict and analyze the survival of lung cancer patients.

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Han, Kim, and Yeom. "Improved Piecewise Linear Transformation for Precise Warping of Very-High-Resolution Remote Sensing Images." Remote Sensing 11, no. 19 (September 25, 2019): 2235. http://dx.doi.org/10.3390/rs11192235.

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A large number of evenly distributed conjugate points (CPs) in entirely overlapping regions of the images are required to achieve successful co-registration between very-high-resolution (VHR) remote sensing images. The CPs are then used to construct a non-linear transformation model that locally warps a sensed image to a reference image’s coordinates. Piecewise linear (PL) transformation is largely exploited for warping VHR images because of its superior performance as compared to the other methods. The PL transformation constructs triangular regions on a sensed image from the CPs by applying the Delaunay algorithm, after which the corresponding triangular regions in a reference image are constructed using the same CPs on the image. Each corresponding region in the sensed image is then locally warped to the regions of the reference image through an affine transformation estimated from the CPs on the triangle vertices. The warping performance of the PL transformation shows reliable results, particularly in regions inside the triangles, i.e., within the convex hulls. However, the regions outside the triangles, which are warped when the extrapolated boundary planes are extended using CPs located close to the regions, incur severe geometric distortion. In this study, we propose an effective approach that focuses on the improvement of the warping performance of the PL transformation over the external area of the triangles. Accordingly, the proposed improved piecewise linear (IPL) transformation uses additional pseudo-CPs intentionally extracted from positions on the boundary of the sensed image. The corresponding pseudo-CPs on the reference image are determined by estimating the affine transformation from CPs located close to the pseudo-CPs. The latter are simultaneously used with the former to construct the triangular regions, which are enlarged accordingly. Experiments on both simulated and real datasets, constructed from Worldview-3 and Kompsat-3A satellite images, were conducted to validate the effectiveness of the proposed IPL transformation. That transformation was shown to outperform the existing linear/non-linear transformation models such as an affine, third and fourth polynomials, local weighted mean, and PL. Moreover, we demonstrated that the IPL transformation improved the warping performance over the PL transformation outside the triangular regions by increasing the correlation coefficient values from 0.259 to 0.304, 0.603 to 0.657, and 0.180 to 0.338 in the first, second, and third real datasets, respectively.

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Ma, Yan, Yan-ling Hao, and Feng-min Tian. "A Novel Model of Conforming Delaunay Triangulation for Sensor Network Configuration." Abstract and Applied Analysis 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/720249.

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Delaunay refinement is a technique for generating unstructured meshes of triangles for sensor network configuration engineering practice. A new method for solving Delaunay triangulation problem is proposed in this paper, which is called endpoint triangle’s circumcircle model (ETCM). As compared with the original fractional node refinement algorithms, the proposed algorithm can get well refinement stability with least time cost. Simulations are performed under five aspects including refinement stability, the number of additional nodes, time cost, mesh quality after intruding additional nodes, and the aspect ratio improved by single additional node. All experimental results show the advantages of the proposed algorithm as compared with the existing algorithms and confirm the algorithm analysis sufficiently.

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Moritani, R., S. Kanai, H. Date, Y. Niina, and R. Honma. "PLAUSIBLE RECONSTRUCTION OF AN APPROXIMATED MESH MODEL FOR NEXT-BEST VIEW PLANNING OF SFM-MVS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLIII-B2-2020 (August 12, 2020): 465–71. http://dx.doi.org/10.5194/isprs-archives-xliii-b2-2020-465-2020.

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Abstract. Structure-from-Motion (SfM) and Multi-View Stereo (MVS) are widely used methods in three dimensional (3D) model reconstruction for an infrastructure maintenance purpose. However, if a set of images is not captured from well-placed positions, the final dense model can contain low-quality regions. Since MVS requires a much longer processing time than SfM as larger amounts of images are provided, it is impossible for surveyors to wait for the SfM–MVS process to complete and evaluate the geometric quality of a final dense model on-site. This challenge results in response inefficiency and the deterioration of dense models in 3D model reconstruction. If the quality of the final dense model can be predicted immediately after SfM, it will be possible to revalidate the images much earlier and to obtain the dense model with better quality than the existing SfM–MVS process. Therefore, we propose a method for reconstructing a more plausible 3D mesh model that accurately approximates the geometry of the final dense model only from sparse point clouds generated from SfM. This approximated mesh model can be generated using Delaunay triangulation for the sparse point clouds and triangle as well as tetrahedron filtering. The approximated model can be used to predict the geometric quality of the final dense model and for an optimization-based view planning. Some experimental results showed that our method is effective in predicting the quality of the final dense model and finding the potentially degraded regions. Moreover, it was confirmed that the average reconstruction errors of the dense model generated by the optimization-based view planning went below tens of millimeters and falls within an acceptable range for an infrastructure maintenance purpose.

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LEE, SANGYOON, CHAN-IK PARK, and CHAN-MO PARK. "AN IMPROVED PARALLEL ALGORITHM FOR DELAUNAY TRIANGULATION ON DISTRIBUTED MEMORY PARALLEL COMPUTERS." Parallel Processing Letters 11, no. 02n03 (June 2001): 341–52. http://dx.doi.org/10.1142/s0129626401000634.

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Delaunay triangulation has been much used in such applications as volume rendering, shape representation, terrain modeling and so on. The main disadvantage of Delaunay triangulation is large computation time required to obtain the triangulation on an input points sets. This time can be reduced by using more than one processor, and several parallel algorithms for Delaunay triangulation have been proposed. In this paper, we propose an improved parallel algorithm for Delaunay triangulation, which partitions the bounding convex region of the input points set into a number of regions by using Delaunay edges and generates Delaunay triangles in each region by applying an incremental construction approach. Partitioning by Delaunay edges makes it possible to eliminate merging step required for integrating subresults. It is shown from the experiments that the proposed algorithm has good load balance and is more efficient than Cignoni et al.'s algorithm and our previous algorithm.

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Chen, Zhi Yu, Jian Zhong Fu, Hong Yao Shen, and Wen Feng Gan. "An Improved Parallel Computation Method for Delaunay Triangulation." Advanced Materials Research 819 (September 2013): 299–303. http://dx.doi.org/10.4028/www.scientific.net/amr.819.299.

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Amongst the flourishing Delaunay Triangulation methods, growth algorithm has been widely accepted because of its reputation of being simple and elegant. However, the parallelization of growth algorithm has not been fully exploited. In this work, a novel Growth algorithm of Delaunay Triangulation is proposed. The point cloud is first divided into two parts by a suitable curve and the separated areas are calculated by incremental algorithm. Triangles which cross with the curve are generated by a growth algorithm associated with uniform grid. At the process of merging, these grew triangles are used to detect incorrect triangles of the incremental algorithm areas. Method about generating triangles on curve is elaborated and a simple way to detect interferential triangles is also explained. With above method, triangulation calculation can be parallelized. Unlike the traditional divide-and-conquer method, no flip operation is needed in the proposed methodology. Thus, three dimensional applications are also made possible. A comparative research between tradition incremental algorithm and the proposed method has been conducted. Results show, the algorithm has a higher performance with less computation time.

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De Floriani, Leila, Bianca Falcidieno, George Nagy, and Caterina Pienovi. "On sorting triangles in a delaunay tessellation." Algorithmica 6, no. 1-6 (June 1991): 522–32. http://dx.doi.org/10.1007/bf01759057.

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Chai, D. "DECOMPOSING IMAGES INTO TRIANGLES BY DELAUNAY POINT PROCESSES." ISPRS Annals of Photogrammetry, Remote Sensing and Spatial Information Sciences V-2-2020 (August 3, 2020): 805–12. http://dx.doi.org/10.5194/isprs-annals-v-2-2020-805-2020.

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Abstract. We propose a method for decomposing images into triangles. Contrary to superpixel methods, our output representation both preserves the geometric information disseminated in input images, and has an attractive storage capacity. Our method relies on the flexibility and efficiency of Delaunay point processes to address the problem. These stochastic models distribute points interacting between each other through Delaunay triangulations. The mechanism for distributing points combines several complementary ingredients including image discontinuity preservation, radiometric homogeneity inside atomic regions as well as priors on the shape of these regions. Said differently, sampled points and induced shapes work in tandem. The potential of our approach is shown through comparisons with existing oversegmentation methods and applications to vision problems.

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Liu, Shao Hua, Jun Tang, Hai Qin Ji, Ke Yan Xiao, and Jia Hua Zhang. "Algorithm Study of the Models Merge Based on Delaunay Triangulation." Advanced Materials Research 734-737 (August 2013): 2634–37. http://dx.doi.org/10.4028/www.scientific.net/amr.734-737.2634.

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It is so valuable that models merging of Delaunay triangulation are used widely in many applications. This paper researches the algorithm of models merging for Delaunay triangulation. A method for obtaining merged intersection lines and a algorithm for searching fast triangles in the extent of merging intersection lines are proposed, and whole process of models merging are expatiated detailedly. The algorithm is tested in experiments, and the result of experiment shows that this algorithm is very efficient.

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Liu, Shao Hua, and Jia Hua Zhang. "The Establishment of DEM and its Application in Road Surveying and Designing." Applied Mechanics and Materials 602-605 (August 2014): 783–86. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.783.

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It is so valuable that models merging of Delaunay triangulation are used widely in many applications. This paper researches the algorithm of models merging for Delaunay triangulation. A method for obtaining merged intersection lines and a algorithm for searching fast triangles in the extent of merging intersection lines are proposed, and whole process of models merging are expatiated detailedly. The algorithm is tested in experiments, and the result of experiment shows that this algorithm is very efficient.

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Rivara, Maria-Cecilia, and Javier Diaz. "Terminal Triangles Centroid Algorithms for Quality Delaunay Triangulation." Computer-Aided Design 125 (August 2020): 102870. http://dx.doi.org/10.1016/j.cad.2020.102870.

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Journal articles on the topic 'Delaunay triangle'

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