Relevant bibliographies by topics / Triangle construction problems

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Triangle construction problems'

Author: Grafiati
Published: 28 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Triangle construction problems"

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Kim, D., A. Bolat, and K. J. Li. "INDOOR SPATIAL DATA CONSTRUCTION FROM TRIANGLE MESH." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-4/W8 (July 11, 2018): 101–8. http://dx.doi.org/10.5194/isprs-archives-xlii-4-w8-101-2018.

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<p><strong>Abstract.</strong> The 3D triangle mesh is widely used to represent indoor space. One of widely used methods of generating 3D triangle mesh data of indoor space is the construction from the point cloud collected using LIDAR. However, there are many problems in using generated triangle mesh data as a geometric representation of the indoor space. First, the number of triangles forming the triangle mesh is very large, which results in a bottleneck of the performance for storage and management. Second, no consideration on the properties of indoor space has been done by the previous work on mesh simplification for indoor geometric representation. Third, there is no research to construct indoor spatial standard data from triangle mesh data. For resolving these problems, we propose the a method for generating triangular mesh data for indoor geometric representation based in the observations mentioned above. First this method removes unnecessary objects and reduces the number of surfaces from the original fine-grained triangular mesh data using the properties of indoor space. Second, it also produces indoor geometric data in IndoorGML &amp;ndash; an OGC standard for indoor spatial data model. In experimental studies, we present a case study of indoor triangle mesh data from real world and compare results with raw data.</p>
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Nirode, Wayne. "Triangles from Three Points." Mathematics Teacher 108, no. 1 (August 2014): 32–38. http://dx.doi.org/10.5951/mathteacher.108.1.0032.

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Ma, Wei. "Technical Risk Assessment of Large-Scale Construction Project Based on Triangle Whitening Weight Function." Advanced Materials Research 989-994 (July 2014): 5294–99. http://dx.doi.org/10.4028/www.scientific.net/amr.989-994.5294.

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Technical risk assessment model of large-scale construction project has been established by using triangle whitening weight function of grey theory against the problems of technical risk assessment of large-scale construction project. In the end, through example verification, this model is approved to be feasible and have certain value of reference and utilization in similar problems.
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Reuveni, Shlomi. "CATALAN'S TRAPEZOIDS." Probability in the Engineering and Informational Sciences 28, no. 3 (March 18, 2014): 353–61. http://dx.doi.org/10.1017/s0269964814000047.

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Named after the French–Belgian mathematician Eugène Charles Catalan, Catalan's numbers arise in various combinatorial problems [12]. Catalan's triangle, a triangular array of numbers somewhat similar to Pascal's triangle, extends the combinatorial meaning of Catalan's numbers and generalizes them [1,5,11]. A need for a generalization of Catalan's triangle itself arose while conducting a probabilistic analysis of the Asymmetric Simple Inclusion Process (ASIP) — a model for a tandem array of queues with unlimited batch service [7–10]. In this paper, we introduce Catalan's trapezoids, a countable set of trapezoids whose first element is Catalan's triangle. An iterative scheme for the construction of these trapezoids is presented, and a closed-form formula for the calculation of their entries is derived. We further discuss the combinatorial interpretations and applications of Catalan's trapezoids.
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Chen, Hui Hui, and Cheng Jia. "US-FE-LSPIM TRI3 Element for Free Vibration Analysis." Applied Mechanics and Materials 246-247 (December 2012): 1278–82. http://dx.doi.org/10.4028/www.scientific.net/amm.246-247.1278.

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For the purpose of construction an effective element model, the US- FE-LSPIM TRI3 element formulation, which is based on the concept of unsymmetric finite element formulation, is established. Classical linear triangle shape functions and FE-LSPIM TRI3 element shape functions are used as test and trial functions respectively. Classical linear triangle shape functions fulfill the requirements of continuity in displacement field for test functions. The FE-LSPIM TRI3 element shape functions synthesize the individual strengths of meshfree and finite element methods so they are more proper for trial functions. The element is applied in free vibration analysis of two dimension solids. Typical benchmark problems are solved. The results show that this element is more accurate and capable of good performances under both regular and irregular meshes.
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Zhang, Zhijun. "Two Classes of Nonlinear Singular Dirichlet Problems with Natural Growth: Existence and Asymptotic Behavior." Advanced Nonlinear Studies 20, no. 1 (February 1, 2020): 77–93. http://dx.doi.org/10.1515/ans-2019-2054.

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AbstractThis paper is concerned with the existence, uniqueness and asymptotic behavior of classical solutions to two classes of models {-\triangle u\pm\lambda\frac{|\nabla u|^{2}}{u^{\beta}}=b(x)u^{-\alpha}}, {u>0}, {x\in\Omega}, {u|_{\partial\Omega}=0}, where Ω is a bounded domain with smooth boundary in {\mathbb{R}^{N}}, {\lambda>0}, {\beta>0}, {\alpha>-1}, and {b\in C^{\nu}_{\mathrm{loc}}(\Omega)} for some {\nu\in(0,1)}, and b is positive in Ω but may be vanishing or singular on {\partial\Omega}. Our approach is largely based on nonlinear transformations and the construction of suitable sub- and super-solutions.
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Ma, Li Qiang, Dong Sheng Zhang, Cheng Guo Zhang, Xin Qi Cao, and Yong Shen Li. "Design of Automatic End-Advanced Hydraulic Support in Coal Face with Deep Dip Angle and Large Mining Height." Advanced Materials Research 160-162 (November 2010): 1524–30. http://dx.doi.org/10.4028/www.scientific.net/amr.160-162.1524.

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ZTZL60000/25/45 Automatic End-Advanced Hydraulic Support is developed to meet the needs of the fully mechanized coal face with deep dip angle and large mining height, mechanizing the advanced support of the end and drift, while greatly reducing the construction personnel's labor intensity. Not only the end support strength is enhanced, which improves the safety and reliability of advanced support and generates methods to solve problems related to reserving triangle coal on the face that enhances the support efficiency and reduces support costs, but also more recovered coal resources become available since the height of roadway increases, spawning a certain amount of economic benefits.
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Tymoshenko, Aleksandr Vasil'evich, Rasul Ahmatovich Kochkarov, and Azret Ahmatovich Kochkarov. "Identification Conditions for the Solvability of NP-complete Problems for the Class of Pre-fractal Graphs." Modeling and Analysis of Information Systems 28, no. 2 (June 11, 2021): 126–35. http://dx.doi.org/10.18255/1818-1015-2021-2-126-135.

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Modern network systems (unmanned aerial vehicles groups, social networks, network production chains, transport and logistics networks, communication networks, cryptocurrency networks) are distinguished by their multi-element nature and the dynamics of connections between its elements. A number of discrete problems on the construction of optimal substructures of network systems described in the form of various classes of graphs are NP-complete problems. In this case, the variability and dynamism of the structures of network systems leads to an "additional" complication of the search for solutions to discrete optimization problems. At the same time, for some subclasses of dynamical graphs, which are used to model the structures of network systems, conditions for the solvability of a number of NP-complete problems can be distinguished. This subclass of dynamic graphs includes pre-fractal graphs. The article investigates NP-complete problems on pre-fractal graphs: a Hamiltonian cycle, a skeleton with the maximum number of pendant vertices, a monochromatic triangle, a clique, an independent set. The conditions under which for some problems it is possible to obtain an answer about the existence and to construct polynomial (when fixing the number of seed vertices) algorithms for finding solutions are identified.
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Garanzha, Vladimir A., Lyudmila N. Kudryavtseva, and Aleksei I. Belokrys-Fedotov. "Single and multiple springback technique for construction and control of thick prismatic mesh layers." Russian Journal of Numerical Analysis and Mathematical Modelling 36, no. 1 (February 1, 2021): 1–15. http://dx.doi.org/10.1515/rnam-2021-0001.

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Abstract We suggest an algorithm for construction of semi-structured thick prismatic mesh layers which guarantees an absence of inverted prismatic cells in resulting layer and allows one to control near-surface mesh orthogonality. Initial mesh is modelled as a thin layer of highly compressed prisms made of hyperelastic material glued to the triangulated surface. In order to compute robust normals at the vertices of the surface mesh we use quadratic programming algorithm based on the nearest ball concept. This pre-stressed material expands, possibly with self-penetration and extrusion to exterior of computational domain until target layer thickness is attained. Special preconditioned relaxation procedure is proposed based on the solution of stationary springback problem. It is shown that preconditioner can handle very stiff problems. Once an offset prismatic mesh is constructed, self-intersections are eliminated using iterative prism cutting procedure.Next, variational advancing front procedure is applied for refinement and precise orthogonalization of prismatic layer near boundaries. We demonstrate that resulting mesh layer is ‘almost mesh-independent’ in a sense that the dependence of thickness and shape of the layer on mesh resolution and triangle quality is weak. It is possible to apply elastic springback technique sequentially layer by layer. We compare single springback technique with multiple springback technique in terms of mesh quality, stiffness of local variational problems and mesh orthogonality or/and layer thickness balance.
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Banihashemi, Sayyid Ali, Mohammad Khalilzadeh, Jurgita Antucheviciene, and Jonas Šaparauskas. "Trading off Time–Cost–Quality in Construction Project Scheduling Problems with Fuzzy SWARA–TOPSIS Approach." Buildings 11, no. 9 (August 31, 2021): 387. http://dx.doi.org/10.3390/buildings11090387.

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The increasing number of construction projects together with the limited resources of organizations led to tough competition for achieving project goals. Time, cost, and quality have been known as the project iron triangle. Project managers attempt to allocate the appropriate resources and make the best decisions for accomplishing projects with the shortest durations, lowest costs, and the highest quality. No study has examined the time–cost–quality trade-off problem with decision-making approaches. In this study, the fuzzy multi-criteria decision-making (MCDM) methods are exploited to choose the best mode for performing each activity. For this purpose, the SWARA method is applied to determine the importance weights of time, cost, and quality. In addition, the TOPSIS (Technique for the Order Preference by Similarity to Ideal Solution) technique is used to rank and select the best activity execution modes. The proposed model is implemented on two medium- and large-size construction projects to evaluate its efficiency. Several execution modes with fuzzy duration, cost, and quality are considered for each project activity. Finally, sensitivity analysis is conducted taking three different conditions into account: the shortest duration of the execution modes, the lowest cost of the execution modes, and the highest quality of execution modes for each activity. The solution of each trade-off is compared with the solution obtained from the fuzzy SWARA–TOPSIS method. The schedule is developed according to the best execution mode for each project activity. The obtained results in two different construction projects show significant improvements in the overall project objectives so that the projects can be completed in fewer durations and costs along with higher quality. Because of the higher importance of cost, the cost of each activity is closer to the lowest cost. The activity duration is also closer to the most likely duration, and quality is closer to the high-quality level. The application of this approach can create new opportunities for research and knowledge development in the field of construction project scheduling.
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Dissertations / Theses on the topic "Triangle construction problems"

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Dyntarová, Miroslava. "Problémy žáků střední školy při řešení konstrukčních úloh." Master's thesis, 2021. http://www.nusl.cz/ntk/nusl-446397.

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Title: Problems of pupils of high school in solving geometric construction exercises Author: Miroslava Dyntarová Department: Department of Mathematics and Mathematical Education Supervisor: Mgr. Michal Zamboj, Ph.D., Department of Mathematics and Mathema- tical Education Abstract: The aim of this thesis is to reveal various errors and issues that high school students face in triangle construction problems. The thesis is divided into two parts for clarity. In the theoretical part we deal with construction problems in general and look into their various solution methods and formal procedures recommended by high school textbooks. Next, we focus on sets of points of a given property (that are part of the high school curriculum), give related denitions, basic properties and use cases. For better understanding of the demonstrated problems the thesis is lled with au- xiliary graphs made in the program GeoGebra. In the last chapter of the theoretical part, we introduce various problems that are expected to occur during geometry con- struction problem solving by students themselves. Those were the main focus of the following study. The preparation of the study, its implementation and subsequent ana- lysis of collected data is described in the practical part of the thesis. The study was conducted with 10 students....
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Books on the topic "Triangle construction problems"

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Lopes, Luís. Manuel de construction de triangles. Boucherville, Québec: QED texte, 1996.

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Book chapters on the topic "Triangle construction problems"

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Marinković, Vesna, and Predrag Janičić. "Towards Understanding Triangle Construction Problems." In Lecture Notes in Computer Science, 127–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-31374-5_9.

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Griffeath, David, and Dean Hickerson. "A Two-Dimensional Cellular Automaton Crystal with Irrational Density." In New Constructions in Cellular Automata. Oxford University Press, 2003. http://dx.doi.org/10.1093/oso/9780195137170.003.0007.

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We solve a problem posed recently by Gravner and Griffeath [4]: to find a finite seed A0 of 1s for a simple {0, l}-valued cellular automaton growth model on Z2 such that the occupied crystal An after n updates spreads with a two-dimensional asymptotic shape and a provably irrational density. Our solution exhibits an initial A0 of 2,392 cells for Conway’s Game Of Life from which An cover nT with asymptotic density (3 - √5/90, where T is the triangle with vertices (0,0), (-1/4,-1/4), and (1/6,0). In “Cellular Automaton Growth on Z2: Theorems, Examples, and Problems” [4], Gravner and Griffeath recently presented a mathematical framework for the study of Cellular Automata (CA) crystal growth and asymptotic shape, focusing on two-dimensional dynamics. For simplicity, at any discrete time n, each lattice site is assumed to be either empty (0) or occupied (1). Occupied sites after n updates grows linearly in each dimension, attaining an asymptotic density p within a limit shape L: . . . n-1 A → p • 1L • (1) . . . This phenomenology is developed rigorously in Gravner and Griffeath [4] for Threshold Growth, a class of monotone solidification automata (in which case p = 1), and for various nonmonotone CA which evolve recursively. The coarse-grain crystal geometry of models which do not fill the lattice completely is captured by their asymptotic density, as precisely formulated in Gravner and Griffeath [4]. It may happen that a varying “hydrodynamic” profile p(x) emerges over the normalized support L of the crystal. The most common scenario, however, would appear to be eq. (1), with some constant density p throughout L. All the asymptotic densities identified by Gravner and Griffeath are rational, corresponding to growth which is either exactly periodic in space and time, or nearly so. For instance, it is shown that Exactly 1 Solidification, in which an empty cell permanently joins the crystal if exactly one of its eight nearest (Moore) neighbors is occupied, fills the plane with density 4/9 starting from a singleton.
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Conference papers on the topic "Triangle construction problems"

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Park, Jungseo, Jae-Hoon Kim, Daekyung Kim, Jonggye Shin, and Kwanghee Ko. "Improved Triangle Heating for Automated Thermal Forming System." In SNAME Maritime Convention. SNAME, 2013. http://dx.doi.org/10.5957/smc-2013-p42.

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In this paper, problems associated with a current method for triangle heating, which is used by an automated thermal forming system, are addressed, and an improved method for handling the problems is proposed. The existing algorithm may yield heating information, which is applicable only for a limited range of plates in terms of thickness and may cause undesirable deformation such as ‘over-bending’ and buckling on the boundary. Therefore, a lot of man-hours are required for the correction of the deformation, which would significantly delay the fabrication process. To solve these problems, new formulae covering an extended range of plates are proposed, and the effect of the initial curvature of a plate is considered in the computation of heating information to prevent unexpected deformation. It is shown that the proposed method can induce a desirable amount of deformation on a plate and improve the accuracy of the automated thermal forming system for forming a convex shape. Various examples used in the ship construction are taken to demonstrate the performance of the proposed method.
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Rose, Michael. "Modal Based Correction Methods for the Placement of Piezoceramic Modules." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80789.

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Conventional Finite-Element programs are able to compute the vibration response of mechanical structures. Increasingly also so-called multi-field problems can be solved. For piezoelectric actuators and sensors, electrical degrees of freedom apart from the mechanical ones have to be considered too. The pure actuator effect can also be modelled using the coefficients of thermal expansion. But regarding the optimal placement of flat piezoceramic modules, which couple in the mechanical part through the d31-effect, it proves to be advantageous to consider them after doing the computational complex modal analysis. In this paper, this modal coupling approach is described in detail. It introduces an additional modelling error, because the effect of the stiffness and mass of the modules is not considered in the construction process of the functional space, from which modal shapes are derived. But due to the comparatively small contribution to the global mass and stiffness of such flat devices, this additional error can generally be accepted. Furthermore this error can be reduced to an arbitrarily small amount, if the number of retained eigenmodes is increased and the gain in computational speed is significant. For the calculations, self-written triangle elements with full electro-mechanical coupling have been used, being coded completely in MATLAB. Finally the optimization procedure for the placement of the piezoceramic modules including their mass and stiffness is demonstrated for a test structure.
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Bezperstova, Liudmyla, Yurii Hulyi, and Roman Bezperstov. "CONSTRUCTIVE METHOD OF SOLVING AND CREATING THE CONDITIONS OF MATHEMATICAL PROBLEM ABOUT UNKNOWN ANGLES IN A TRIANGLE." In PARADIGMATIC VIEW ON THE CONCEPT OF WORLD SCIENCE. European Scientific Platform, 2020. http://dx.doi.org/10.36074/21.08.2020.v1.41.

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Shinoda, Junichi, Olga Egorova, Haozhi Qu, and Ichiro Hagiwara. "Characteristic Topology Method for Quadrilateral Mesh Without Self-Intersection of Dual Cycles." In ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/cie-34470.

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The Dual Cycle Elimination method was proposed by Mu¨ller-Hannemann for hexahedral mesh generation. The method begins with a surface quadrilateral mesh whose dual cycles have no self-intersections and, after the elimination of dual cycles, a hexahedral mesh is generated while tracing back the reverse order of eliminations and supplementing hexahedrons inside the object step by step. This paper presents the Characteristic Topology Method as a means to prescribe a quadrilateral surface mesh that can be initial data for further hexahedral mesh generation. The goal of this method is to stress the topology of the given surface and thus use construction of the loops within the algorithm. The surface is given in a nodal polygonal model and then decomposed into a triangle-quadrilateral model. Templates are used to determine the loops. Then due to some rules every loop is implemented by special additional Dual Cycles. The total mesh is the dual graph to the graph of dual cycles. The problem of self-intersections that may appear comes from Mu¨ller-Hannemann’s approach stated above and that is also implemented in this work as a sketch.
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