Relevant bibliographies by topics / Coordinate geometry

Contents

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

Academic literature on the topic 'Coordinate geometry'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Coordinate geometry"

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Dil, Emre, and Talha Zafer. "Transformation Groups for a Schwarzschild-Type Geometry in f(R) Gravity." Journal of Gravity 2016 (November 2, 2016): 1–8. http://dx.doi.org/10.1155/2016/7636493.

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We know that the Lorentz transformations are special relativistic coordinate transformations between inertial frames. What happens if we would like to find the coordinate transformations between noninertial reference frames? Noninertial frames are known to be accelerated frames with respect to an inertial frame. Therefore these should be considered in the framework of general relativity or its modified versions. We assume that the inertial frames are flat space-times and noninertial frames are curved space-times; then we investigate the deformation and coordinate transformation groups between a flat space-time and a curved space-time which is curved by a Schwarzschild-type black hole, in the framework of f(R) gravity. We firstly study the deformation transformation groups by relating the metrics of the flat and curved space-times in spherical coordinates; after the deformation transformations we concentrate on the coordinate transformations. Later on, we investigate the same deformation and coordinate transformations in Cartesian coordinates. Finally we obtain two different sets of transformation groups for the spherical and Cartesian coordinates.
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CAMACHO, A. "AHARONOV–BOHM EFFECT AND COORDINATE TRANSFORMATIONS." Modern Physics Letters A 14, no. 21 (July 10, 1999): 1445–53. http://dx.doi.org/10.1142/s0217732399001541.

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Resorting to a Gedankenexperiment which is very similar to the famous Aharonov–Bohm proposal it will be shown that, in the case of a Minkowskian space–time, we may use a nonrelativistic quantum particle and a noninertial coordinate system and obtain geometric information of regions that are, to this particle, forbidden. This shows that the outcome of a nonrelativistic quantum process is determined not only by the features of geometry at those points at which the process takes place, but also by geometric parameters of regions in which the quantum system cannot enter. From this fact we could claim that geometry at the quantum level plays a nonlocal role. Indeed, the measurement outputs of some nonrelativistic quantum experiments are determined not only by the geometry of the region in which the experiment takes place, but also by the geometric properties of space–time volumes which are, in some way, forbidden in the experiment.
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Terc, Michael. "Coordinate Geometry—Art and Mathematics." Arithmetic Teacher 33, no. 2 (October 1985): 22–24. http://dx.doi.org/10.5951/at.33.2.0022.

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Our sutudents cry for self-expression, for a chance to see mathematics in action. Frequently, however, the structure of mathematics does not lend itself to individual style or variation. Problem solving can tend to be dull and monotonous rather than exciting and stimulating.
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BHATTACHARYA, AMRITA, and ALEXANDER A. POTAPOV. "BENDING OF LIGHT IN ELLIS WORMHOLE GEOMETRY." Modern Physics Letters A 25, no. 28 (September 14, 2010): 2399–409. http://dx.doi.org/10.1142/s0217732310033748.

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A recent work by Dey and Sen derived the approximate light deflection angle α by an Ellis wormhole in terms of proper radial distance ℓ that covers the entire spacetime. On the other hand, Bodenner and Will calculated the expressions for light bending in Schwarzschild geometry using various coordinates and showed that they all reduce to a single formula when re-expressed in the coordinate independent language of "circumferential radius" rC identified with the standard radial coordinate rS. We shall argue that the coordinate invariant language for two-way wormholes should be ℓ rather than rS. Hence here we find the exact deflection α in Ellis wormhole geometry first in terms of ℓ and then in terms of rS. We confirm the latter expression using three different methods. We argue that the practical measurement scheme does not necessarily single out either ℓ or rS. Some errors in the literature are corrected.
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Shvets, S. V., and V. P. Astakhov. "Effect of Insert Angles on Cutting Tool Geometry." Journal of Engineering Sciences 7, no. 2 (2020): A1—A6. http://dx.doi.org/10.21272/jes.2020.7(2).a1.

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An analysis of publications has shown that mechanically clamped indexable inserts are predominantly used in modern tool manufacturing. Each insert has its shape and geometry in the tool coordinate system. The static system’s required geometry is achieved by the tilting of the insert pocket in the radial and axial directions. Therefore, it is of great importance in the tool design to know the relationships between the insert’s geometry parameters in the tool coordinate system where the geometry paraments of the insert are defined and working geometry parameters of the tool defined in the static coordinate system. The paper presents the developed methodology for determining the insert pocket base surface position to ensure the required values of the tool geometry parameters of the selected indexable insert in the static coordinate system. The graphs of the dependence of each of the angles of the insert geometry on the angles of rotation of this insert in the front and profile planes are presented as the level lines for practical use. Using these graphs, one can optimize all geometric insertion parameters in the static coordinate system. The model of the calculations of the mechanism of the insert clamping by a screw is developed. The basic size and tolerance of the output link determine the distance from the intersection line of the base surfaces to the thread axis on the pocket and the minimum amount of the screw stroke on the insert clamping in the pocket. Keywords: indexable insert, cutting tool, coordinate system, base surfaces, geometric parameters.
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Iofa, Mikhail Z. "Kodama-Schwarzschild versus Gaussian Normal Coordinates Picture of Thin Shells." Advances in High Energy Physics 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/5632734.

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Geometry of the spacetime with a spherical shell embedded in it is studied in two coordinate systems: Kodama-Schwarzschild coordinates and Gaussian normal coordinates. We find explicit coordinate transformation between the Kodama-Schwarzschild and Gaussian normal coordinate systems. We show that projections of the metrics on the surface swept by the shell in the 4D spacetime in both cases are identical. In the general case of time-dependent metrics we calculate extrinsic curvatures of the shell in both coordinate systems and show that the results are identical. Applications to the Israel junction conditions are discussed.
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Hawryluk, Marek, Marek Kuran, and Jacek Ziemba. "The use of replicas in the measurement of machine elements with use of contact coordinate measurements." Mechanik 91, no. 11 (November 12, 2018): 958–60. http://dx.doi.org/10.17814/mechanik.2018.11.169.

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Modern technology allows to design and manufacture machine elements with complex geometry that makes it difficult or even impossible to use coordinate measuring machines for verification of them. The article presents the possibility of using replicas of product geometry to control geometric features using contact measurements on a coordinate machine.
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Matsuura, Ryota, and Sarah Sword. "Illuminating Coordinate Geometry with Algebraic Symmetry." Mathematics Teacher 108, no. 6 (February 2015): 470–73. http://dx.doi.org/10.5951/mathteacher.108.6.0470.

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Westegaard, Susanne K. "Activities: Stitching Quilts into Coordinate Geometry." Mathematics Teacher 91, no. 7 (October 1998): 587–600. http://dx.doi.org/10.5951/mt.91.7.0587.

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Quilts—useful items, visually appealing, steeped in history, and an integral part of our culture—can also be the jumping-off point for many mathematical investigations” (Morrow and Bassarear 1996). The history behind many quilt patterns offers an opportunity for crossdisciplinary projects with art and social studies classes. Such children's books as Eight Hands Round (Paul 1991) and Selina and the Bear Paw Quilt (Smucker 1995) connect mathematics with literature.
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Wenxiang, Zhang. "Plücker Coordinate Geometry and its Applications to Studies of Instantaneous Axial Planes of Generating Gears." International Journal of Mechanical Engineering Education 22, no. 4 (October 1994): 235–44. http://dx.doi.org/10.1177/030641909402200401.

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After an introduction of the Plücker coordinate geometry, a discussion is made of the expression of screws in Plücker coordinates and the addition of screws. As a result, the geometry of generating gears is re-studied and a formula is derived for calculating the axode length of hypoid gears.
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Dissertations / Theses on the topic "Coordinate geometry"

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Zhao, Haibin. "Multisensor integration and discrete geometry processing for coordinate metrology." Cachan, Ecole normale supérieure, 2010. http://tel.archives-ouvertes.fr/tel-00451244/fr/.

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L'intégration de systèmes multi-capteurs est la réponse la plus adaptée aux besoins croissants en matière de complexité et d'exactitude de mesures en métrologie par coordonnées. Des efforts importants sont consacrés à développer des systèmes multi-capteurs qui permettent d'assurer une mesure globale de la géométrie avec une incertitude réduite. Cette thèse a pour objectif l'intégration de systèmes multi-capteurs en métrologie par coordonnées selon deux aspects: la modélisation des fonctions et des données et le traitement de la géométrie discrète. La modélisation des fonctions et des données permet une meilleure compréhension des exigences des fonctions du système et des spécifications des données pour l'intégration de systèmes multi-capteurs. Des modèles hiérarchiques fonctionnels du système sont construits en utilisant la méthodologie IDEF0 et sont décomposés en quatre activités de base. Une démarche à base d'ontologies est utilisée pour modéliser les différentes données et leur représentation structurée. Quatre domaines de données et de leurs relations sont spécifiés pour gérer les données multiples dans l'intégration des systèmes multi-capteurs. Des méthodes efficaces et robustes pour le traitement de la géométrie discrète dans le cadre de l'intégration multi-capteurs sont l'objet principal de cette thèse. Une estimation fiable de la normale et des courbures est essentielle pour le traitement des formes discrètes. Une méthode basée sur le tenseur de courbure est utilisée pour l'estimation des courbures discrètes. Une analyse comparative montre que la méthode proposée fournit de meilleures performances par rapport à d'autres méthodes existantes
Multisensor integration systems are used to fulfill the increasing requirements on the complexity and accuracy of coordinate metrology. Significant efforts are being devoted to develop multisensor integration systems that achieve holistic geometrical measurement with reduced uncertainty. This thesis investigates on the achievement of multisensor integration in coordinate metrology from two main parts: system function and data modeling, and discrete geometry processing. System function and data modeling allow obtaining clear understanding of function requirements and data specification of the multisensor integration system. Hierarchical function models of the system are built using IDEF0 methodology, which are decomposed into four basic activities. An ontology based method is employed to model the various data in the system with structured representation. Four data domains and their inter-relationships are specified to manage the multiple data in multisensor integration system clearly. Efficient and robust methods for discrete geometry processing to support multisensor integration are the main focus of this dissertation. This requires efficient methods for discrete differential geometry properties estimation, registration of discrete shapes, shape recognition and segmentation. Reliable estimation of normal and curvatures is essential for discrete shapes processing. Most discrete geometry processing procedures are based on the normal and curvatures’ information. A tensor based method is used for discrete curvature estimation. The proposed method provides better performance according to a comparative analysis. Registration is one of the most important and decisive steps of multisensor integration. Registration algorithms enable to align the different point data captured in the respective sensor’s coordinate system. A registration method is proposed to align different discrete shapes with unknown correspondences. A combination of curvature information and Euclidean distance is used to improve the performances of the classical ICP algorithm. Discrete shape recognition and segmentation are required in many applications. A new method based on shape index and curvedness is developed. The local surface type of a vertex is recognized according to its shape index value. The vertices are then clustered according to their local surfaces. A connected region algorithm is then implemented to generate the segmentation results. Considerable cases are tested and the method provides satisfying results. The above methods have been implemented in a new computerized system called DSP-COMS. A detailed case study of an industrial workpiece digitized by laser scanning and touch probing is presented. The measured point data are then processed using DSP-COMS. The results show the robustness of the above methods
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Tråsdahl, Øystein. "High order methods for partial differential equations: geometry representation and coordinate transformations." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-17077.

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Li, Feng. "Integrated tactile-optical coordinate measurement for the reverse engineering of complex geometry." Thesis, University of Huddersfield, 2014. http://eprints.hud.ac.uk/id/eprint/23725/.

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Complex design specifications and tighter tolerances are increasingly required in modern engineering applications, either for functional or aesthetic demands. Multiple sensors are therefore exploited to achieve both holistic measurement information and improved reliability or reduced uncertainty of measurement data. Multi-sensor integration systems can combine data from several information sources (sensors) into a common representational format in order that the measurement evaluation can benefit from all available sensor information and data. This means a multi-sensor system is able to provide more efficient solutions and better performances than a single sensor based system. This thesis develops a compensation approach for reverse engineering applications based on the hybrid tactile-optical multi-sensor system. In the multi-sensor integration system, each individual sensor should be configured to its optimum for satisfactory measurement results. All the data measured from different equipment have to be precisely integrated into a common coordinate system. To solve this problem, this thesis proposes an accurate and flexible method to unify the coordinates of optical and tactile sensors for reverse engineering. A sphere-plate artefact with nine spheres is created and a set of routines are developed for data integration of a multi-sensor system. Experimental results prove that this novel centroid approach is more accurate than the traditional method. Thus, data sampled by different measuring devices, irrespective of their location can be accurately unified. This thesis describes a competitive integration for reverse engineering applications where the point cloud data scanned by the fast optical sensor is compensated and corrected by the slower, but more accurate tactile probe measurement to improve its overall accuracy. A new competitive approach for rapid and accurate reverse engineering of geometric features from multi-sensor systems based on a geometric algebra approach is proposed and a set of programs based on the MATLAB platform has been generated for the verification of the proposed method. After data fusion, the measurement efficiency is improved 90% in comparison to the tactile method and the accuracy of the reconstructed geometric model is improved from 45 micrometres to 7 micrometres in comparison to the optical method, which are validated by case study.
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Fields, Lisa Ann. "Use of Web-Based Technology to Enhance Instruction of Virginia's Seventh and Eighth Grade Geometry Standards of Learning." Digital Commons @ East Tennessee State University, 2007. https://dc.etsu.edu/etd/2087.

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The purpose of this thesis is to develop web-based modules for enhancing instruction of the geometry sections of the Virginia Standards of Learning in the seventh and eighth grades. While all of Virginia's seventh and eighth grade Standards of Learning strands are certainly worthy of these types of modules, geometry appeals to me most because of the vast amount of web-based resources that will be valuable when organized into modules. It is my hope that teachers of these grades will find this useful in their instruction of geometry.
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Soares, Júnior Luiz. "Sistemática para Garantia da Qualidade na Medição de Peças com Geometria Complexa e Superfície com Forma Livre Utilizando Máquina de Medir por Coordenadas." Universidade Federal da Paraí­ba, 2010. http://tede.biblioteca.ufpb.br:8080/handle/tede/5420.

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Parts with complex geometry and with free-form surface are of great interest in many industrial applications, either for functional or aesthetic issue. Its spread is due to advances in CAD / CAM systems and coordinate measuring technology. Despite technological advances, product design remains a major problem in industry. The problems range from design conception to those inherent in the manufacturing process and control, which are often discovered only in the product application phase. The dimensional variations of shape and surface texture are specified in the technical drawing using geometric and dimensional tolerance. To part with complex geometry variations are allowable tolerances specified by line and surface profile. Their control typically consists of a comparison of the coordinate points measured on the surface to the CAD model available. This paper contains a proposal to systematize procedures for quality assurance of measurement of parts with complex geometry and free-form surface by using coordinate measuring machines. The proposal was based on extensive study on the subject, the findings of problems revealed in visits to six companies that use technology to coordinate measurement and the results of case studies from a company in the automotive sector. The system focuses on the major sources of errors of coordinate measuring and proved easy to be applied in the selected company.
Peças com geometria complexa e superfície com forma livre são de grande interesse em muitas aplicações industriais, seja por questão funcional ou estética. Sua disseminação deve-se, em parte, aos avanços nos sistemas CAD/CAM e na tecnologia de medição por coordenadas. Apesar dos avanços tecnológicos, o projeto do produto continua sendo um dos maiores problemas da indústria. Os problemas vão desde a concepção do projeto até àqueles inerentes ao processo de fabricação e controle, que muitas vezes são descobertos somente na aplicação do produto. As variações dimensionais, de forma e de textura da superfície são especificadas no desenho técnico através de tolerância dimensional e geométrica. Para peça com geometria complexa as variações admissíveis são especificadas através de tolerâncias de perfil de linha e de superfície. O seu controle tipicamente consiste na comparação dos pontos coordenados medidos sobre a superfície com o modelo CAD disponível. Este trabalho contém uma proposta de sistematização de procedimentos para garantia da qualidade da medição de peças com geometria complexa e superfície com forma livre através de máquina de medir por coordenadas cartesianas. A proposta foi baseada no amplo estudo sobre o tema, nas constatações de problemas evidenciados nas visitas realizadas em seis empresas que utilizam a tecnologia de medição por coordenadas e nos resultados de estudos de casos realizados numa empresa do setor automotivo. A sistemática foca nas principais fontes de erros da medição por coordenadas e demonstrou ser de fácil aplicação na empresa selecionada.
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Turaça, Angélica. "As coordenadas de Fenchel-Nielsen." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45132/tde-27082015-073617/.

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Nesta dissertação, definimos a geometria hiperbólica usando o disco de Poincaré (D2) e o semiplano superior (H2) com as respectivas propriedades. Além disso, apresentamos algumas funções e relações importantes da geometria hiperbólica; conceituamos as superfícies de Riemann, analisando suas propriedades e representações; estudamos o espaço de Teichmüller com a devida decomposição em calças. Esses temas são ferramentas necessárias para atingir o objetivo da dissertação: definir as coordenadas de Fenchel Nielsen como um sistema de coordenadas locais do espaço de Teichmüller Tg.
In this dissertation, we defined the hyperbolic geometry using the Poincares disk (D2) and upper half-plane (H2) with its properties. Besides, we presented some functions and important relations of the hyperbolic geometry; we conceptualize the Riemann surfaces, analyzing its properties and representations; we studied the Teichmüller Space with proper decomposition pants. These themes are essential tools to reach the goal of the work: The definition of the Fenchel Nielsen coordenates as local coordinate system of the Teichmüller space Tg.
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Lidberg, Petter. "Barycentric and harmonic coordinates." Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-179487.

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Soares, Vanessa Ribeiro. "Batalha naval e suas aplicações." Universidade Federal de Goiás, 2016. http://repositorio.bc.ufg.br/tede/handle/tede/5909.

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This work has the purpose contribute to the improvement in some teaching contents of analytic geometry and trigonometry in high school . The content work was based on the National Curriculum Parameters, highlighting de nitions, theorems and properties necessary for the development of student learning. The theme was chosen after a practical experience involving the Naval Battle game in order to reduce the students' di culties. The playful work, as the game, has a practical application that does the student become familiar with the content. That's an interesting way to propose problems and solutions involving the content. Thus becomes something attractive to the student and encourages creativity in nding problems solutions.
O trabalho tem como objetivo contribuir para o aprimoramento no ensino de alguns conteúdos de Geometria Analítica e Trigonometria no Ensino Médio. Dentro dos Parâmetros Curriculares Nacionais, trabalhamos o conteúdo destacando de nições, teoremas e propriedades necessárias para o desenvolvimento de aprendizagem do aluno. O tema foi escolhido depois de uma experiência prática envolvendo o jogo Batalha Naval a m de diminuir as di culdades dos alunos. O trabalho lúdico, como o jogo, tem uma aplicação prática que faz o aluno se familiarizar com os conceitos. É uma forma interessante de propor problemas e soluções envolvendo o conceitos. Assim se torna algo atrativo para o aluno e favorece a criatividade na busca de soluções para os problemas.
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White, Edward C. Jr. "Polar - legendre duality in convex geometry and geometric flows." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24689.

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Guimarães, Amanda Ribeiro. "Funções de Base Gaussianas Geradas pelo Método da Coordenada Geradora Aplicadas em Cálculos Quânticos Moleculares." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/75/75134/tde-23102018-113531/.

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O conjunto de funções de base gaussianas, o p-GCHF, foi gerado para os átomos Na, Al, Si, P, S e Cl pelo Método da Coordenada Geradora (MCG) através da expansão integral polinomial para discretizar (DIP) as equações de Griffin-Hill-Wheeler-Hartree-Fock (GHW-HF). A base p-GCHF, de qualidade 7Z, foi contraída por meio do programa Contract que opera segundo os preceitos de contração de Davidson. O processo de contração resultou em 9 funções do tipos e 7 funções p para os átomos de Na e Mg e de 9 funções s e 8 funções p para os átomos de Al, Si, P, S e Cl. Expoentes de polarização foram gerados através do programa Polarization em nível CISD para os átomos de H, B, C, N, O, F, Na, Mg, Al, Si, P, S e Cl. Foram necessários não mais do que 2p1d expoentes de polarização para compor a base p-GCHF para o átomo de H, 2d1f para os átomos da primeira fila e 3d2f, para os átomos da segunda fila da tabela periódica. Cálculos moleculares revelaram que a base p-GCHF é competitiva em energia com as bases cc-pVQZ e cc-pV5Z, entretanto apresentando custos computacionais bem menores que as mencionadas bases de Dunning. Análises das frequências vibracionais e das geometrias de otimização dos pontos estacionários, tanto mínimos quanto de estado de transição, também apontam similaridades entre o conjunto de base p-GCHF e a base cc-pVQZ, porém com diferenças de tempos de CPU que apontam a base gerada pelo MCG como computacionalmente vantajosa. Um conjunto de base capaz de descrever um dado sistema de maneira equivalente à célebres conjuntos de base da literatura, mas trazendo consigo o benefício da economia de tempo computacional é absolutamente oportuno principalmente àqueles que têm como objeto de estudo moléculas com um número considerável de átomos.
The gaussian basis sets p-GCHF was generated for a set of atoms from Na to Cl through the Generator Coordinate Method (GCM) based on a polynomial integral expansion to discretize the Griffin-Wheeler-Hartree-Fock equations. The p-GCHF is a 7z type basis sets and was contracted through the Contract program which works based on the Davidson\'s contraction model. The contraction process provided a set of 9s7p functions for Na and Mg atoms and 9s8p functions for Al, Si, P, S e Cl atoms. Polarizations exponents were acquired through the Polarization program at CISD level of theory for H, B, C, N, O, F, Na, Mg, Al, Si, P, S e Cl atoms. No more than 2p1d polarization exponents were necessary to compose the p-GCHF basis set for hydrogen atom, 2d1f for the first row of the periodic table and 3d2f for the second row one. Molecular calculations show that p-GCHF works like cc-pVQZ and cc-pV5Z basis sets but with less computational cost than the Dunning\'s ones. Vibrational frequency analysis and optimization geometry to the stationary points minimum as well as transition state, revealed similarities between p-GCHF and cc-pVQZ basis sets, but again with the GCM basis sets being computationally advantageous. A basis sets capable to describe a system like the main gaussian basis sets known in the literature but demanding less computational effort is very helpful above all for those who work with massive molecular systems.
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Books on the topic "Coordinate geometry"

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Coordinate geometry. Mineola, N.Y: Dover Publications, 2005.

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M, Pang K., ed. Calculus and coordinate geometry. Hong Kong: Vision, 1992.

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Mark, June. Geography of the coordinate plane: Teaching guide. Portsmouth, NH: firsthand/Heinemann, 2014.

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Ross, Debra. Master math: Geometry : including everything from triangles, polygons, proofs, and deductive reasoning to circles, solids, similarity, and coordinate geometry. Clifton Park, NY: Thomson/Delmar Learning, 2005.

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Master math: Trigonometry : including everything from trigonometric functions, equations, triangle, and graphs to identities, coordinate systems, and complex numbers. Clifton Park, NY: Thomson/Delmar Learning, 2002.

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Ciarlet, Philippe G. An introduction to differential geometry with applications to elasticity. Dordrecht: Springer, 2010.

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Anderson, Moira. Grid coordinates by land, air, and sea. Mankato, Minn: Capstone Press, 2010.

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ill, Kenyon Tony, ed. Plotting points and position. Brookfield, Conn: Copper Beech Books, 1998.

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ill, Geehan Wayne, ed. Sir Cumference and the Viking's map. Watertown, MA: Charlesbridge, 2012.

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Coordinate-free multivariable statistics: An illustrated geometric progression from Halmos to Gauss and Bayes. Oxford: Clarendon Press, 1987.

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Book chapters on the topic "Coordinate geometry"

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Parkin, Alan. "Coordinate Geometry." In Digital Imaging Primer, 61–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-85619-1_6.

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Celia, C. W., A. T. F. Nice, and K. F. Elliott. "Coordinate geometry." In Advanced Mathematics 3, 343–95. London: Macmillan Education UK, 1985. http://dx.doi.org/10.1007/978-1-349-06711-4_10.

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Cohn, P. M. "Coordinate geometry." In Elements of Linear Algebra, 88–115. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4899-3286-0_7.

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Fenn, Roger. "Coordinate Geometry." In Springer Undergraduate Mathematics Series, 29–62. London: Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-0325-7_2.

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Angell, Ian O. "Two-Dimensional Coordinate Geometry." In Advanced Graphics with the IBM Personal Computer, 48–69. London: Macmillan Education UK, 1985. http://dx.doi.org/10.1007/978-1-349-07338-2_3.

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Angell, Ian O. "Three-Dimensional Coordinate Geometry." In Advanced Graphics with the IBM Personal Computer, 141–58. London: Macmillan Education UK, 1985. http://dx.doi.org/10.1007/978-1-349-07338-2_7.

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Haines, Betty, Roger Haines, and Andrew May. "Graphs and coordinate geometry." In Mathematics A Level, 54–64. London: Macmillan Education UK, 1996. http://dx.doi.org/10.1007/978-1-349-13850-0_6.

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Paranjape, Kapil. "Axiomatic and Coordinate Geometry." In Analysis, Geometry and Probability, 140–60. Gurgaon: Hindustan Book Agency, 1996. http://dx.doi.org/10.1007/978-93-80250-87-8_8.

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Gliklikh, Yuri E. "Elements of Coordinate — Free Differential Geometry." In Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics, 1–44. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8634-4_1.

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Bottema, O., and Reinie Erne. "Coordinate Systems with Respect to a Triangle." In Topics in Elementary Geometry, 1–4. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-78131-0_6.

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Conference papers on the topic "Coordinate geometry"

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Hermann, Gyula, and Gyorgy Hermann. "Application of computational geometry in coordinate measurement." In 2015 IEEE 10th Jubilee International Symposium on Applied Computational Intelligence and Informatics (SACI). IEEE, 2015. http://dx.doi.org/10.1109/saci.2015.7208258.

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Karasik, Yevgeny B. "Power of local coordinate transformations in optical computational geometry." In SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, edited by Robert A. Melter, Angela Y. Wu, and Longin J. Latecki. SPIE, 1996. http://dx.doi.org/10.1117/12.251791.

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Ge, Q. J., and Donglai Kang. "Geometric Design of Smooth Composite Ruled Surface Strips Using Dual Spherical Geometry." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0086.

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Abstract This paper deals with geometric construction of smooth composite ruled surface strips. Oriented lines that constitute the rulings of the ruled surfaces are represented by unit vectors with three components over the ring of dual numbers. The problem of designing a smooth ruled surface is studied as that of designing a one-real-parametric curve on the unit dual sphere. Geometric conditions for piecing two ruled surfaces smoothly are developed using differential geometry of curves on the dual sphere. A coordinate-frame invariant method for line segmentation is also presented. Finally, a geometric algorithm is presented for constructing composite Bézier ruled surface strips with second-order geometric continuity. The resulting surface strips are coordinate-frame invariant and their rulings are more uniformly parameterized than those obtained with other methods.
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Trager, Matthew, Martial Hebert, and Jean Ponce. "Coordinate-Free Carlsson-Weinshall Duality and Relative Multi-View Geometry." In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2019. http://dx.doi.org/10.1109/cvpr.2019.00031.

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Ngampitipan, Tritos, Petarpa Boonserm, and Apisit Kinreewong. "The Modified Techniques for Generating Perfect Fluid Sphere in Isotropic Coordinate." In 6th Annual International Conference on Computational Mathematics, Computational Geometry & Statistics (CMCGS 2017). Global Science & Technology Forum (GSTF), 2017. http://dx.doi.org/10.5176/2251-1911_cmcgs17.20.

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Fogle, Martin A., and J. Kirk Wu. "A Relative Coordinate Formulation for Variational Solid Modeling." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0102.

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Abstract A minimal formulation using relative coordinates is presented for variational solid modeling. Computational methods developed for the kinematic modeling of mechanical systems are used to derive a minimal problem formulation. First, the concept of arbitrary coordinates is introduced to reduce the dimension of the constraint vector. Next, the variational problem is divided into two sub-problems. This is done by modeling the problem as a graph, which is then analyzed to identify open loops and decoupled loops. The third method used to reduce the size of the variational problem is to transform the sub-problems from a Cartesian coordinate formulation to a relative coordinate formulation. Once identified, the open loop sub-problem is solved trivially. Finally, the decoupled loop sub-problem is solved by optimization techniques which minimize the total constraint violation. Compared to the traditional approach, the relative coordinate method has a much smaller formulation, is highly convergent, and is able to evaluate under constrained geometry.
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Siddappaji, Kiran, Mark G. Turner, Soumitr Dey, Kevin Park, and Ali Merchant. "Optimization of a 3-Stage Booster: Part 2—The Parametric 3D Blade Geometry Modeling Tool." In ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/gt2011-46664.

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A parametric approach for blade geometry design has been developed to obtain 3D blade models. The geometry of the blade is defined by a basic set of parameters that are first obtained from an axisymmetric solver. These parameters include the leading edge meridional coordinates, flow angles, axial chord, and the meridional coordinates of streamlines. Other parameters such as thickness to chord ratio need to be defined. Using these parameters the 2D airfoils are created and are stacked radially using one of the many multiple options that define the stacking axes from several additional parameters. The tool produces the desired number of 2D sections in a normalized coordinate system. Each blade section is then transformed to a 3D Cartesian coordinate system. Using Unigraphics-NX (CAD package), these sections are lofted and a 3D blade model is obtained. Parametric update of the spline points defining the 3D blade sections results in new blade shapes without going directly back into the CAD system. The importing of the geometry into a CFD solver, and a finite element solver to determine mode shapes and stresses is demonstrated. Full details of the blade procedure is presented for a 3-Stage Booster design. This parametric approach for defining blade geometry and how it lays a groundwork for a high-fidelity optimization procedure is described.
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Arikan, M. A. Sahir, and Mustafa Tamar. "Tooth Contact and 3-D Stress Analysis of Involute Helical Gears." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0059.

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Abstract An involute helical gear tooth is modelled by using helical gear geometry and a solid modelling package, and this model is used to determine the load distribution on contact lines of mating teeth, and to make the stress analysis by using three-dimensional tetrahedron finite elements with four nodes. Tooth contact analysis is made by using the theory of gearing. Geometry of the cutting tool is used to determine the surface equations of the pinion and the gear in their own coordinate systems, then these equations are transformed to a fixed coordinate system to make the tooth contact analysis and to find the coordinates of contact points. Found contact point coordinates are then transformed back to the original coordinate systems and contact lines on helical gear teeth are formed. Results of this analysis is used to determine the application points and directions of the forces acting on the tooth. Then the stiffnesses of meshing teeth and the load distributions on contact lines are found, which are then used for stress analysis.
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Msiza, Ishmael S., Brain Leke-Betechuoh, Fulufhelo V. Nelwamondo, and Ntsika Msimang. "A fingerprint pattern classification approach based on the coordinate geometry of singularities." In 2009 IEEE International Conference on Systems, Man and Cybernetics - SMC. IEEE, 2009. http://dx.doi.org/10.1109/icsmc.2009.5346860.

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Shabana, Ahmed A., Ashraf M. Hamed, Abdel-Nasser A. Mohamed, Paramsothy Jayakumar, and Michael D. Letherwood. "Limitations of B-Spline Geometry in the Finite Element/Multibody System Analysis." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47168.

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This paper examines the limitations of using B-spline representation as an analysis tool by comparing its geometry with the nonlinear finite element absolute nodal coordinate formulation (ANCF) geometry. It is shown that while both B-spline and ANCF geometries can be used to model non-structural discontinuities using linear connectivity conditions, there are fundamental differences between B-spline and ANCF geometries. First, while B-spline geometry can always be converted to ANCF geometry, the converse is not true; that is, ANCF geometry cannot always be converted to B-spline geometry. Second, because of the rigid structure of the B-spline recurrence formula, there are restrictions on the order of the parameters and basis functions used in the polynomial interpolation; this in turn can lead to models that have significantly larger number of degrees of freedom as compared to those obtained using ANCF geometry. Third, in addition to the known fact that B-spline does not allow for straight forward modeling of T-junctions, B-spline representation cannot be used in a straight forward manner to model structural discontinuities. It is shown in this investigation that ANCF geometric description can be used to develop new spatial chain models governed by linear connectivity conditions which can be applied at a preprocessing stage allowing for an efficient elimination of the dependent variables. The modes of the deformations at the definition points of the joints that allow for rigid body rotations between ANCF finite elements are discussed. The use of the linear connectivity conditions with ANCF spatial finite elements leads to a constant inertia matrix and zero Coriolis and centrifugal forces. The fully parameterized structural ANCF finite elements used in this study allow for the deformation of the cross section and capture the coupling between this deformation and the stretch and bending. A new chain model that employs different degrees of continuity for different coordinates at the joint definition points is developed in this investigation. In the case of cubic polynomial approximation, C1 continuity conditions are used for the coordinate line along the joint axis; while C0 continuity conditions are used for the other coordinate lines. This allows for having arbitrary large rigid body rotation about the axis of the joint that connects two flexible links. Numerical examples are presented in order to demonstrate the use of the formulations developed in this paper.
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Reports on the topic "Coordinate geometry"

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D. G. McKenzie, III. ESF/REPOSITORY INTERFACE LAYOUT COORDINATE GEOMETRY ANALYSIS. Office of Scientific and Technical Information (OSTI), November 1995. http://dx.doi.org/10.2172/891096.

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D. McKenzie III. ESF/REPOSITORY INTERFACE LAYOUT COORDINATE GEOMETRY ANALYSIS. Office of Scientific and Technical Information (OSTI), November 1995. http://dx.doi.org/10.2172/862352.

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D. G. McKenzie. ESF/REPOSITORY INTERFACE LAYOUT COORDINATE GEOMETRY ANALYSIS. Office of Scientific and Technical Information (OSTI), November 1995. http://dx.doi.org/10.2172/891097.

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Doerry, Armin W., and Douglas L. Bickel. Spotlight SAR Data Collection Geometry from ECEF Coordinates. Office of Scientific and Technical Information (OSTI), July 2020. http://dx.doi.org/10.2172/1641881.

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