Relevant bibliographies by topics / Geometry, Analytic. Curves, Plane

Contents

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

Academic literature on the topic 'Geometry, Analytic. Curves, Plane'

Author: Grafiati
Published: 4 June 2021
Last updated: 17 February 2022

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Journal articles on the topic "Geometry, Analytic. Curves, Plane"

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Гирш and A. Girsh. "Foci of Algebraic Curves." Geometry & Graphics 3, no. 3 (November 30, 2015): 4–17. http://dx.doi.org/10.12737/14415.

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Curves have always been part geometry. Initially, there were lines and circle, then it was added to a conic section and later, with the advent of analytic geometry, they added more complex curves. Particularly in a number of lines are algebraic curves that are described by algebraic equations. Curves found application mostly in mechanics. Today algebraic curves used in engineering and in mathematics, in number theory, knot theory, computer science, criminology, etc. With the bringing to account of complex numbers became possible to consider curves in the complex plane. It has expanded the horizons of geometry and enriched their knowledge on curves, particularly on algebraic curves. Our goal is to give a geometric picture of the foci of algebraic curves clearly show the position of the foci in the plane, show how the number of foci associated with a class curve. The solution of this problem we see in the application we have developed ways to visualize imaginary images to the study of foci and focal centers of algebraic curves. This article explains the concept of the foci of algebraic curves shows the basic principle of the curve-theory and offers a method for the identification of the foci. The geometric picture of the foci is shown in a diagram, which is putted together from two tables. One table shows the real curve with her foci, the other table shows an imaginary cut of the curve, on which the isotropic line contacts the cut and under them intersects in a real point. The point is a focal point of the real curve. This project shows 16 diagrams for conic, cubes and quadrics.
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Chou, Kai-Seng, and Xi-Ping Zhu. "Shortening complete plane curves." Journal of Differential Geometry 50, no. 3 (1998): 471–504. http://dx.doi.org/10.4310/jdg/1214424967.

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Chen, Bingkui, Dong Liang, and Yane Gao. "Geometry design and mathematical model of a new kind of gear transmission with circular arc tooth profiles based on curve contact analysis." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 17 (March 11, 2014): 3200–3208. http://dx.doi.org/10.1177/0954406214526866.

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A new meshing relationship for gear drive to characterize the conjugation geometry is studied in this paper based on conjugate curves. Conjugate curves are described as two smooth curves always keep continuous and tangent contact with each other in given contact direction under motion law. The general principle of curve meshing is developed for the given spatial or plane curve. The meshing equation along arbitrary direction of contact angle is derived. The properties of geometric and motion of the contact of conjugate curves are discussed. According to the equidistance-enveloping method, tubular meshing surfaces are proposed to build up circular arc tooth profiles, which inherit all properties of conjugate curves. The geometry design and mathematical model of the gears are established. Three types of contact pattern of tooth profiles are generated: convex-to-convex, convex-to-plane and convex-to-concave. A calculation example for convex-to-concave tooth profiles of gears is provided. Theoretical and numerical results demonstrate the feasibility and correctness of proposed conjugate curves theory and it lays the foundation for the design of high performance gear transmission.
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Гирш and A. Girsh. "Envelope of a Family of Curves." Geometry & Graphics 4, no. 4 (December 19, 2016): 14–18. http://dx.doi.org/10.12737/22839.

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A one-parameter family of algebraic curves has an envelope line, which may be imaginary in certain cases. Jakob Steiner was right, considering the imaginary images as creation of analysis. In the analysis a real number is just a part of a complex number and in certain conditions the initial real values can give an imaginary result. But Steiner was wrong in denying the imaginary images in geometry. The geometry, in contrast to the single analytical space exists in several spaces: Euclidean geometry operates only on real figures valid and does not contain imaginary figures by definition; pseudo-Euclidean geometry operates on imaginary images and constructs their images, taking into account its own features. Geometric space is complex and each geometric object in it is the complex one, consisting of the real figure (core) having the "aura" of an imaginary extension. Thus, any analytical figure of the plane is present at every point of the plane or by its real part or by its imaginary extension. Would the figure’s imaginary extension be visible or not depends on the visualization method, whether the image has been assumed on superimposed epures – the Euclideanpseudo-Euclidean plane, or the image has been traditionally assumed only in the Euclidean plane. In this paper are discussed cases when a family of algebraic curves has an envelope, and is given an answer to a question what means cases of complete or partial absence of the envelope for the one-parameter family of curves. Casts some doubt on widely known categorical st
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Korotkiy, Viktor. "Cubic Curves in Engineering Geometry." Geometry & Graphics 8, no. 3 (November 24, 2020): 3–24. http://dx.doi.org/10.12737/2308-4898-2020-3-24.

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In this paper are considered historically the first (the 60’s of the 20th century) computational methods for algebraic cubic curves constructing. The analysis of a general cubic curve equation r(t)=a3t3+a2t2+a1t+a0 has been carried out. As an example has been considered the simplest cubic curve r(t)=it3+jt2+kt. Based on the general cubic curve equation have been obtained equations of a cubic curve passing through two predetermined points and having predetermined tangents at these points. The equations have been presented both in Ferguson and Bézier forms. It has been shown that the cubic curve vector equation (for example, the standard equation of a Bezier curve) can be represented in a point form. Have been considered examples for constructing segments of cubic curves meeting the given boundary conditions. The generalized cubic curve equation, containing weight coefficients, has been obtained by the method of exit into four-dimensional space. Has been considered a vector parametric equation of a conical section, passing through two given points and touching predetermined straight lines at these points. The conical section is considered as a special case of a cubic curve. Curvature can be specified as an additional boundary condition. Has been considered the possibility for constructing a cubic curve with fixed positions of contacting planes at end points and given radii of curvature. Has been proposed an algorithm for constructing a plane cubic curve with a given curvature at the end points. Have been considered algorithms for constructing smooth compound Ferguson-Bezier curves. Smoothness conditions are imposed on a compound curve: 1) at any of its points, the curve must have a tangent (no fractures are allowed), 2) the curvature vector must be changed continuously from point to point (no discontinuous jump in the curvature vector is allowed neither in modulus no in direction). Have been proposed examples for constructing compound Ferguson-Bézier curves. Has been performed comparison of polynomial cubic spline with compound parametrically defined curves. Have been given examples for constructing cubic splines with fastened and free ends. The paper is for educational purposes, and intended for in-depth study of computer graphics basics.
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Tsai, Dong-Ho. "Geometric expansion of starshaped plane curves." Communications in Analysis and Geometry 4, no. 3 (1996): 459–80. http://dx.doi.org/10.4310/cag.1996.v4.n3.a5.

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Le Maire, Pauline, and Marc Munschy. "2D potential theory using complex algebra: New equations and visualization for the interpretation of potential field data." GEOPHYSICS 83, no. 2 (March 1, 2018): J1—J13. http://dx.doi.org/10.1190/geo2016-0611.1.

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The shape of an anomaly (magnetic or gravity) along a profile provides information on the geometry, horizontal location, depth, and magnetization of the source. For a 2D source, the horizontal location, depth, and geometry of a source are determined through the analysis of the curve of the analytic signal. However, the amplitude of the analytic signal is independent of the dips of the structure, the apparent inclination of magnetization, and the regional magnetic field. To better characterize the parameters of the source, we have developed a new approach for studying 2D potential field equations using complex algebra. Complex equations for different geometries of the sources are obtained for gravity and magnetic anomalies in the spatial and spectral domains. In the spatial domain, these new equations are compact and correspond to logarithmic or power functions with a negative integer exponent. We found that modifying the shape of the source changes the exponent of the power function, which is equivalent to differentiation or integration. We developed anomaly profiles using plots in the complex plane, which is called mapping. The obtained complex curves are loops passing through the origin of the plane. The shape of these loops depends only on the geometry and not on the horizontal location of the source. For source geometries defined by a single point, the loop shape is also independent of the source depth. The orientation of the curves in the complex plane is related to the order of differentiation or integration, the geometry and dips of the structures, and the apparent inclination of magnetization and of the regional magnetic field. The application of these equations and mapping on total field magnetic anomalies across a magmatic dike in Norway shows coherent results, allowing us to determine the geometry and the apparent inclination of magnetization.
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Petrovic, Maja, Bojan Banjac, and Branko Malesevic. "The geometry of trifocal curves with applications in architecture, urban and spatial planning." Spatium, no. 32 (2014): 28–33. http://dx.doi.org/10.2298/spat1432028p.

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In this paper we consider historical genesis of trifocal curve as an optimal curve for solving the Fermat?s problem (minimizing the sum of distance of one point to three given points in the plane). Trifocal curves are basic plane geometric forms which appear in location problems. We also analyze algebraic equation of these curves and some of their applications in architecture, urbanism and spatial planning. The area and perimeter of trifocal curves are calculated using a Java application. The Java applet is developed for determining numerical value for the Fermat-Torricelli-Weber point and optimal curve with three foci, when starting points are given on an urban map. We also present an application of trifocal curves through the analysis of one specific solution in South Stream gas pipeline project.
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Steward, David R., Philippe Le Grand, Igor Janković, and Otto D. L. Strack. "Analytic formulation of Cauchy integrals for boundaries with curvilinear geometry." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2089 (October 30, 2007): 223–48. http://dx.doi.org/10.1098/rspa.2007.0138.

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A general framework for analytic evaluation of singular integral equations with a Cauchy kernel is developed for higher order line elements of curvilinear geometry. This extends existing theory which relies on numerical integration of Cauchy integrals since analytic evaluation is currently published only for straight lines, and circular and hyperbolic arcs. Analytic evaluation of Cauchy integrals along straight elements is presented to establish a context coalescing new developments within the existing body of knowledge. Curvilinear boundaries are partitioned into sectionally holomorphic elements that are conformally mapped from a local curvilinear Z -plane to a straight line in the -plane. Cauchy integrals are evaluated in these planes to achieve a simple representation of the complex potential using Chebyshev polynomials and a Taylor series expansion of the conformal mapping. Bell polynomials and the Faà di Bruno formula provide this Taylor series for mappings expressed as inverse mappings and/or compositions. Examples illustrate application of the general framework to boundary-value problems with boundaries of natural coordinates, Bezier curves and B-splines. Strings formed by the union of adjacent curvilinear elements form a large class of geometries along which Dirichlet and/or Neumann conditions may be applied. This provides a framework applicable to a wide range of fields of study including groundwater flow, electricity and magnetism, acoustic radiation, elasticity, fluid flow, air flow and heat flow.
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Watanabe, S. "The genera of Galois closure curves for plane quartic curves." Hiroshima Mathematical Journal 38, no. 1 (March 2008): 125–34. http://dx.doi.org/10.32917/hmj/1207580347.

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Dissertations / Theses on the topic "Geometry, Analytic. Curves, Plane"

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Holanda, Felipe D'Angelo. "Introduction to differential geometry of plane curves." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=15052.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior
A intenÃÃo desse trabalho serà de abordar de forma bÃsica e introdutÃria o estudo da Geometria Diferencial, que por sua vez tem seus estudos iniciados com as Curvas Planas. Serà necessÃrio um conhecimento de CÃlculo Diferencial, Integral e Geometria AnalÃtica para melhor compreensÃo desse trabalho, pois como seu prÃprio nome nos transparece Geometria Diferencial vem de uma junÃÃo do estudo da Geometria envolvendo CÃlculo. Assim abordaremos subtemas como curvas suaves, vetor tangente, comprimento de arco passando por fÃrmulas de Frenet, curvas evolutas e involutas e finalizaremos com alguns teoremas importantes, como o teorema fundamental das curvas planas, teorema de Jordan e o teorema dos quatro vÃrtices. O que, basicamente representa, o capÃtulo 1, 4 e 6 do livro IntroduÃÃo Ãs Curvas Planas de HilÃrio Alencar e Walcy Santos.
The intention of this work is to address in basic form and introductory study of Differential Geometry, which in turn has started his studies with Planas curves. It will require a knowledge of Differential Calculus, Integral and Analytic Geometry for better understanding of this work, because as its name says in Differential Geometry comes from the joint study of geometry involving Calculation. So we discuss sub-themes as smooth curves, tangent vector, arc length through formulas of Frenet, evolutas curves and involute and conclude with some important theorems, as the fundamental theorem of plane curves, Jordan 's theorem and the theorem of four vertices. What basically is, Chapter 1, 4 and 6 of the book Introduction to Plane Curves HilÃrio Alencar and Walcy Santos.
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Nichols, Margaret E. "Intersection Number of Plane Curves." Oberlin College Honors Theses / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1385137385.

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Neovius, Sofia. "René Descartes’ Foundations of Analytic Geometry and Classification of Curves." Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202147.

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Sheppardson, Laura. "Disjoint paths in planar graphs." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/29862.

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Collins, John P. "Gluing Bridgeland's stability conditions and Z₂-equivariant sheaves on curves /." Connect to title online (Scholars' Bank) Connect to title online (ProQuest), 2009. http://hdl.handle.net/1794/10218.

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Cohen, Camron Alexander Robey. "CURVING TOWARDS BÉZOUT: AN EXAMINATION OF PLANE CURVES AND THEIR INTERSECTION." Oberlin College Honors Theses / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin159345184740689.

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Fowler, Thomas George. "Unique coloring of planar graphs." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/30358.

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Jaramillo, Puentes Andrés. "Rigid isotopy classification of real quintic rational plane curves." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066116/document.

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Afin d’étudier les classes d'isotopie rigide des courbes rationnelles nodales de degré 5 dans RPP, nous associons à chaque quintique avec un point double réel marque une courbe trigonale dans la surface de Hirzebruch Sigma3 et le dessin reel nodal correspondant dans CP/(z mapsto bar{z}). Les dessins sont des versions réelles, proposées par S. Orevkov dans cite{Orevkov}, des dessins d'enfants de Grothendieck. Un dessin est un graphe contenu dans une surface topologique, muni d'une certaine structure supplémentaire. Dans cette thèse, nous étudions les propriétés combinatoires et les recompositions des dessins correspondants aux courbes trigonales nodales C subset Sigma dans les surfaces réglées réelles Sigma . Les dessins uninodaux sur une surface a bord quelconque et les dessins nodaux sur le disque peuvent être décomposés en blocs correspondant aux dessins cubiques sur le disque D2 , ce qui conduit a une classification des ces dessins. La classification des dessins considérés mène à une classification à isotopie rigide des courbes rationnelles nodales de degré 5 dans RPP
In order to study the rigid isotopy classes of nodal rational curves of degree $5$ in $\RPP$, we associate to every real rational quintic curve with a marked real nodal point a trigonal curve in the Hirzebruch surface $\Sigma_3$ and the corresponding nodal real dessin on~$\CP/(z\mapsto\bar{z})$. The dessins are real versions, proposed by S. Orevkov~\cite{Orevkov}, of Grothendieck's {\it dessins d'enfants}. The {\it dessins} are graphs embedded in a topological surface and endowed with a certain additional structure. We study the combinatorial properties and decompositions of dessins corresponding to real nodal trigonal curves~$C\subset \Sigma$ in real ruled surfaces~$\Sigma$. Uninodal dessins in any surface with non-empty boundary and nodal dessins in the disk can be decomposed in blocks corresponding to cubic dessins in the disk~$\mathbf{D}^2$, which produces a classification of these dessins. The classification of dessins under consideration leads to a rigid isotopy classification of real rational quintics in~$\RPP$
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Duran, James Joseph. "Differential geometry of surfaces and minimal surfaces." CSUSB ScholarWorks, 1997. https://scholarworks.lib.csusb.edu/etd-project/1542.

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Beltrami, Reginaldo Silva. "Algumas técnicas utilizando o software GeoGebra no processo de resolução de problemas geométricos do ensino básico: situações de máximos e mínimos e lugares geométricos." Universidade Federal de Roraima, 2016. http://www.bdtd.ufrr.br/tde_busca/arquivo.php?codArquivo=342.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Tendo em vista as mudanças ocorridas ao longo do tempo, provenientes dos avanços tecnológicos e contidas em todos os setores, a vida humana tem sido atingida significativamente. Particularmente, procura-se fazer uso dessas novas tecnologias, objetivando motivar a aprendizagem do indivíduo e nos métodos utilizados na educação. E no que diz respeito a consolidação no processo pedagógico, os softwares de matemática dinâmica têm como objetivo auxiliar os modelos tradicionais de ensino e contribuir para a evolução do cenário educacional. No Ensino Básico, espera-se que os alunos saibam utilizar essas ferramentas tecnológicas para uma melhor compreensão ou visualização de problemas geométricos. Dessa forma, o principal objetivo desta dissertação é apresentar algumas técnicas que contribuam como facilitadoras do entendimento de problemas geométricos relacionados à geometria plana com abordagem em situações variáveis, utilizando funções reais, o conceito de lugar geométrico e o software GeoGebra. Por fim, apresenta-se um acervo de dez problemas geométricos relacionados mais intimamente com os conceitos de lugar geométrico, de máximo e de mínimo, nos quais servirão como referencial para os professores e alunos que desejam explorar essa poderosa ferramenta chamada GeoGebra.
In view of the changes over time, from the technological advances and contained in all sectors, human life has been affected significantly. In particular, one seeks to make use of these new technologies, aiming to motivate learning of the individual and the methods used in education. And, with regard to consolidation in the educational process, the dynamic software are designed to help traditional models of education and contribute to the development of the educational setting. In basic education, it is expected that students know how to use these technological tools for better understanding and visualization of geometric problems. Thus, the main objective of this dissertation is to present some techniques that contribute to facilitating the understanding of geometric problems related to the flat geometry approach to changing situations using real functions, the concept of locus and GeoGebra software. Finally, we present a collection of ten related geometric problems more closely with the concepts of locus, maximum and minimum, in which will serve as a reference for teachers and students who wish to explore this powerful tool called GeoGebra.
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Books on the topic "Geometry, Analytic. Curves, Plane"

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1960-, Zaslavskiĭ A. A., ed. Geometry of conics. Providence, R.I: American Mathematical Society, 2007.

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Salmon, George. A treatise on conic sections. 6th ed. Providence, RI: AMS Chelsea Pub., 2005.

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Horst, Knörrer, ed. Plane algebraic curves. Basel: Birkhäuser Verlag, 1986.

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Fowler, R. H. The elementary differential geometry of plane curves. Mineola, N.Y: Dover Publications, 2005.

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Calculus and analytic geometry. 4th ed. Glenview, Ill: Scott, Foresman, 1988.

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Shenk, Al. Calculus and analytic geometry. 4th ed. Glenview, Ill: Scott, Foresman, 1988.

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A, Schmidt Philip, ed. Geometry: Includes plane, analytic, and transformational geometries. 4th ed. New York: McGraw Hill, 2009.

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Zwikker, C. The advanced geometry of plane curves and their applications. Mineola, N.Y: Dover Publications, 2005.

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Barnett, Raymond A. Analytic trigonometry with applications. 8th ed. New York: John Wiley, 2003.

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R, Ziegler Michael, and Byleen Karl, eds. Analytic trigonometry with applications. 7th ed. Pacific Grove: Brooks/Cole Pub. Co., 1999.

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Book chapters on the topic "Geometry, Analytic. Curves, Plane"

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Brieskorn, Egbert, and Horst Knörrer. "Synthetic and analytic geometry." In Plane Algebraic Curves, 66–102. Basel: Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-5097-1_2.

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Brieskorn, Egbert, and Horst Knörrer. "2. Synthetic and analytic geometry." In Plane Algebraic Curves, 66–101. Basel: Springer Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-0493-6_2.

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de Jong, Theo, and Gerhard Pfister. "Plane Curve Singularities." In Local Analytic Geometry, 171–224. Wiesbaden: Vieweg+Teubner Verlag, 2000. http://dx.doi.org/10.1007/978-3-322-90159-0_5.

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Gonzalez-Corbalan, A., and T. Recio. "Shape invariant lists and realization as plane real algebraic curves with double points." In Real Analytic and Algebraic Geometry, 149–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0083917.

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Berger, Marcel. "Plane curves." In Geometry Revealed, 249–340. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-540-70997-8_5.

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Musili, C. "Plane Curves." In Algebraic Geometry for Beginners, 187–270. Gurgaon: Hindustan Book Agency, 2001. http://dx.doi.org/10.1007/978-93-86279-05-7_5.

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Zelenka, Miloslav. "Plane Analytic Geometry." In Survey of Applicable Mathematics, 167–94. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-015-8308-4_5.

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Borceux, Francis. "Plane Curves." In A Differential Approach to Geometry, 55–138. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-01736-5_2.

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Aarts, J. M., and R. Erne. "Curves." In Plane and Solid Geometry, 1–109. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-78241-6_4.

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Sathaya, Avinash, and Jon Stenerson. "Plane Polynomial Curves." In Algebraic Geometry and its Applications, 121–42. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-2628-4_6.

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Conference papers on the topic "Geometry, Analytic. Curves, Plane"

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Jauregui, Juan C., Diego Cardenas, Hugo Elizalde, and Oliver Probst. "Dynamic Modelling of Blades Based on a Novel Curved Thin Walled Beam Theory." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-76016.

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There are several Thin-Walled Beam models for straight beams, but few TWB models consider beams with arbitrary curvatures. Although, a curved beam can be modelled using finite elements, the number of degrees of freedom is too large and a nonlinear dynamic solution is very cumbersome, if not impossible. In this work, a general description of arbitrary three-dimensional curves, based on the Frenet-Serret field frame, is applied to determine the dynamic stresses in wing turbines blades. The dynamic model is developed using the Isogeometric Analysis (IGA) and the in plane and out-of-plane curvature’s gradients are found in an Euler-type formulation, allowing the treatment of cases with highly-curved geometry. An Isogeometrical (IGA) formulation relies on a linear combination of Non-Uniform Rational B-Splines (NURBS) to represent not just the model’s geometry, a standard practice in most Computer-Aided Design (CAD) platforms, but also the unknown solution field of each sought variable. For the unified model hitherto described, these variables are represented by a NURBS curve.
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Карабчевский, Виталий, and Vitaliy Karabchevskiy. "The research of conic sections in AutoCAD environment." In 29th International Conference on Computer Graphics, Image Processing and Computer Vision, Visualization Systems and the Virtual Environment GraphiCon'2019. Bryansk State Technical University, 2019. http://dx.doi.org/10.30987/graphicon-2019-1-188-190.

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The application of solid modelling tools is considered when creating three-dimensional models of a straight circular cone and when studying its sections in AutoCAD. The results are presented that AutoCAD allows obtaining for a section by planes almost parallel to one or two generators. The boundary values of the angles between the plane and the generators, which determine the presence or absence of parallelism, are found. Methods are proposed for obtaining the parameters of the canonical equations of curves representing conical sections for cases when the corresponding curve (hyperbola or parabola) is modelled in AutoCAD using splines. The application of the proposed methods in the educational process is described, which makes it possible to strengthen the relationship of what is stated in the study of sections of descriptive geometry of the material with the development of methods for generating three-dimensional models, solid-state modelling tools and analytical geometry.
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Latecki, Longin J., and Azriel Rosenfeld. "Differentialless geometry of plane curves." In Optical Science, Engineering and Instrumentation '97, edited by Robert A. Melter, Angela Y. Wu, and Longin J. Latecki. SPIE, 1997. http://dx.doi.org/10.1117/12.279677.

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Wang, Z. X., Y. J. Chao, and P. S. Lam. "Crack Growth in 18G2A Steels With Different Constraint." In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26435.

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A constraint theory in fracture mechanics is used to analyze the test data of 18G2A steels using single edge-notched bend (SENB) specimens with various crack depth to specimen width ratios (a/W). A bending correction factor is included in the two-parameter (J-A2) asymptotic solution to improve the theoretical prediction of the stress field for deep cracks under large scale yielding condition, where J is the J-integral and A2 is the constraint parameter, which depends on the in-plane geometry of the cracked body (a/W). As a result, the valid region for a traditional J-controlled crack growth is extended, and the ASTM specimen size requirements for fracture toughness testing can be relaxed. In addition, it is shown that the functional dependence of J-R curves on A2 for 18G2A steels is established with test data; and the predicted J-R curves agree very well with the experimental curves. This ensures the transferability of laboratory test data to an actual structure provided the constraint level (A2) of the cracked structure is known or determined. This allows an appropriate J-R curve with the same constraint level to be constructed and used in flaw stability analysis of any cracked body.
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5

Udyawar, Anees, J. Brian Hall, Justin Webb, and Alexandria Carolan. "Demonstrate ASME Section XI Appendix G Margins for Pressurized Water Reactor Inlet and Outlet Nozzle Corner Regions." In ASME 2018 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/pvp2018-84345.

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Since the implementation of pressure-temperature (P-T) limit curves in the 1960s for light water reactors, the P-T limit curves have been based on the limiting locations in the reactor coolant system, which are typically the irradiated reactor pressure vessel (RPV) region adjacent to the core (beltline) and the closure head flange. Recently, it has been questioned as to whether the reactor vessel inlet or outlet nozzle corners could be more limiting due to the stress concentration at these locations. The discussion presented in this paper provides technical justification that the RPV nozzle corner P-T limit curves are bounded by the traditional P-T limit curves for the pressurized water reactors (PWRs). The current approach in evaluating the Pressurized Water Reactor Inlet and Outlet nozzle corner regions with respect to plant heatup and cooldown Pressure Temperature Limit Curves contains a number of conservatisms. These conservatisms include postulation of a large 1/4T flaw at the nozzle corner region, use of RTNDT (reference nil-ductility temperature), and fracture toughness prediction based on plane strain fracture toughness. The paper herein discusses several factors that can be considered to improve the pressure temperature limit curves for nozzle corners and increase the operating window for nuclear power plant operations. Prior to the 2013 edition, the ASME Section XI Appendix G did not require the use of a 1/4T flaw for the nozzle corners; furthermore, a smaller postulated flaw size is permissible. Based on inspection capability and experience, a smaller flaw size can easily be justified. The use of a smaller flaw size reduces the stress intensity factors and allows for the benefit of being able to take advantage of increased material toughness due to the loss of constraint at the nozzle corner geometry. The analysis herein considers the calculation of stress intensity factors for small postulated nozzle corner flaws based on a 3D finite element analysis for Westinghouse PWR inlet and outlet nozzle corner regions. The Finite Element Analysis (FEA) stress intensity factors along the crack front are used in the determination of allowable pressures for the cooldown transient Pressure-Temperature limit curves.
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6

Sta˘na˘s¸el, Iulian, Ioan Mihaila, and Adrian Ghionea. "Contributions to the Study of Generation of the Flanks of the Generating Hook of Cylindrical Curved Gear in Oblong Cycloidal Arc." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/ptg-48099.

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The paper has proposed to determine the equation of flanks of generation hook with oblong cycloidal arc taking into account two types of cutting tool: a cutting tool that generates the hole of the tooth, respectively a cutting tool that generates the tooth. The curved cylindrical teeth with cycloidal flanks is generated by rolling with straight mobile line and continuous division by using a milling cutter with 1, 2, 3, 4 or 5 groups of knifes equidistantly placed, fixed on an adaptable device on a Phauter toothing machine. The two curves which defines the flank are simultaneously generated by correlated motions. In order to make the analytical study of motions and geometry of the flanks, several 3D coordinating systems were first defined, each of them being bounded by an element that participates in the generating process. There were established the equations of cutting edged of the tool in Ss system, the equations of the flanks of the generating hook are obtained by changing the reference system of edges of the tool from Ss to SCG. The line of the flanks is studied in the reference plane and in parallel plans with this, and. the profile of the flanks is determined in perpendicular plans on the workpiece axis. . It was made a calculation program in MATLAB, that allowed to obtain data, which were used to plot the line and the profile of the flanks of the generating hook. By analysing the obtained shape they result conclusions used for the manufacturing of the involute-tooth gear with curved oblong cycloidal arc.
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7

Donato, Gustavo Henrique B., and Felipe Cavalheiro Moreira. "Effects of Side-Grooves and 3-D Geometries on Compliance Solutions and Crack Size Estimations Applicable to C(T), SE(B) and Clamped SE(T) Specimens." In ASME 2013 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/pvp2013-98018.

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Engineering procedures for design and integrity assessment of structural components containing crack-like defects are highly dependent on accurate fracture toughness and Fatigue Crack Growth (FCG) experimental data. Considering ductile and high toughness structural materials, crack growing curves (e.g. J-R curves) and FCG data (in terms of da/dN vs. ΔK or ΔJ) assumed paramount relevance. In common, these two types of mechanical properties severely depend on real-time and precise crack size estimations during laboratory testing. Optical measurement, electric potential drop or (most commonly) elastic unloading compliance (C) techniques can be employed. In the latter method, crack size estimation derives from C using a dimensionless parameter (μ) which incorporates specimen’s thickness (B), elasticity (E) and compliance itself. Plane stress and plane strain solutions for μ are available in several standards regarding C(T), SE(B) and M(T) specimens, among others. Current challenges include: i) real specimens are in neither plane stress nor plane strain-modulus vary between E (plane stress) and E/(1−ν2) (plane strain); ii) furthermore, side-grooves affect specimen’s stiffness, leading to an “effective thickness”. Results from Shen et al. and from current authors revealed deviations larger than 10% in crack size estimations following existing practices, especially for shallow cracks and side-grooved samples. In addition, compliance solutions for the emerging SE(T) specimens are not yet standardized. As a step in this direction, this work investigates 3-D and side-groove effects on compliance solutions applicable to C(T), SE(B) and clamped SE(T) specimens. Refined 3-D elastic FE-models provide Load-CMOD evolutions. The analysis matrix includes crack depths between a/W = 0.1 and a/W = 0.7 on 1/2T, 1T and 2T geometries. The 1T geometry is taken as the reference and presents width to thickness ratio W/B = 2. Side-grooves of 5%, 10% and 20% are considered. The results include compliance solutions incorporating 3D and side-groove effects to provide accurate crack size estimation during laboratory fracture and FCG testing. The proposals were verified against current standardized solutions and deviations were strongly reduced.
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8

Eigenwillig, Arno, Michael Kerber, and Nicola Wolpert. "Fast and exact geometric analysis of real algebraic plane curves." In the 2007 international symposium. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1277548.1277570.

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9

Le Delliou, Patrick, Ste´phane Marie, Yann Kayser, and Bruno Barthelet. "Development of a J-Estimation Scheme for Surface Cracks in Piping Welds." In 16th International Conference on Nuclear Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/icone16-48393.

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The RSE-M Code provides rules and requirements for in-service inspection of French Pressurized Water Reactor power plants. The Code gives non mandatory guidance for analytical evaluation of flaws. Flaw assessment procedures rely on fracture mechanics analyses based on simplified methods (i.e. analytical). Analytical methods were developed under a cooperative program between EDF, CEA and AREVA NP to calculate the J integral in various cracked piping components (straight pipe, tapered transition, elbow and pipe-to-elbow junction). These methods are available for mechanical loading (in-plane bending moment, pressure, torsion moment), thermal loading as well as for combined loading. Moreover, they can be used either for materials with Ramberg-Osgood stress-strain curves or for real materials (stainless steels and carbon manganese steels, including those with yield plateaus). However, for the analysis of cracks in welds, they use the tensile properties of the weakest material between the base material and the weld material. This induces some conservatism on the estimated J values. A cooperative program was launched in 2004 to develop a J estimation scheme which takes into account the strength mismatch effects. The scheme relies on the definition of an ‘equivalent’ stress-plastic strain curve, as proposed in the R6 rule (section III.8: allowance for strength mismatch effects). This curve is then used with the analytical methods for homogeneous cracked components. In a first step, the method is developed for circumferential surface cracks in straight buttwelded pipes submitted to mechanical loading. It takes into account the geometry of the weld joint (V-shaped), as well as the location of the crack within the weld. This paper presents the current state of development of this J estimation-scheme.
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Miura, Kenjiro, Sho Suzuki, R. Gobithaasan, Shin Usuki, Jun-ichi Inoguchi, Masayuki Sato, Kenji Kajiwara, and Yasuhiro Shimizu. "Fairness Metric of Plane Curves Defined with Similarity Geometry Invariants." In CAD'17. CAD Solutions LLC, 2017. http://dx.doi.org/10.14733/cadconfp.2017.311-316.

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