Relevant bibliographies by topics / Non-uniform B-spline curves

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  1. Journal articles
  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Non-uniform B-spline curves'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Non-uniform B-spline curves"

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Dube, Mridula, and Reenu Sharma. "Cubic TP B-Spline Curves with a Shape Parameter." International Journal of Engineering Research in Africa 11 (October 2013): 59–72. http://dx.doi.org/10.4028/www.scientific.net/jera.11.59.

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In this paper a new kind of splines, called cubic trigonometric polynomial B-spline (cubic TP B-spline) curves with a shape parameter, are constructed over the space spanned by As each piece of the curve is generated by three consecutive control points, they posses many properties of the quadratic B-spline curves. These trigonometric curves with a non-uniform knot vector are C1 and G2 continuous. They are C2 continuous when choosing special shape parameter for non-uniform knot vector. These curves are closer to the control polygon than the quadratic B-spline curves when choosing special shape parameters. With the increase of the shape parameter, the trigonometric spline curves approximate to the control polygon. The given curves posses many properties of the quadratic B-spline curves. The generation of tensor product surfaces by these new splines is straightforward.
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Munira, Ali, Nur Najmiyah Jaafar, Abdul Aziz Fazilah, and Z. Nooraizedfiza. "Review on Non Uniform Rational B-Spline (NURBS): Concept and Optimization." Advanced Materials Research 903 (February 2014): 338–43. http://dx.doi.org/10.4028/www.scientific.net/amr.903.338.

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This paper is to provide literature review of the Non Uniform Rational B-Splines (NURBS) formulation in the curve and surface constructions. NURBS curves and surfaces have a wide application in Computer Aided Geometry Design (CAGD), Computer Aided Design (CAD), image processing and etc. The formulation of NURBS showing that NURBS curves and surfaces requires three important parameters in controlling the curve and also modifying the shape of the curves and surfaces. Yet, curves and surfaces fitting are still the major problems in the geometrical modeling. With this, the researches that have been conducted in optimizing the parameters in order to construct the intended curves and surfaces are highlighted in this paper.
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Li, Ai Min, and Hai Bo Tian. "A Multiresolution Fairing Approach for NURBS Curves." Applied Mechanics and Materials 215-216 (November 2012): 1205–8. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.1205.

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Curve fairing has an important influence on curve editing and geometric modeling. Though there has been several different kinds of fairing methods, Multiresolution curve fairing has higher efficiency and simpler algorithms. Different from existing multiresolution curve fairing, a new multiresolution approach is presented based on non-uniform semiorthogonal B-spline wavelets, which can be applied for NURBS curve fairing. It has no restriction to B-spline curves’ knot sequence. This method effectively overcomes the limit of uniform or quasi-uniform B-spline wavelets for fairing. A detailed example is given to show the effectiveness of this multiresolution fairing method.
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Majeed, Abdul, Muhammad Abbas, Faiza Qayyum, Kenjiro T. Miura, Md Yushalify Misro, and Tahir Nazir. "Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter." Mathematics 8, no. 12 (November 24, 2020): 2102. http://dx.doi.org/10.3390/math8122102.

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Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.
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Wang, Kai, and Guicang Zhang. "New Trigonometric Basis Possessing Denominator Shape Parameters." Mathematical Problems in Engineering 2018 (October 24, 2018): 1–25. http://dx.doi.org/10.1155/2018/9569834.

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Four new trigonometric Bernstein-like bases with two denominator shape parameters (DTB-like basis) are constructed, based on which a kind of trigonometric Bézier-like curve with two denominator shape parameters (DTB-like curves) that are analogous to the cubic Bézier curves is proposed. The corner cutting algorithm for computing the DTB-like curves is given. Any arc of an ellipse or a parabola can be exactly represented by using the DTB-like curves. A new class of trigonometric B-spline-like basis function with two local denominator shape parameters (DT B-spline-like basis) is constructed according to the proposed DTB-like basis. The totally positive property of the DT B-spline-like basis is supported. For different shape parameter values, the associated trigonometric B-spline-like curves with two denominator shape parameters (DT B-spline-like curves) can be C2 continuous for a non-uniform knot vector. For a special value, the generated curves can be C(2n-1) (n=1,2,3,…) continuous for a uniform knot vector. A kind of trigonometric B-spline-like surfaces with four denominator shape parameters (DT B-spline-like surface) is shown by using the tensor product method, and the associated DT B-spline-like surfaces can be C2 continuous for a nonuniform knot vector. When given a special value, the related surfaces can be C(2n-1) (n=1,2,3,…) continuous for a uniform knot vector. A new class of trigonometric Bernstein–Bézier-like basis function with three denominator shape parameters (DT BB-like basis) over a triangular domain is also constructed. A de Casteljau-type algorithm is developed for computing the associated trigonometric Bernstein–Bézier-like patch with three denominator shape parameters (DT BB-like patch). The condition for G1 continuous jointing two DT BB-like patches over the triangular domain is deduced.
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Dung, Van Than, and Tegoeh Tjahjowidodo. "A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting." PLOS ONE 12, no. 3 (March 20, 2017): e0173857. http://dx.doi.org/10.1371/journal.pone.0173857.

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Hu, Liangchen, Huahao Shou, and Shiaofen Fang. "A PIA optimization algorithm for non-uniform B-spline curves and surfaces." International Journal of Modelling and Simulation 37, no. 3 (April 10, 2017): 167–77. http://dx.doi.org/10.1080/02286203.2017.1309260.

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Tuo, Ming-Xiu, Gui-Cang Zhang, and Kai Wang. "A New Quasi Cubic Rational System with Two Parameters." Symmetry 12, no. 7 (June 30, 2020): 1070. http://dx.doi.org/10.3390/sym12071070.

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The purpose of this article is to develop a new system for the construction of curves and surfaces. Making the new system not only has excellent properties of the orthodox Bézier and the B-spline method but also has practical properties such as variation diminishing and local shape adjustability. First, a new set of the quasi-cubic rational (QCR) system with two parameters is given, which is verified on an optimal normalized totally positive system (B-system). The related QCR Bézier curve is defined, and the de Casteljau-type algorithm are given. Next, a group of non-uniform QCR B-spline system is shown based on the linear combination of the proposed QCR system, the relative properties of the B-spline system are analyzed. Then, the definition and properties of non-uniform QCR B-spline curves are discussed in detail. Finally, the proposed QCR system is extended to the triangular domain, which is called the quasi-cubic rational Bernstein-Bézier (QCR-BB) system, and its related definition and properties of patches are given at length. The experimental image obtained by using MATLAB shows that the newly constructed system has excellent properties such as symmetry, totally positive, and C 2 continuity, and its corresponding curve has the properties of local shape adjustability and C 2 continuity. These extended systems in the extended triangular domain have symmetry, linear independence, etc. Hence, the methods in this article are suitable for the modeling design of complex curves and surfaces.
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Li, J.-G., M.-M. Qiu, T.-H. Zhang, and Z.-X. Li. "A practical real-time non-uniform rational B-spline curve interpolator for computer numerical control machining." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 226, no. 4 (September 7, 2011): 1068–83. http://dx.doi.org/10.1177/0954406211418026.

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Non-uniform rational B-spline (NURBS) interpolator, a key technique in computer numerical control (CNC) machining, has many advantages over linear and circular interpolator. A practical real-time NURBS interpolator based on an off-line algorithm, which is developed to handle the limitation of velocity and acceleration, is presented in this article. Two processing modules are employed to realize the real-time interpolator. In one module, a NURBS curve is split into shorter NURBS curves or approximated as continuous line segments according to the minimum splitting length first, and then the velocity planning of a short curve is applied. Inthe other module, the interpolation according to the velocity planning results is implemented. The proposed algorithm realizes the real-time velocity planning and interpolation of a NURBS curve regardless of the curve length or the continuity. It is also applicable to three-dimensional surface designed by computer-aided design system, which is composed of multiple NURBS curves or both NURBS curves and continuous line segments. Both the simulation and experiment results have proved the effectiveness of the proposed practical real-time NURBS interpolator.
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Zhang, Wen Jie. "The Research of the NURBS Curve Interpolation Algorithm." Advanced Engineering Forum 2-3 (December 2011): 614–18. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.614.

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In this article, the definition, the nature and the parameter of the NURBS (Non-Uniform Rational B-spline) curves are defined, the more thorough analysis and research of the real-time NURBS curve interpolation algorithm and the feed rate adaptive control are carried out.
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Dissertations / Theses on the topic "Non-uniform B-spline curves"

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Marcaly, Fred W. "Data reduction and knot removal for non-uniform B-spline surfaces." Thesis, Virginia Tech, 1991. http://hdl.handle.net/10919/40638.

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Qu, Ruibin. "Recursive subdivision algorithms for curve and surface design." Thesis, Brunel University, 1990. http://bura.brunel.ac.uk/handle/2438/5447.

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In this thesis, the author studies recursIve subdivision algorithms for curves and surfaces. Several subdivision algorithms are constructed and investigated. Some graphic examples are also presented. Inspired by the Chaikin's algorithm and the Catmull-Clark's algorithm, some non-uniform schemes, the non-uniform corner cutting scheme and the recursive subdivision algorithm for non-uniform B-spline curves, are constructed and analysed. The adapted parametrization is introduced to analyse these non-uniform algorithms. In order to solve the surface interpolation problem, the Dyn-Gregory-Levin's 4-point interpolatory scheme is generalized to surfaces and the 10-point interpolatory subdivision scheme for surfaces is formulated. The so-called Butterfly Scheme, which was firstly introduced by Dyn, Gregory Levin in 1988, is just a special case of the scheme. By studying the Cross-Differences of Directional Divided Differences, a matrix approach for analysing uniform subdivision algorithms for surfaces is established and the convergence of the 10-point scheme over both uniform and non-uniform triangular networks is studied. Another algorithm, the subdivision algorithm for uniform bi-quartic B-spline surfaces over arbitrary topology is introduced and investigated. This algorithm is a generalization of Doo-Sabin's and Catmull-Clark's algorithms. It produces uniform Bi-quartic B-spline patches over uniform data. By studying the local subdivision matrix, which is a circulant, the tangent plane and curvature properties of the limit surfaces at the so-called Extraordinary Points are studied in detail.
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Lin, Yang-Jie, and 林揚傑. "Non-Uniform Rational B-spline Curve Interpolator Apply to Selective Laser Sintering Electrical Circuits." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/c88nsm.

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碩士
國立交通大學
機械工程系所
105
In this thesis, we developed a selective laser sintering (SLS) system with NURBS curve interpolator, and sintering the silver nanoparticles ink on a flexible substrate. Take advantage of laser for reducing thermal damage of substrate, which allow us to use lower laser power to sinter the silver nanoparticles ink. To ensure that sintered silver nanoparticles can be used for conductive line, the experiment are designed for laser power in the range of 100 ~250 mW and the scanning speed in the range of 2~5 mm/s. The best electrical conductivity of the experiment result is used in the following experiment. In order to show if NURBS interpolator can effectively improve the continuity of laser scanning speed, by using a butterfly-shaped of NURBS curve as example to analyze the path of the motion stage. After sintering, traditional method (G01) with purposed method (G06) for the change rate of linewidth in the corner of the path are compared. At last, a planar spiral inductance for application is demonstrated.
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Lin, Dong-Ying, and 林東瑩. "The Design and Implementation of a Non-Uniform Rational B-Spline Curve and Surface Chip." Thesis, 2000. http://ndltd.ncl.edu.tw/handle/29069599169491932475.

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碩士
國立臺灣科技大學
電子工程系
88
B-Splines and Non-Uniform Rational B-Splines (NURBS) have become the essential modeling primitives in computer graphics and geometric modeling applications. In this thesis, we propose a modified NURBS algorithm incorporated with two useful properties, sum up to one and dynamic denominator. This novel algorithm provides less order and fewer division operations than the traditional algorithm reported in the literature. Based on this algorithm, a unified architecture for the computation of various types of B-Spline curves and surfaces is presented. The resultant chip, consisting of approximately 752 K transistors, occupies 3.1 mm by 3.1 mm area in the 0.35-μm SPQM CMOS technology. It operates at 100 MHz with two 16-bit data outputs and consumes only 920mW at a supply voltage of 3.3V. The output data rate is two 16-bit words per cycle, which corresponds to a pair of the coordinate values of a point and its normal on a curve/surface.
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Book chapters on the topic "Non-uniform B-spline curves"

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Hu, Liangchen, Huahao Shou, and Shiaofen Fang. "Progressive Iterative Approximation of SOR for Non-uniform Cubic B-spline Curve and Surface Interpolation." In Simulation Tools and Techniques, 339–49. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72792-5_29.

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Conference papers on the topic "Non-uniform B-spline curves"

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Xie, Jin, Lixiang Xu, Meilan Sun, Chengjun Xie, and Jie Zhang. "Quadratic Non-uniform Hyperbolic B-spline Curves." In 2012 International Conference on Computer Science and Electronics Engineering (ICCSEE). IEEE, 2012. http://dx.doi.org/10.1109/iccsee.2012.297.

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Zhu Ping and Wang Guozhao. "Non-uniform hyperbolic blending B-spline curves." In 2011 IEEE International Conference on Computer Science and Automation Engineering (CSAE). IEEE, 2011. http://dx.doi.org/10.1109/csae.2011.5953176.

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Yang, Huixian, WenLong Yue, Yabin He, Huixian Huang, and Haixia Xia. "The Deduction of Coefficient Matrix for Cubic Non-Uniform B-Spline Curves." In 2009 First International Workshop on Education Technology and Computer Science. IEEE, 2009. http://dx.doi.org/10.1109/etcs.2009.396.

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Malhotra, Alok, James H. Oliver, and Weizhen Tu. "Synthesis of Spatially and Intrinsically Constrained Curves Using Simulated Annealing." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0080.

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Abstract A general technique is presented for automatic generation of B-spline curves in a spatially constrained environment, subject to specified intrinsic shape properties. Spatial constraints are characterized by a distance metric relating points on the curve to polyhedral models of obstacles which the curve should avoid. The shape of the curve is governed by constraints based on intrinsic curve properties such as parametric variation and curvature. To simultaneously address the independent goals of global obstacle avoidance and local control of intrinsic shape properties, curve synthesis is formulated as a combinatorial optimization problem and solved via simulated annealing. Several example applications are presented which demonstrate the robustness of the technique. The synthesis of both uniform and non-uniform B-spline curves is also demonstrated. An extension of the technique to general sculptured surface model synthesis is briefly described, and a preliminary example of simple surface synthesis presented.
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Vinnakota, Ravi, Alley Butler, and Steven LeClair. "Development of a Voronoi Tree for Cavities by Hodograph-Hodograph Intersection." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/cie-9112.

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Abstract This paper reports on research efforts to efficiently find a Voronoi tree for cavities described by Non-Uniform Non-Rational B-Spline Curves. It examines the motivation for solving this problem, and it reviews the literature on splines and their hodographs (or offset curves). This paper then offers a technique for finding a Voronoi tree for cavities by intersecting hodograph curves. The possibilities for an analytical determination of intersection are considered, and a numerical methodology is presented. This numerical method is demonstrated on two different types of problems: a symmetric cavity problem and an asymmetric cavity problem. Finally, conclusions are drawn about this work.
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Chen, J. M., Yu Wang, E. L. Guroz, and Fritz B. Prinz. "Parametric Surface Intersections for Geometric Modeling." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0167.

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Abstract A surface-surface intersection algorithm is an important element in the development of a geometric modeler. This paper presents a new algorithm for calculating the intersection curves of two parametric surfaces. Combining the merits of subdivision and global exploration methods, this algorithm is efficient and robust in dealing with the issues related to small loops and singularities. This algorithm is demonstrated with examples of non-uniform rational B-spline surfaces.
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Caputi, Antonio, Miri Weiss Cohen, Caterina Rizzi, and Davide Russo. "Truss Design and Optimization Using Stress Analysis and NURBS Curves." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87728.

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This paper presents a novel design methodology, which combines topology and shape optimization to define material distribution in the structural design of a truss. Firstly, in order to identify the best layout, the topology optimization process in the design domain is carried out by applying the BESO (Bidirectional Evolutionary Structural Optimization) method. In this approach, the low energy elements are eliminated from an initial mesh, and a new geometry is constructed. This new geometry consists of a set of elements with a higher elastic energy. This results in a new division of material providing different zones, some subjected to higher stress and others containing less elastic energy. Moreover, the elements of the final mesh are re-arranged and modified, considering the distribution of tension. This new arrangement is constructed by aligning and rotating the original mesh elements coherently to the principal directions. In the Shape Optimization stage, the resulting TO (Topology Optimization) geometry is refined. A process of replacing the tabular mesh is performed by rearranging the remaining elements. The vertices of the mesh are set as control polygon vertices and used as reference to define the NURBS (Non-Uniform Rational B-Spline) curves. This provides a parametric representation of the boundaries, outlining the high elastic energy zones. The final stage is the optimization of the continuous and analytically defined NURBS curve outlining the solid material domain. The Shape Optimization is carried out applying a gradient-based optimization method.
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Yang, Jingzhou, Karim Abdel-Malek, and Jim Cremer. "An Approach to Sweeping NURBS." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/dac-21150.

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Abstract This paper presents a method of determining the swept volume of Non-Uniform rational B-Spline (NURBS) curves and surfaces. Characteristic (also called singular) points or curves are determined by obtaining local and global maxima points at discrete frames during the motion and with respect to a local moving coordinate system. This coordinate system is calculated in reference to the direction of motion of the rigid body as determined from its composite velocity vector. The aim is to develop a rigorous method for identifying and visualizing a NURBS swept volume. NURBS have become the industry standard for the representation, design, and data exchange of geometric information processed by computers. On the other hand, sweeping operations are valuable tools for the CAD user to shape and create primitives. In this paper, we extend our previous method used in determining the swept volume of implicit and parametric surfaces and those that are as a result of multiple sweeping. The method and numerical algorithm are illustrated through examples.
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Sharifi, Hamid. "Finite Element-Boundary Element Mesh Generation Technique for Fluid Structure Problems." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30951.

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In this article an approach for fully automatic mesh generation for two dimensional fluid structure problems that respect the integrity of the geometrical boundaries is presented. This approach is based on the modified Quadtree method. First, interior quadrants of the solid structure are created as the original Quadtree method. Boundary quadrants of the solid structure are created between the boundary curves and the interior quadrants using a simple projection algorithm. As a result, the problem of cut quadrants of the original modified Quadtree method is eliminated here. Boundary elements of the fluid region are created on the boundary curves using calculated projection points. The use of closed non uniform composite B-spline curves, for a unified representation of boundaries curves, simplifies the projection algorithm. On the other hand using this type of boundaries representation reduces geometrical incompatibilities of the generated mesh and produces a perfect compatibility between boundary elements and finite elements. This method can be extended to problems of three dimensional mesh generation and eliminate all cases of cut octants. An object-oriented prototype program in C++ has been written and application example is presented in this paper. Several algorithms of this method are suitable for an implementation on parallel computers.
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Sugimura, Kazuyuki. "Aerodynamic Shape Optimization and Knowledge Mining of Centrifugal Fans Using Simulated Annealing Coupled With a Neural Network." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99189.

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An aerodynamic shape optimization method suitable for “inexpensive” centrifugal impellers and diffusers has been developed. The shapes are parameterized using non-uniform rational B-spline curves with special attention being paid to the blade’s edge profiles. A hybrid algorithm combining simulated annealing and a neural network is employed for collaborative optimization. The simulated annealing and neural network take turns in controlling the optimization processes, not only for maximizing the efficiency of global exploration, but also for minimizing the risks of automation failures or of reaching an incorrect optimum. A statistical analysis was also conducted using the neural network to extract design knowledge. By applying the proposed method to a centrifugal impeller and diffuser design problem, we obtained innovative shapes for the leading edge of the impeller and the trailing edge of the diffuser. Important design parameters related to the new shapes were identified through the design space analysis.
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