Relevant bibliographies by topics / Non Uniform Rational B-Splines

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Academic literature on the topic 'Non Uniform Rational B-Splines'

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Published: 6 September 2023

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Journal articles on the topic "Non Uniform Rational B-Splines"

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Liu, Jiankang, Hongya Fu, Jihao Qin, and Hongyu Jin. "Sliding look-ahead window-based real-time feedrate planning for non-uniform rational B-splines curves." Advances in Mechanical Engineering 10, no. 12 (December 2018): 168781401881692. http://dx.doi.org/10.1177/1687814018816926.

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This article presents an online three-axis non-uniform rational B-splines preprocessing and feedrate scheduling method with chord error, axial velocity, acceleration, and jerk limitations. A preprocessing method is proposed to accurately locate the critical points by reducing pre-interpolation feedrate in feedrate limit violation regions. In the preprocessing stage, the non-uniform rational B-splines curve is subdivided into segments by the critical points and the corresponding feedrate constraints are obtained. A sliding look-ahead window-based feedrate scheduling method is proposed to generate smooth feedrate profile for the buffered non-uniform rational B-splines segments. The feedrate profile corresponding to each non-uniform rational B-splines block is constructed according to the block length and the given limits of acceleration and jerk. The feedrate modification method for non-schedulable short blocks is also described which aimed at avoiding feedrate discontinuity at the junction of two non-uniform rational B-splines blocks. With the proposed method, a successful feedrate profile could be generated with sufficient look-ahead trajectory length in the buffer, which enables that the preprocessing and feedrate planning to be performed progressively online. Simulation and experimental tests with different non-uniform rational B-splines curves are carried out to validate the feasibility and advantages of the proposed method. The results show that the proposed method is capable of making a balance between the machining efficiency, machining precision, and computational complexity.
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Cheng, Ming-Yang, Hung-Wen Wu, and Alvin Wen-Yu Su. "On Non-Uniform Rational B-Splines Surface Neural Networks." Neural Processing Letters 28, no. 1 (May 10, 2008): 1–15. http://dx.doi.org/10.1007/s11063-008-9078-9.

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SUN, Shufeng. "Design of Spatial Cam Based on Non-uniform Rational B-splines." Journal of Mechanical Engineering 45, no. 08 (2009): 125. http://dx.doi.org/10.3901/jme.2009.08.125.

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Audoux, Y., M. Montemurro, and J. Pailhes. "A surrogate model based on Non-Uniform Rational B-Splines hypersurfaces." Procedia CIRP 70 (2018): 463–68. http://dx.doi.org/10.1016/j.procir.2018.03.234.

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Peng, Bao Ying, and Qiu Shi Han. "Cam Grinding Interpolation Research Based on Cubic Non-Uniform Rational B-Splines." Advanced Materials Research 443-444 (January 2012): 843–49. http://dx.doi.org/10.4028/www.scientific.net/amr.443-444.843.

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With the development of auto industry and aviation industry,the cam quality requirements higher and higher. The NURBS curve has excellent natures that can smooth the cam grinding path and improve its processing quality. Combined with existing CAD software and CNC systems, respectively, from reverse and forward two aspects of NURBS curve to illustrate the non-uniform B-spline principle and given the relevant formulas. Choosing X-C coordinates points of the cam grinding as the research object, adopt reverse and forward NURBS curve interpolation to fit the cam grinding path. Analysed the fitting error caused by line segment fit NURBS curve and cam lift error caused by NURBS interpolation. Summarized the advantages and disadvantages of two ways Nurbs interpolation discussed the method to improve NURBS interpolation for cam grinding.
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Xuan, Guantao, Yuanyuan Shao, and Lei Liu. "Optimal Design of Grooved Cam Profile Using Non-uniform Rational B-splines." MATEC Web of Conferences 139 (2017): 00047. http://dx.doi.org/10.1051/matecconf/201713900047.

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Steuben, John C., Cameron J. Turner, and Richard H. Crawford. "Robust engineering design optimization with non-uniform rational B-splines-based metamodels." Engineering Optimization 45, no. 7 (July 2013): 767–86. http://dx.doi.org/10.1080/0305215x.2012.709509.

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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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Müller, Mario, Mathias Hüsing, Agnes Beckermann, and Burkhard Corves. "Linkage and Cam Design with MechDev Based on Non-Uniform Rational B-Splines." Machines 8, no. 1 (January 21, 2020): 5. http://dx.doi.org/10.3390/machines8010005.

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Several software products exist in order to support engineers during the mechanism design process. The software “Mechanism Developer” (abbr. MechDev) is one of these products. MechDev provides many functionalities concerning the kinematic and kinetostatic analysis of mechanisms based on revolute, prismatic as well as cam joints. This paper will introduce the software MechDev and will outline these functionalities. Furthermore, it will name the advantages of MechDev compared to other software products. In order to give an impression of the functionality of the software, this paper also includes a special use case. This use case describes a cam mechanism with a prismatic roller-follower. In order to optimize the transmission angle of the cam mechanism, the cam is actuated by a servo drive. To mathematically model the angular input of the servo drive, Non-Uniform Rational B-Splines (NURBS) are described and applied. Thus, a nearly arbitrary input function can be described by few parameters.
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Lan, Peng, Zuqing Yu, Liang Du, and Nianli Lu. "Integration of non-uniform Rational B-splines geometry and rational absolute nodal coordinates formulation finite element analysis." Acta Mechanica Solida Sinica 27, no. 5 (October 2014): 486–95. http://dx.doi.org/10.1016/s0894-9166(14)60057-4.

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Dissertations / Theses on the topic "Non Uniform Rational B-Splines"

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Zhang, Xingchen. "CAD-based geometry parametrisation for shape optimisation using non-uniform rational B-splines." Thesis, Queen Mary, University of London, 2018. http://qmro.qmul.ac.uk/xmlui/handle/123456789/43186.

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With the continuous growth in computing power, numerical optimisation is increasingly applied in shape optimisation using Computational Fluid Dynamics (CFD). Since CFD computations are expensive, gradient-based optimisation is preferable when the number of design variables is large. In particular the recent progress with adjoint solvers is important, as these solvers allow to compute the gradients at constant computational cost regardless of the number of design variables, and as a consequence enable the use of automatically derived and rich design spaces. One of the crucial steps in shape optimisation is the parametrisation of the geometry, which directly determines the design space and thus the nal results. This thesis focuses on CAD-based parametrisations with the CAD model continuously updated in the design loop. An existing approach that automatically derives a parametrisation from the control points of a net of B-Spline patches is extended to include NURBS. Continuity constraints for water-tightness, tangency and curvature across patch interfaces are evaluated numerically and a basis for the resulting design space is computed using Singular Value Decomposition (SVD). A CAD-based shape optimisation framework is developed, coupling a flow solver, an adjoint solver, the in-house CAD kernel and a gradient-based optimiser. The flow sensitivities provided by the adjoint solver and the geometric sensitivities computed through automatic differentiation (AD) are assembled and provided to the optimiser. An extension to maintain the design space and hence enables use of a quasi-Newton method such as the BFGS algorithm is also presented and the convergence improvements are demonstrated. The framework is applied to three shape optimisation cases to show its effectiveness. The performance is assessed and analysed. The effect of parameters that can be chosen by the user are analysed over a range of cases and best practice choices are identified.
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Kesper, Björn. "Konzeption eines Geo-Datenmodells unter Verwendung von Freiformkörpern auf der Basis von volume non uniform rational b-splines." [S.l. : s.n.], 2001. http://www.sub.uni-hamburg.de/disse/567/Disse.pdf.

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Audoux, Yohann. "Développement d’une nouvelle méthode de réduction de modèle basée sur les hypersurfaces NURBS (Non-Uniform Rational B-Splines)." Thesis, Paris, ENSAM, 2019. http://www.theses.fr/2019ENAM0016/document.

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Malgré des décennies d’incontestables progrès dans le domaine des sciences informatiques, un certain nombre de problèmes restent difficiles à traiter en raison, soit de leur complexité numérique (problème d’optimisation, …), soit de contraintes spécifiques telle que la nécessité de traitement en temps réel (réalité virtuelle, augmentée, …). Dans ce contexte, il existe des méthodes de réduction de modèle qui permettent de réduire les temps de calcul de simulations multi-champs et/ou multi-échelles complexes. Le processus de réduction de modèle consiste à paramétrer un métamodèle qui requiert moins de ressources pour être évalué que le modèle complexe duquel il a été obtenu, tout en garantissant une certaine précision. Les méthodes actuelles nécessitent, en général, soit une expertise de l’utilisateur, soit un grand nombre de choix arbitraires de sa part. De plus, elles sont bien souvent adaptées à une application spécifique mais difficilement transposable à d’autres domaines. L’objectif de notre approche est donc d’obtenir, s'il n'est pas le meilleur, un bon métamodèle quel que soit le problème considéré. La stratégie développée s’appuie sur l’utilisation des hypersurfaces NURBS et se démarque des approches existantes par l’absence d’hypothèses simplificatrices sur les paramètres de celles-ci. Pour ce faire, une méta heuristique (de type algorithme génétique), capable de traiter des problèmes d’optimisation dont le nombre de variables n’est pas constant, permet de déterminer automatiquement l’ensemble des paramètres de l’hypersurface sans transférer la complexité des choix à l’utilisateur
Despite undeniable progress achieved in computer sciences over the last decades, some problems remain intractable either by their numerical complexity (optimisation problems, …) or because they are subject to specific constraints such as real-time processing (virtual and augmented reality, …). In this context, metamodeling techniques can minimise the computational effort to realize complex multi-field and/or multi-scale simulations. The metamodeling process consists of setting up a metamodel that needs less resources to be evaluated than the complex one that is extracted from by guaranteeing, meanwhile, a minimal accuracy. Current methods generally require either the user’s expertise or arbitrary choices. Moreover, they are often tailored for a specific application, but they can be hardly transposed to other fields. Thus, even if it is not the best, our approach aims at obtaining a metamodel that remains a good one for whatever problem at hand. The developed strategy relies on NURBS hypersurfaces and stands out from existing ones by avoiding the use of empiric criteria to set its parameters. To do so, a metaheuristic (a genetic algorithm) able to deal with optimisation problems defined over a variable number of optimisation variables sets automatically all the hypersurface parameters so that the complexity is not transferred to the user
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Shang, Xiaolei. "Adaptive 3D modelling based on single images using non-uniform rational B-spline technique." Thesis, University of Derby, 2005. http://hdl.handle.net/10545/196649.

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Flores, Melvin Estuardo Murray Richard M. Murray Richard M. "Real-time trajectory generation for constrained nonlinear dynamical systems using non-uniform rational B-spline basis functions /." Diss., Pasadena, Calif. : California Institute of Technology, 2008. http://resolver.caltech.edu/CaltechETD:etd-02192008-153449.

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Rajab, Khairan. "Knowledge Guided Non-Uniform Rational B-Spline (NURBS) for Supporting Design Intent in Computer Aided Design (CAD) Modeling." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3302.

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For many years, incompatible computer-aided design (CAD) packages that are based on Non-uniform Rational B-Spline (NURBS) technology carried out the exchange of models and data through either neutral file formats (IGES or STEP) or proprietary formats that have been accepted as quasi industry standards. Although it is the only available solution at the current time, the exchange process most often produces unsatisfactory results. Models that are impeccable in the original modeling system usually end up with gaps or intersections between surfaces on another incompatible system. Issues such as loss of information, change of data accuracy, inconsistent tolerance, and misinterpretation of the original design intent are a few examples of problems associated with migrating models between different CAD systems. While these issues and drawbacks are well known and cost the industry billions of dollars every year, a solution to eradicate problems from their sources has not been developed. Meanwhile, researchers along with the industries concerned with these issues have been trying to resolve such problems by finding means to repair the migrated models either manually or by using specialized software. Designing in recent years is becoming more knowledge intensive and it is essential for NURBS to take its share of the ever increasing use of knowledge. NURBS are very powerful modeling tools and have become the de facto standard in modeling. If we stretch their strength and make them knowledge driven, benefits beyond current expectations can be achieved easily. This dissertation introduces knowledge guided NURBS with theoretical and practical foundations for supporting design intent capturing, retrieval, and exchange among dissimilar CAD systems. It shows that if NURBS entities are tagged with some knowledge, we can achieve seamless data exchange, increase robustness, and have more reliable computations, all of which are ultimate objectives many researchers in the field of CAD have been trying to accomplish for decades. Establishing relationships between a NURBS entity and its origin and destinations can aid with seamless CAD model migration. The type of the NURBS entity and the awareness of any irregularities can lead to more intelligent decisions on how to proceed with many computations to increase robustness and achieve a high level of reliability. As a result, instead of having models that are hardly modifiable because of migrating raw numerical data in isolation, the knowledge driven migration process will produce models that are editable and preserve design intent. We have addressed the issues not only theoretically but also by developing a prototype system that can serve as a test bed. The developed system shows that a click of a button can regenerate a migrated model instead of repairing it, avoiding delay and corrective processes that only limit the effective use of such models.
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Nguyen, Thi Thanh Nga [Verfasser], Burkhard [Akademischer Betreuer] Corves, and Mathias [Akademischer Betreuer] Hüsing. "Motion design of cam mechanisms by using non-uniform rational B-Spline / Thi Thanh Nga Nguyen ; Burkhard Corves, Mathias Hüsing." Aachen : Universitätsbibliothek der RWTH Aachen, 2018. http://d-nb.info/1176422006/34.

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Saiz, Ipiña Juan Antonio. "Análisis de sistemas radiantes sobre geometrías arbitrarias definidas por superficies paramétricas." Doctoral thesis, Universidad de Cantabria, 1995. http://hdl.handle.net/10803/10678.

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En esta tesis se presenta un método para analizar antenas montadas sobre estructuras arbitrarias. La Optica Geométrica (GO) y la Teoría Uniforme de la difraccion (UTD), han sidoempleadas para analizar los efectos que la estructura produce sobre el diagrama de radiación de la antena emisora. Para la descripción geométrica de la estructura, han sido utilizados parches NURBS (Non Uniform Rational B-Spline), por lo que el método presentado, es compatible con la mayoría de los programas gráficos disponibles en el mercado.EL tratamiento de geometrías arbitrarias requiere un código eficiente en el análisis de tres dimensiones.Por otro lado, para obtener resultados satisfactorios, la descripción de la superficie de la estructura, debe ser muy próxima al modelo real, sin embargo, esto complica el tratamiento computacional. Aquí la estructura es modelada mediante un conjunto de parches NURBS, que unidos entre sí, describen el modelo completo. Esta descripción permite manipular superficies arbitrarias con un bajo numero de parches, lo que significa un volumen de información reducido.La descripción inicial por NURBS del modelo, es acompañada con información complemetaria como por ejemplo: la tipología de las superficies, las curvas frontera, el tipo de material, etc. Esto es imprescindible para la aplicación de criterios de selección dedicados a la aceleración del proceso.El método tras leer la descripción del modelo, descompone los parches NURBS en superficies racionales de Bezier. Un parche de Bezier es también una superficie paramétrica definida en términos de una combinación lineal de los polinomios de Bernstein.Las antenas son modeladas usando modelos numéricos simples basados en agrupaciones de dipolos infinitesimales eléctricos y magnéticos. Esta caracterización de la antena es muyventajosa ya que con un numero reducido de datos de entrada, la fuente queda definida para cualquier dirección del espacio y el valor del campo radiado puede ser calculado fácilmente.El análisis electromagnético de los efectos que contribuyen al campo dispersado por la geometría comienza con una selección rigurosa de la geometría iluminada desde la fuente.Unicamente los parches de Bezier iluminados serán almacenados por el ordenador durante el análisis. La filosofía de este proceso es descartar aquella parte de la geometría que no contribuye a los efectos de dispersión.El campo total calculado es la superposición de los siguientes efectos pertenecientes a la GO y a la UTD: campo directo procedente de la fuente, campo reflejado por los parches de Bezier, campo difractado por las aristas del modelo definidas como curvas de Bezier, ondas de superficie, dobles reflexiones, reflexione-difraccion y difraccion-reflexión. El método ha sido diseñado para analizar campo cercano y lejano. El mayor gasto computacional se debe a la búsqueda de los puntos de dispersión, por lo que antes de emplear los algoritmos de intersección es necesario aplicar un conjunto de criterios rápidos dependientes de la dirección de observación.El principio de Fermat en combinación con el Gradiente Conjugado (CGM) es usado para obtener de manera eficiente los puntos de dispersión sobre la estructura. Para cada efecto, laposible ocultación de la trayectoria completa del rayo es examinada, por ello, si el rayo corta alguno de los parches de Bezier su contribución será descartada. Los dobles efectos son tratados como una generalización de los simples efectos.El método desarrollado es eficiente ya que precisa de un numero reducido de superficies para modelar objetos complejos lo que se traduce en bajos requerimientos de memoria y reducidos tiempos de calculo.
In this thesis a method to analyze antennas on board of complex bodies is presented. The Geometrical Optics (GO) and Uniform Theory of Diffraction (UTD) have been used to analyze the effect of the structure in the radiation pattern of the antennas. The bodies are geometrically modelled by using NURBS (Non Uniform Rational B-Spline) surfaces. In addition to be accurate and efficient, the method is compatible with most of the modern CAGD (Computer Aided Geometric Design) available programs.The treatment of arbitrary geometries requires a code which can carry out an efficient 3D analysis. To obtain accurate results the description of the surface must be close to the real model, however this complicates the computational procedure. Here the structure is modeled by a collection of individual N.U.R.B.S. surface patches joined to form a complete description of the surface model. The NURBS description is able to manipulate free form surfaces with a low number of patches, and therefore, with a low amount of information. The initial description of the model by NURBS surfaces is accompanied with other complementary data for example : the topology of the surfaces, the boundary curves, the types of material and other inputs. It is very interesting to apply criteria to make the complete analysis faster.The method reads the NURBS description of the model and transforms the NURBS into the rational BEZIER surfaces. A rational BEZIER patch is also a parametric surface defined in terms of a linear combination of Bernstein polynomials.The antennas are modelled using simple numerical models based on arrays of electric and magnetic infinitesimal dipoles. This antenna modelization is very advantageous because with a little input data, the source is defined in any direction and the field value is readily accessible.The electromagnetic analysis of the contributive effects to the scattering field by the geometry, starts with the rigorous selection of the geometry illuminated from the source. Only the Bezier patches illuminated will be in memory of the computer during the analysis. The philosophy of this previous process is to discard in the process the part of the geometry which does not contribute to the scattering effects.The total field is the superposition of the following GO and UTD field components: direct field from the source, reflected fields from the Bezier patches of the model, diffracted fields from the arbitrary edges defined as a Bezier curves, creeping waves, double reflected field and diffracted-reflected and reflected-diffracted fields. The search of specular and diffraction points are the most CPU time consuming, thus before using the intersection algorithms it is necessary to apply a set of fast selection criteria which depend on the observation direction.The Fermat principle in conjunction with the Conjugate Gradient Method (CGM) is used for obtaining efficiently the reflection points and diffraction points on the structure. For each effect the complete ray path is examined to see whether or not it is interrupted by any Bezier patch of the model, in this case the field component is not computed. The double effects are treated using a generalization of the single effects algorithms. The method has been developed to analyze the near and far field cases for different frequencies.The developed method is quite efficient because it makes use of a small number of surfaces to model complex bodies, so it requires few memory and low computing time.
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Sevilla, Cárdenas Rubén. "NURBS-Enhanced Finite Element Method (NEFEM)." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5857.

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Aquesta tesi proposa una millora del clàssic mètode dels elements finits (finite element method, FEM) per a un tractament eficient de dominis amb contorns corbs: el denominat NURBS-enhanced finite element method (NEFEM). Aquesta millora permet descriure de manera exacta la geometría mitjançant la seva representació del contorn CAD amb non-uniform rational B-splines (NURBS), mentre que la solució s'aproxima amb la interpolació polinòmica estàndard. Per tant, en la major part del domini, la interpolació i la integració numèrica són estàndard, retenint les propietats de convergència clàssiques del FEM i facilitant l'acoblament amb els elements interiors. Només es requereixen estratègies específiques per realitzar la interpolació i la integració numèrica en elements afectats per la descripció del contorn mitjançant NURBS.

La implementació i aplicació de NEFEM a problemes que requereixen una descripció acurada del contorn són, també, objectius prioritaris d'aquesta tesi. Per exemple, la solució numèrica de les equacions de Maxwell és molt sensible a la descripció geomètrica. Es presenta l'aplicació de NEFEM a problemes d'scattering d'ones electromagnètiques amb una formulació de Galerkin discontinu. S'investiga l'habilitat de NEFEM per obtenir solucions precises amb malles grolleres i aproximacions d'alt ordre, i s'exploren les possibilitats de les anomenades malles NEFEM, amb elements que contenen singularitats dintre d'una cara o aresta d'un element. Utilitzant NEFEM, la mida de la malla no està controlada per la complexitat de la geometria. Això implica una dràstica diferència en la mida dels elements i, per tant, suposa un gran estalvi tant des del punt de vista de requeriments de memòria com de cost computacional. Per tant, NEFEM és una eina poderosa per la simulació de problemes tridimensionals a gran escala amb geometries complexes. D'altra banda, la simulació de problemes d'scattering d'ones electromagnètiques requereix mecanismes per aconseguir una absorció eficient de les ones scattered. En aquesta tesi es discuteixen, optimitzen i comparen dues tècniques en el context de mètodes de Galerkin discontinu amb aproximacions d'alt ordre.

La resolució numèrica de les equacions d'Euler de la dinàmica de gasos és també molt sensible a la representació geomètrica. Quan es considera una formulació de Galerkin discontinu i elements isoparamètrics lineals, una producció espúria d'entropia pot evitar la convergència cap a la solució correcta. Amb NEFEM, l'acurada imposició de la condició de contorn en contorns impenetrables proporciona resultats precisos inclús amb una aproximació lineal de la solució. A més, la representació exacta del contorn permet una imposició adequada de les condicions de contorn amb malles grolleres i graus d'interpolació alts. Una propietat atractiva de la implementació proposada és que moltes de les rutines usuals en un codi d'elements finits poden ser aprofitades, per exemple rutines per realitzar el càlcul de les matrius elementals, assemblatge, etc. Només és necessari implementar noves rutines per calcular les quadratures numèriques en elements corbs i emmagatzemar el valor de les funciones de forma en els punts d'integració. S'han proposat vàries tècniques d'elements finits corbs a la literatura. En aquesta tesi, es compara NEFEM amb altres tècniques populars d'elements finits corbs (isoparamètics, cartesians i p-FEM), des de tres punts de vista diferents: aspectes teòrics, implementació i eficiència numèrica. En els exemples numèrics, NEFEM és, com a mínim, un ordre de magnitud més precís comparat amb altres tècniques. A més, per una precisió desitjada NEFEM és també més eficient: necessita un 50% dels graus de llibertat que fan servir els elements isoparamètrics o p-FEM per aconseguir la mateixa precisió. Per tant, l'ús de NEFEM és altament recomanable en presència de contorns corbs i/o quan el contorn té detalls geomètrics complexes.
This thesis proposes an improvement of the classical finite element method (FEM) for an efficient treatment of curved boundaries: the NURBSenhanced FEM (NEFEM). It is able to exactly represent the geometry by means of the usual CAD boundary representation with non-uniform rational Bsplines (NURBS), while the solution is approximated with a standard piecewise polynomial interpolation. Therefore, in the vast majority of the domain, interpolation and numerical integration are standard, preserving the classical finite element (FE) convergence properties, and allowing a seamless coupling with standard FEs on the domain interior. Specifically designed polynomial interpolation and numerical integration are designed only for those elements affected by the NURBS boundary representation.

The implementation and application of NEFEM to problems demanding an accurate boundary representation are also primary goals of this thesis. For instance, the numerical solution of Maxwell's equations is highly sensitive to geometry description. The application of NEFEM to electromagnetic scattering problems using a discontinuous Galerkin formulation is presented. The ability of NEFEM to compute an accurate solution with coarse meshes and high-order approximations is investigated, and the possibilities of NEFEM meshes, with elements containing edge or corner singularities, are explored. With NEFEM, the mesh size is no longer subsidiary to geometry complexity, and depends only on the accuracy requirements on the solution, whereas standard FEs require mesh refinement to properly capture the geometry. This implies a drastic difference in mesh size that results in drastic memory savings, and also important savings in computational cost. Thus, NEFEM is a powerful tool for large-scale scattering simulations with complex geometries in three dimensions. Another key issue in the numerical solution of electromagnetic scattering problems is using a mechanism to perform the absorption of outgoing waves. Two perfectly matched layers are discussed, optimized and compared in a high-order discontinuous Galerkin framework.

The numerical solution of Euler equations of gas dynamics is also very sensitive to geometry description. Using a discontinuous Galerkin formulation and linear isoparametric elements, a spurious entropy production may prevent convergence to the correct solution. With NEFEM, the exact imposition of the solid wall boundary condition provides accurate results even with a linear approximation of the solution. Furthermore, the exact boundary representation allows using coarse meshes, but ensuring the proper implementation of the solid wall boundary condition. An attractive feature of the proposed implementation is that the usual routines of a standard FE code can be directly used, namely routines for the computation of elemental matrices and vectors, assembly, etc. It is only necessary to implement new routines for the computation of numerical quadratures in curved elements and to store the value of shape functions at integration points.

Several curved FE techniques have been proposed in the literature. In this thesis, NEFEM is compared with some popular curved FE techniques (namely isoparametric FEs, cartesian FEs and p-FEM), from three different perspectives: theoretical aspects, implementation and performance. In every example shown, NEFEM is at least one order of magnitude more accurate compared to other techniques. Moreover, for a desired accuracy NEFEM is also computationally more efficient. In some examples, NEFEM needs only 50% of the number of degrees of freedom required by isoparametric FEs or p-FEM. Thus, the use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details.
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Coe, David H. "Skinning engineering models with non-uniform, hierarchical B-spline surfaces." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-09052009-040656/.

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Books on the topic "Non Uniform Rational B-Splines"

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Hong, Qin. D-NURBS: dynamic non-uniform rational B-splines. Toronto: University of Toronto, Dept. of Computer Science, 1995.

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Urso, Agostino. Rappresentazione e cultura digitale: Da Cartesio alle "Non Uniform Rational Bézier-Splines". Reggio Calabria: Laruffa, 2004.

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Hong, Qin. D-NURBS: Dynamic non-uniform rational B-splines. 1995.

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Book chapters on the topic "Non Uniform Rational B-Splines"

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Zhang, Xingchen, Rejish Jesudasan, and Jens-Dominik Müller. "Adjoint-Based Aerodynamic Optimisation of Wing Shape Using Non-uniform Rational B-Splines." In Computational Methods in Applied Sciences, 143–58. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-89890-2_10.

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Fisher, T. R., and R. Q. Wales. "Three Dimensional Solid Modeling of Geo-Objects Using Non-Uniform Rational B-Splines (NURBS)." In Three-Dimensional Modeling with Geoscientific Information Systems, 85–105. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2556-7_9.

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Ruiu, Jeremy, Guillaume Caumon, Sophie Viseur, and Christophe Antoine. "Modeling Channel Forms Using a Boundary Representation Based on Non-uniform Rational B-Splines." In Lecture Notes in Earth System Sciences, 581–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-32408-6_127.

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Incesu, Muhsin, Sara Yilmaz Evren, and Osman Gursoy. "On the Bertrand Pairs of Open Non-Uniform Rational B-Spline Curves." In Springer Proceedings in Mathematics & Statistics, 167–84. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-8177-6_11.

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Shi, Xianghang, Jing Liu, Jingzhou Xu, and Mingli Lu. "A Lung Segmentation Method Based on an Improved Convex Hull Algorithm Combined with Non-uniform Rational B-Sample." In Lecture Notes in Computer Science, 311–19. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09726-3_28.

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Qu, Ruibin, and John A. Gregory. "A Subdivision Algorithm For Non—Uniform B—Splines." In Approximation Theory, Spline Functions and Applications, 423–36. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2634-2_30.

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Montemurro, Marco, Thibaut Rodriguez, Paul Le Texier, and Jérôme Pailhès. "Multi-Displacement Requirement in a Topology Optimization Algorithm Based on Non-uniform Rational Basis Spline Hyper-Surfaces." In Advances in Mechanics and Mathematics, 223–57. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-90051-9_9.

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Kermarrec, Gaël, Vibeke Skytt, and Tor Dokken. "LR B-Splines for Representation of Terrain and Seabed: Data Fusion, Outliers, and Voids." In Optimal Surface Fitting of Point Clouds Using Local Refinement, 57–80. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-16954-0_5.

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AbstractPerforming surface approximation of geospatial point clouds with locally refined (LR) B-splines comes with several challenges: (i) Point clouds have varying data density, (ii) outliers should be eliminated without deleting features, (iii) voids, also called holes, or data gaps should be treated specifically to avoid the drop of the approximated surface in domains without points. These factors tend to be even more challenging when point clouds acquired from different sensors having different noise characteristics are fused together. The data set becomes non-uniform and the fusing process itself involves a risk of an increased noise level. In this chapter, we provide some tools to answer those specific challenges. We will use terrain and seabed data and show didactically how to perform adaptive surface approximation with local refinement and to select customized parameters. We will further address the problem of choosing an appropriate tolerance for performing an adaptive fitting, and discuss the refinement strategies within the context of LR B-splines. The latter is shown to provide a promising framework for surface fitting of heterogeneous point clouds from various sources.
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"Surrogate Modeling with Non-Uniform Rational B-splines." In Advances in Computers and Information in Engineering Research, Volume 1, 345–75. ASME Press, 2014. http://dx.doi.org/10.1115/1.860328_ch14.

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Beinstingel, A., M. Heider, B. Pinnekamp, and S. Marburg. "Gear mesh excitation and non-uniform rational B-splines." In International Conference on Gears 2022, 91–102. VDI Verlag, 2022. http://dx.doi.org/10.51202/9783181023891-91.

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Conference papers on the topic "Non Uniform Rational B-Splines"

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Fiasconaro, James G., and David S. Maitiand. "Non-Uniform Rational B-Splines." In Computer Graphics Conference and Exposition. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, 1987. http://dx.doi.org/10.4271/870877.

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Davenport, Thomas L. R. "Non-uniform-rational-B-splines (NURBS) in illumination design." In Frontiers in Optics. Washington, D.C.: OSA, 2003. http://dx.doi.org/10.1364/fio.2003.tuw2.

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Yau, Hong-Tzong, and Kuei-Wu Chen. "General Form Tolerance Evaluation Using Non-Uniform Rational B-Splines." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/dac-1048.

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Abstract Tolerance evaluation is critical to quality assurance in modern manufacturing. In contrast to traditional measurement which relies on specific hard gauges, coordinate measuring machines provide more flexibility for dimensional measurement and tolerance evaluations. To fully automate CMM inspection and tolerance evaluation, CAD/CMM integration is an important key. Although the subject of CAD-directed inspection has been widely researched, CAD model-based tolerance evaluation has received less attention. This paper presents a CAD model-based approach for evaluating general form tolerances using non-uniform rational B-splines. Unlike classical methods which construct substitute geometric features from the measurement data, this method evaluates form tolerances by comparing the measurement data with a nominal CAD model. Nonuniform rational B-splines (NURBS) is used to represent general form features since NURBS offers a common format for modeling precisely all the different form features. With this unified database, a general best-fit algorithm is developed that can be applied to the evaluation of various form tolerances. Computer simulations have been performed on different form features to study the robustness and efficiency of the algorithm. Application to the measurement of turbine wheel die segment is also presented.
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Turner, Cameron J., and Richard H. Crawford. "Adapting Non-Uniform Rational B-Spline Fitting Approaches to Metamodeling." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85544.

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Modern engineering design requires the exploration of complex nonlinear design spaces that relate large numbers of design variables and performance criteria. Effective exploration and decision making requires the availability of efficient representations of high dimensional design spaces. Techniques from the field of metamodeling, which builds models of models, are often used to represent complex design relationships. We have developed an alternative, spline-based metamodeling technique that is amenable to adaptive representation of high dimensional spaces and facilitates optimization-based exploration of such spaces. This paper describes our technique for fitting Non-Uniform Rational B-splines (NURBs) to points in a design space generated from simulations or experiments. The algorithm is illustrated with examples from metamodeling and nonlinear optimization literature. The results indicate that our method achieves an average global correlation of more than 99% and an average maximum local RMS error of less than 3% of full scale.
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Ibrahim, Abdul Rahman, Siti Mariyam Shamsuddin, and Aida Ali. "Improving Non-Uniform Rational B-splines' Knot Removal with Particle Swarm Optimization." In 2009 Sixth International Conference on Computer Graphics, Imaging and Visualization (CGIV). IEEE, 2009. http://dx.doi.org/10.1109/cgiv.2009.95.

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Silbermann, M. J., P. V. Sankar, and L. A. Ferrari. "Implementation of non uniform rational B-splines (NURBs) using a derivative recurrence." In Twenty-Third Asilomar Conference on Signals, Systems and Computers, 1989. IEEE, 1989. http://dx.doi.org/10.1109/acssc.1989.1201059.

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Wessels, Francois J. L., G. Venter, and T. W. Von Backström. "An Efficient Scheme for Describing Airfoils Using Non-Uniform Rational B-Splines." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-69468.

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In the well developed field of airfoil design there are a number of established schemes for describing airfoils, each with its own limitations and suitability to a particular application. Although less parsimonious, B-splines are often used to find solutions unconstrained by the characteristics of these schemes. They have proven useful to improve on existing designs and are useful in a numerical optimization process. As part of a numerical design project of a small wind turbine, a parametric scheme using Non-Uniform Rational B-Splines (NURBS) offering intuitive control over airfoil shape and unambiguous definitions for chord length and angle of attack is needed. These features are achieved at the lowest number of variables possible to ensure numerical optimization efficiency. Two previously uninvestigated NURBS arrangements are defined and investigated. The quality of the resulting airfoil reproductions are geometrically and aero-dynamically investigated and based on the results, the use of a thickness-camber scheme is motivated.
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Pushkin, Sergey V., Guennady I. Podoprigora, Laurent Comas, Hatem Boulahdour, Jean-Claude Cardot, Michel Baud, Yaroslav R. Nartsissov, and Oleg Blagosklonov. "A Computational Model of Rat Cerebral Blood Flow using Non-Uniform Rational B-splines." In 2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, 2007. http://dx.doi.org/10.1109/iembs.2007.4352487.

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Singh, Aditya Kumar, Anuj Aggarwal, Manik Vashisht, and Rajesh Siddavatam. "Robot motion planning in a dynamic environment using offset Non-Uniform Rational B-Splines (NURBS)." In 2011 IEEE International Conference on Industrial Technology (ICIT 2011). IEEE, 2011. http://dx.doi.org/10.1109/icit.2011.5754393.

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Mashrouteh, Shamim, Ahmad Barari, and Ebrahim Esmailzadeh. "Flow-Induced Nonlinear Vibration of Non-Uniform Nanotubes." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-68208.

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This paper focuses on nonlinear forced vibration analysis of a free-form conveying fluid nanotube. Non-Uniform Rational B-Splines (NURBS) is used to model the free-form curvature of the nanotube, analytically. In order to develop the ordinary differential equations of motion, the Euler-Bernoulli beam theory and Galerkin method are implemented and the frequency response and the primary resonance of the nanotube under a harmonic excitation are studied. The effects of the free-form curvature of the nanotube and its physical characteristic on the nonlinear vibration behavior of the system are discussed as a parametric study.
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Reports on the topic "Non Uniform Rational B-Splines"

1

Yapp, Clifford W. An Investigation into Conversion from Non-Uniform Rational B-Spline Boundary Representation Geometry to Constructive Solid Geometry. Fort Belvoir, VA: Defense Technical Information Center, December 2015. http://dx.doi.org/10.21236/ada624518.

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