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1
Elsaesser, Bernhard. "Approximation mit rationalen B-Spline Kurven und Flaechen. Approximation with rational B-spline curves and surfaces." Phd thesis, Shaker, 1998. https://tuprints.ulb.tu-darmstadt.de/1126/1/elsaesser.pdf.
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Dag, Idris. "Studies of B-spline finite elements." Thesis, Bangor University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358041.
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Rojas, Roberto. "Geometric trimming of B-spline surfaces." Thesis, Virginia Tech, 1994. http://hdl.handle.net/10919/40634.
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Pereira, Larissa Rocha. "Ajuste de curva B-spline fechada com peso." Universidade Federal de Uberlândia, 2014. https://repositorio.ufu.br/handle/123456789/14947.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The aim of this work is to develop a method of curve fitting using closed B-spline closed for
application on reconstruction of cross-sections of objects. For this study specifically where
the sections are closed curves, it has been implemented a method to close the curve B-spline
curve, in such way that the curve is smooth on the closing point. The developed method is
based on least squares approximation with weights, which defines that the curve should be as
close as possible to the real curve. The weights in this case are responsible for the tightness
of the approximation to each data points, whose points represent the coordinate of the object
section that will be rebuild. Moreover, adjustments and impositions on the curve have been
proposed so that it has a better result and represent more accurately the desired cross section.
Particular characteristics of the curve were used to help enforce and define the settings. For
the analysis, B-spline curves using the developed method, were obtained showing good
results.<br>O objetivo desse trabalho é desenvolver um método de ajuste de curvas B-spline fechada para
a aplicação na reconstrução de seções transversais de um objeto. Por especificamente nesse
trabalho as seções serem seções fechadas, foi implementado um método para o fechamento da
curva B-spline, de modo que a mesma possuía suavidade no seu fechamento. O método
desenvolvido e utilizado foi baseado na aproximação por mínimos quadrados com pesos, que
define que a curva obtida deva ser mais próxima possível da curva real. Os pesos nesse caso
são responsáveis pela aproximação ou afastamento da curva em relação aos pontos dados,
pontos esses que melhor representam as coordenadas da seção do objeto que se deseja
reconstruir. Além disso, foram desenvolvidos ajustes e imposições na curva para que ela
tivesse um melhor resultado e representasse de forma mais fiel a seção transversal desejada.
Para a imposição e definição dos ajustes foram utilizadas características particulares da curva.
Para a análise, curvas B-spline utilizando o método desenvolvido, foram traçadas e foram
constatados os resultados desejados.<br>Mestre em Engenharia Mecânica
5
Elsässer, Bernhard [Verfasser]. "Approximation mit rationalen B-Spline Kurven und Flaechen. Approximation with rational B-spline curves and surfaces / Bernhard Elsaesser." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2008. http://d-nb.info/1104177943/34.
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Aggarwal, Aditya Mohan. "B-Spline Boundary Element Method for Ships." ScholarWorks@UNO, 2008. http://scholarworks.uno.edu/td/853.
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The development of a three dimensional B-Spline based method, which is suitable for the steady-state potential flow analysis of free surface piercing bodies in hydrodynamics, is presented. The method requires the B-Spline or Non Uniform Rational B-Spline (NURBS) representation of the body as an input. In order to solve for the unknown potential, the source surface, both for the body as well as the free surface, is represented by NURBS surfaces. The method does not require the body surface to be discritized into flat panels. Therefore, instead of a mere panel approximation, the exact body geometry is utilized for the computation. The technique does not use a free surface Green's function, which already satisfies the linear free surface boundary conditions, but uses a separate source patch for the free surface. By eliminating the use of a free surface Green's function, the method can be extended to considering non-linear free surface conditions, thus providing the possibility for wave resistance calculations. The method is first applied to the double body flow problem around a sphere and a Wigley hull. Some comparisons are made with exact solutions to validate the accuracy of the method. Results of linear free surface conditions are then presented.
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Mößner, Bernhard. "B-splines als Finite Elemente /." Aachen : Shaker, 2006. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015210875&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
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Lampis, Alberto. "Sul Calcolo di B-Spline Tchebycheffiane Multi-Order." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23217/.
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Viene descritto un nuovo algoritmo numericamente stabile per il calcolo di B-spline Tchebycheffiane multi-order, basato sull'espressione delle matrici relative alla procedura di knot insertion in termini dei coefficienti di Greville generalizzati dello spazio in analisi.
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Armstrong, Curtis A. "Vectorization of Raster Images Using B-Spline Surfaces." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1513.pdf.
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Aggarwal, Bhavya. "B-spline finite elements for plane elasticity problems." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4849.
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The finite element method since its development in the 1950âÂÂs has been used
extensively in solving complex problems involving partial differential equations. The
conventional finite element methods use piecewise Lagrange interpolation functions for
approximating displacements. The aim of this research is to explore finite element
analysis using B-spline interpolation. B-splines are piecewise defined polynomial curves
which provide higher continuity of derivatives than piecewise Lagrange interpolation
functions. This work focuses on the implementation and comparison of the B-spline
finite elements in contrast with the conventional finite elements. This thesis observes
that the use of B-spline interpolation functions can reduce the computational cost
significantly. It is an efficient technique and can be conveniently implemented into the
existing finite element programs.
11
Ingram, Christopher. "A Geometric B-Spline Over the Triangular Domain." Thesis, University of Waterloo, 2003. http://hdl.handle.net/10012/1039.
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For modelling curves, B-splines [3] are among the most versatile control schemes. However, scaling this technique to surface patches has proven to be a non-trivial endeavor. While a suitable scheme exists for rectangular patches in the form of tensor product B-splines, techniques involving the triangular domain are much less spectacular.
The current cutting edge in triangular B-splines [2] is the DMS-spline. While the resulting surfaces possess high degrees of continuity, the control scheme is awkward and the evaluation is computationally expensive. A more fundamental problem is the construction bears little resemblance to the construction used for the B-Spline. This deficiency leads to the central idea of the thesis; what happens if the simple blending functions found at the heart of the B-Spline construction are used over higher dimension domains?
In this thesis I develop a geometric generalization of B-Spline curves over the triangular domain. This construction mimics the control point blending that occurs with uniform B-Splines. The construction preserves the simple control scheme and evaluation of B-Splines, without the immense computational requirements of DMS-splines. The result is a new patch control scheme, the G-Patch, possessing <i>C</i>0 continuity between adjacent patches.
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Wong, Chee Kiang. "Intersection of B-spline surfaces by elimination method." Thesis, This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-03032009-040559/.
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Haq, Shaiq A. "Filament winding machine control using B-spline interpolation." Thesis, University of Nottingham, 1994. http://eprints.nottingham.ac.uk/14216/.
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Filament winding is a process for the placement of reinforcement fibres on to a rotating surface in a specified geometric pattern. A conventional straight line interpolation controller is not very appropriate for filament winding because the fibre pay-out-eye is at some distance away from the mandrel surface and its movement from one point to another may disturb the position of previously laid fibre on the mandrel. Filament winding demands a controller which can produce fast and smooth carriage movements, and have a path-anticipation capability so that while moving around curves the effect of pay-out-eye movement on previous fibre positions is minimised. This problem can be overcome by using an interpolation technique which determines the pay-out-eye path by considering more than two data points, and whose profile is continuous in nature up to its second derivative. In this project an IDM PC based filament winding controller, using B-spline interpolation technique, is developed. To test the performance of the controller a 3-axis CNC filament winding machine was designed and manufactured. For optimum performance, emphasis was given to the low inertia of the machine carriage, while at the same time maintaining the system's structural stiffness. To reduce the machine carriage weight, the DC servomotors were installed on the machine's frame, instead of the carriage, and a timing belt arrangement was used for power transmission. The controller's electronic hardware was assembled using servo amplifiers, DAC cards, and a purpose built optical encoder interface card. The controller software was developed using TURBO C++ as the main programming language, whereas the hardware interface routines were written in Assembly Language. Problems of winding path deviation as a result of B-spline approximation were tackled using knowledge based programming techniques. The results showed a considerable improvement in winding speed and less fibre slippage in the case of non-geodesic winding patterns, resulting in higher accuracy of fibre placement on the mandrel.
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Jain, Aashish. "Error Visualization in Comparison of B-Spline Surfaces." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/35319.
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Geometric trimming of surfaces results in a new mathematical description of the matching surface. This matching surface is required to closely resemble the remaining portion of the original surface. Typically, the approximation error in such cases is measured with a view to minimize it. The data associated with the error between two matching surfaces is large and needs to be filtered into meaningful information.This research looks at suitable norms for achieving this data reduction or abstraction with a view to provide quantitative feedback about the approximation error. Also, the differences between geometric shapes are easily discerned by the human eye but are difficult to characterize or describe. Error visualization tools have been developed to provide effective visual inputs that the designer can interpret into meaningful information.<br>Master of Science
15
Loop, Charles Teorell. "Generalized B-spline surfaces of arbitrary topological type /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/6888.
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Xu, Bo. "Multiresolution editing for B-spline curves and surfaces." [Ames, Iowa : Iowa State University], 2008.
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Kaya, Hikmet Emre. "A comparative study between the cubic spline and b-spline interpolation methods in free energy calculations." Master's thesis, Faculty of Science, 2020. http://hdl.handle.net/11427/32228.
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Numerical methods are essential in computational science, as analytic calculations for large datasets are impractical. Using numerical methods, one can approximate the problem to solve it with basic arithmetic operations. Interpolation is a commonly-used method, inter alia, constructing the value of new data points within an interval of known data points. Furthermore, polynomial interpolation with a sufficiently high degree can make the data set differentiable. One consequence of using high-degree polynomials is the oscillatory behaviour towards the endpoints, also known as Runge's Phenomenon. Spline interpolation overcomes this obstacle by connecting the data points in a piecewise fashion. However, its complex formulation requires nested iterations in higher dimensions, which is time-consuming. In addition, the calculations have to be repeated for computing each partial derivative at the data point, leading to further slowdown. The B-spline interpolation is an alternative representation of the cubic spline method, where a spline interpolation at a point could be expressed as the linear combination of piecewise basis functions. It was proposed that implementing this new formulation can accelerate many scientific computing operations involving interpolation. Nevertheless, there is a lack of detailed comparison to back up this hypothesis, especially when it comes to computing the partial derivatives. Among many scientific research fields, free energy calculations particularly stand out for their use of interpolation methods. Numerical interpolation was implemented in free energy methods for many purposes, from calculating intermediate energy states to deriving forces from free energy surfaces. The results of these calculations can provide insight into reaction mechanisms and their thermodynamic properties. The free energy methods include biased flat histogram methods, which are especially promising due to their ability to accurately construct free energy profiles at the rarely-visited regions of reaction spaces. Free Energies from Adaptive Reaction Coordinates (FEARCF) that was developed by Professor Kevin J. Naidoo has many advantages over the other flat histogram methods. iii Because of its treatment of the atoms in reactions, FEARCF makes it easier to apply interpolation methods. It implements cubic spline interpolation to derive biasing forces from the free energy surface, driving the reaction towards regions with higher energy. A major drawback of the method is the slowdown experienced in higher dimensions due to the complicated nature of the cubic spline routine. If the routine is replaced by a more straightforward B-spline interpolation, sampling and generating free energy surfaces can be accelerated. The dissertation aims to perform a comparative study between the cubic spline interpolation and B-spline interpolation methods. At first, data sets of analytic functions were used instead of numerical data to compare the accuracy and compute the percentage errors of both methods by taking the functions themselves as reference. These functions were used to evaluate the performances of the two methods at the endpoints, inflections points and regions with a steep gradient. Both interpolation methods generated identically approximated values with a percentage error below the threshold of 1%, although they both performed poorly at the endpoints and the points of inflection. Increasing the number of interpolation knots reduced the errors, however, it caused overfitting in the other regions. Although significant speed-up was not observed in the univariate interpolation, cubic spline suffered from a drastic slowdown in higher dimensions with up to 103 in 3D and 105 in 4D interpolations. The same results applied to the classical molecular dynamics simulations with FEARCF with a speed-up of up to 103 when B-spline interpolation was implemented. To conclude, the B-spline interpolation method can enhance the efficiency of the free energy calculations where cubic spline interpolation has been the currently-used method.
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Jones, Robert W. "Intersection and filleting of non-uniform B-spline surfaces." Thesis, Virginia Tech, 1991. http://hdl.handle.net/10919/42189.
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<p>Preliminary aircraft design codes requIre a more complete and integrated geometry
definition than that used by conceptual design codes. This thesis documents the design
and creation of an interactive CAD system which converts the geometry descriptions
commonly used in conceptual aircraft design codes to descriptions that meet the
requirements of preliminary design systems. In particular, the conversion of ACSYNT
Hermite surface data of aircraft models to the non-uniform hi-cubic B-Spline surface
representation is addressed. The topics discussed in this thesis include the design and
development of an interactive graphics user interface, the design and coding of an
intersection method for non-uniform hi-cubic B-Spline surfaces utilizing subdivision
techniques and the development of a one-dimensional filleting algorithm for blending
surfaces along iso-parametric curves.<br>Master of Science
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Jayaram, Uma. "Extracting dimensional geometric parameters from B-spline surface models." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/37877.
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In an integrated design environment, the common thread between the different design stages is usually the geometric model of the part. However, the requirements for the geometric definition of the design is usually different for each stage. The transformation of data between these different stages is essential for the success of the integrated design environment. For example, conceptual design systems usually deal with geometric dimensional parameters (e.g. length, radius, etc.) whereas preliminary design systems frequently require the geometry definition to be in the form of surface models.
This dissertation presents the necessity and scope of creating and implementing methodologies to obtain dimensional geometric parameters from the surface description of an object. Since the study of geometric modeling and parametric surfaces is a new field, few classical methods are applicable. Methods and algorithms for the extraction of various geometry parameters are created. A few methods to pre-process and manipulate these surfaces before the parameter extraction methods can be applied are outlined.
One of the most important applications of parameter extraction is in the field of aircraft design. There are two important aspects of geometry data conversion in the design cycle. The first is the conversion from conceptual CAD models to CFD compatible models. The second is the conversion from surface representations of CFD models to obtain component parameters (e.g. wing span, fuselage fineness ratio, moments of inertia, etc.). The methods created in this dissertation are used to extract geometric parameters of importance in aircraft design. This enables the design cycle to be complete and promotes integrated design.
These methods have been implemented in the aircraft design software, ACSYNT. Examples of the conversion of data from B-spline surface models to dimensional geometric parameters using these methods are included.
The emphasis of this dissertation is on non-uniform B-spline surfaces. Methods for obtaining geometric parameters from aircraft models described by characteristic points are also considered briefly.<br>Ph. D.
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Nafziger, John S. "Reverse parameterization of B-spline surfaces for data transfer." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-06302009-040414/.
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Argenti, Luca. "The B-spline K-matrix Method in Atomic Physics." Doctoral thesis, Scuola Normale Superiore, 2009. http://hdl.handle.net/11384/85858.
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In the course of this thesis the B-spline K-matrix method, a theoretical technique
capable of reproducing the single ionization continuum of atoms, was developed.
Two systems were addressed in particular: helium and boron, as representatives
of two- and three-active-electron atoms.
Some of the findings presented here resulted in original cont
ributions to the scientific literature. Total and partial photoionization cros
s sections and asymmetry parameters of the fundamental helium state were examined up
to the sixth ionization threshold, yielding the first
ab initio reproduction of the first intruder state
effects below N=4 threshold, the first reproduction of dipole
asymmetry parameters below N=6 threshold and of nondipole anisotropy param
eter γ below N=2 threshold.
Most of the material presented here relies on the multiple ba
sis implementation of the B-spline K-matrix method which allows the reprod
uction of almost arbitrarily excited metastable satellites below a prescri
bed threshold. The new technique, when used to investigate helium triplet states,
yielded the most accurate and extensive existing characterization of triplet me
tastable states up to the fifth ionization threshold. Within more than 1700 natural and unnatural S, P and D doubly excited states, eleven intruder states were discov
ered, entirely unknown before.
At least two experimental groups, at ELETTRA in Trieste and at BESSY II in Berlin, are recently tackling the problem of measuring the m
etastable 2^3S helium photoionization cross section. We therefore undertook a parallel theoretical investigation of the photoionization process of both the fundame
ntal and the excited ^3S helium states. The latter prelude to the future investigati
on of the radiative decay of doubly excited states and already revealed interesting p
eculiar features.
To this purpose, we devised an extension of the K-matrix method to treat the
atom-radiation interaction non perturbatively.
A general three electron package has been developed and appl
ied to study boron resonances. Specific formulas were derived to obtain arbitrary tensorial one-particle and scalar two-particle matrix elements between three electron states on non-orthogonal basis as required for an efficient exploitation of B-splines.
A detailed study of the B-spline effective completeness led to a general result
which assure that B-spline based methods are well conditioned for a large class of
knot grids.
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Silva, Luiz Marcelo Chiesse da. "Geração de b-splines via FPGA." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/18/18152/tde-10102012-084652/.
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As b-splines são utilizadas em sistemas CAD/CAM/CAE para representar e definir curvas e superfícies complexas, sendo adotada pelos principais padrões da computação gráfica devido a características como representação matemática de forma compacta, flexibilidade e transformações afins. Em sistemas de aquisição de dados 3D e sistemas CAM-CNC integrados, a utilização da b-spline na transferência de informações geométricas e na reconstrução da superfície de objetos resulta em um significativo incremento na eficiência do processo, geralmente implementado em sistemas embarcados. Nestes sistemas embarcados, integrados no auxílio a máquinas de manufatura, a utilização de FPGAs é incipiente, sem circuitos para b-splines disponibilizados em lógica reconfigurável de circuito aberto (open core), razão pela qual este projeto propõe o desenvolvimento de um circuito de geração b-spline aberto, em um sistema embarcado FPGA, utilizando algoritmos adaptados para os circuitos, elaborados em linguagem Verilog HDL, padronizada para a síntese de circuitos em lógica reconfigurável. Os circuitos foram desenvolvidos, utilizando-se um barramento de dados padronizado em circuito aberto, nas seguintes implementações para processamento paralelo das b-splines: o BFEA, o método baseado em funções base fixas, ambos projetados para circuitos integrados, e o fast Cox-de Boor, desenvolvido para FPGAs. Foram comparados o tempo de execução e o consumo de recursos disponíveis no FPGA utilizado, entre cada implementação. Os resultados evidenciaram que os circuitos de funções base fixas apresentaram o processamento mais rápido para a geração de b-splines em um FPGA, com um tempo de execução em média 20% menor em relação às outras implementações. Os circuitos BFEA apresentaram a menor utilização de elementos lógicos, em média 50% menor em relação aos outros circuitos implementados. O circuito fast Cox-de Boor apresentou a melhor escalabilidade, devido à modularidade da implementação, com tempos de execução similares aos circuitos de funções base fixas.<br>The b-splines are used in CAD/CAM/CAE systems to represent and define complex curves and surfaces, being adopted by the main computer graphics standards due to features like compact mathematic representation, flexibility and affine transformations. In 3D acquisition systems and integrated CAM-CNC systems, the use of the b-spline in the geometric information data transfer and in the object surface reconstruction results in a increase in the process efficiency, generally implemented in embedded systems. In these embedded systems, integrated in the aid to manufacturing machines, the use of FPGAs is incipient, without available b-splines open core circuits in reconfigurable logic, the reason why this project propose the development of a b-spline generation open core circuit, in a FPGA embedded system, using adaptated algorithms for the circuits, made in Verilog HDL language, standardized for the circuit synthesis in reconfigurable logic. The circuits were developed, using an open core standardized data bus, in the following implementations of b-spline parallel processing: the BFEA, fixed basis functions based method, both designed for integrated circuits, and the fast Cox-de Boor, developed for FPGAs. The execution time and available resource consumption in the FPGA were compared, between each implementation. The results show that the fixed basis functions circuits presented the fastest processing for the b-splines generation in a FPGA, with a 20% mean execution time reduction in relation to the other implementations. The BFEA circuits presented the lowest logic elements use, in mean 50% fewer in relation to the other implemented circuits. The fast Cox-De Boor circuit presented the best scalability, due to the implementation modularity, with execution times similar to the fixed basis functions circuits.
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Grove, Olya. "Heterogeneous Modeling of Medical Image Data Using B-Spline Functions." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3130.
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Ongoing developments in the field of medical imaging modalities have pushed the frontiers of modern medicine and biomedical engineering, prompting the need for new applications to improve diagnosis, treatment and prevention of diseases.
Biomedical data visualization and modeling rely predominately on manual processing and utilization of voxel and facet based homogeneous models. Biological structures are naturally heterogeneous and in order to accurately design and biomimic biological structures, properties such as chemical composition, size and shape of biological constituents need to be incorporated in the computational biological models.
Our proposed approach involves generating a density point cloud based on the intensity variations in a medical image slice, to capture tissue density variations through point cloud densities. The density point cloud is ordered and approximated with a set of cross-sectional least-squares B-Spline curves, based on which a skinned B-Spline surface is generated. The aim of this method is to capture and accurately represent density variations within the medical image data with a lofted surface function.
The fitted B-Spline surface is sampled at uniformly distributed parameters, and our preliminary results indicate that the bio-CAD model preserves the density variations of the original image based point cloud. The resultant surface can thus be visualized by mapping the density in the parametric domain into color in pixel domain. The B-Spline function produced from each image slice can be used for medical visualization and heterogeneous tissue modeling. The process can be repeated for each slice in the medical dataset to produce heterogeneous B-Spline volumes.
The emphasis of this research is placed on accuracy and shape fidelity needed for medical operations.
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Gloudemans, James R. "Filleting of aircraft components using non-uniform B-spline surfaces." Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/44637.
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<p>Conceptual and preliminary aircraft design codes have different geometry requirements.
Conceptual design codes use component based models, while preliminary design codes
require a more complete and integrated geometry. An automatic procedure to convert
between the two types of models would prevent geometry inconsistencies and speed up
the design process. This thesis describes some of the concepts and algorithms necessary
to develop such a procedure. Specifically, the theory and development of C2 continuous
fillets between aircraft components is discussed. B-spline surface generation from
conceptual geometry data and the relimiting of e surfaces is also presented.
</p.<br>Master of Science
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Tjung, Jie Wen. "Projection, design, and representation of curves on B-spline surfaces." Thesis, Virginia Tech, 1992. http://hdl.handle.net/10919/41412.
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Zhang, Xinyu. "Optimal Geometric Trimming of B-spline Surfaces for Aircraft Design." Diss., Virginia Tech, 2005. http://hdl.handle.net/10919/28270.
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B-spline surfaces have been widely used in aircraft design to represent different types of components in a uniform format. Unlike the visual trimming of B-spline surfaces, which hides unwanted portions in rendering, the geometric trimming approach provides a mathematically clean representation. This dissertation focuses on the geometric trimming of fuselage and wing components represented by B-spline surfaces.
To trim two intersecting surfaces requires finding their intersections effectively. Most of the existing algorithms focus on providing intersections suitable for rendering. In this dissertation, an intersection algorithm suitable for geometric trimming of B-spline surfaces is presented. The number of intersection points depends on the number of isoparametric curves selected, and thus is controllable and independent of the error bound of intersection points.
Trimming curves are classified and a new scheme for trimming by a closed trimming curve is provided to improve the accuracy. The surface trimmed by a closed trimming curve is subdivided into four patches and the trimming curve is converted into two open trimming curves. Two surface patches are created by knot insertion, which match the original surface exactly. The other two surface patches are trimmed by the converted open trimming curves. Factors affecting the trimming process are discussed and metrics are provided to measure trimming errors.
Exact trimming is precluded due to the high degree of intersections. The process may lead to significant deviation from the corresponding portion on the original surface. Optimizations are employed to minimize approximation errors and obtain higher accuracy. The hybrid Parallel Tempering and Simulated Annealing optimization method, which is an effective algorithm to overcome the slow convergence waiting dilemma and initial value sensitivity, is applied for the minimization of B-spline surface representation errors. The results confirm that trimming errors are successfully reduced.<br>Ph. D.
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Bindiganavle, Karthik. "An optimal approach to geometric trimming of B-spline surfaces." Thesis, Virginia Tech, 2000. http://hdl.handle.net/10919/31767.
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Geometric trimming of a surface involves removal of unwanted portions of the surface and providing a new mathematical description for the trimmed patch. This entails creating a new geometry for the trimmed patch, which closely approximates the corresponding portion on the original patch. The procedure is shown to involve obtaining data points on the B-spline surface that lie within the region specified by the parameter values for the trimming curve and describing a new surface which interpolates this new set of data points. This research looks at optimizing the procedure described above by basing the choice of parameter values for the trimming curve, at points where curvature optima occur over the surface. A visualization tool kit has been developed using OpenGL, as a means to discern the difference between the two surfaces. In order to quantify and aid in minimizing the error (difference) in approximating the original surface with the trimmed patch, an error measurement tool developed in MATLAB has been employed.<br>Master of Science
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Wang, Hongrui. "Error and stability analysis for B-spline finite element methods." Thesis, University of Strathclyde, 2015. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=26570.
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The thesis studies the approximation properties of splines with maximum smoothness. We are interested in the behaviour of the approximation as the degree of the spline increases (so does its smoothness). By studying B-spline interpolation, we obtain error estimates measured in the semi-norm that are explicit in terms of mesh size, degree and smoothness. This new result also gives a higher approximation order than existing estimations. With the results, we investigate the B-spline finite element approximation with k-refinement, which is a strategy of improving the accuracy by increasing the degree and smoothness. The problem is studied in the setting of heat equations and wave equations. We give B-spline FEM schemes for the problems, and obtain error estimates. Moreover, by proving a Markov-type inequality for splines, where an exact constant is derived, we deduce how the stability of the scheme behaves with the k-refinements. We also improve the efficiency of the schemes for problems with periodic boundary conditions by applying the fast Fourier transform. The thesis also focuses on developing algorithms for efficiently evaluating the element system matrices in finite element methods with Berstein-Bâezier splines as shape functions, where the splines are of arbitrary order and defined on quadrilaterals and hexahedrons. The algorithms achieve the optimal complexity by making use of the sum factorial procedure. We test the algorithms in C++ implementation, and the numerical results illustrate that the optimal cost and expected accuracy are achieved.
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Tjung, Jie Wen. "Projection, design, and representation of curves on B-spline surfaces /." This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-03042009-040805/.
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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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Nandihalli, Sunil S. "A B-spline geometric modeling methodology for free surface simulation." Master's thesis, Mississippi State : Mississippi State University, 2004. http://library.msstate.edu/etd/show.asp?etd=etd-04072004-185017.
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Almeida, Adriano Del Vigna de. "B-Spline : CAEP - algoritmos culturais para a geração de trajetórias B-Spline de robôs móveis / Adriano Del Vigna de Almeida ; orientador, Leandro dos Santos Coelho." reponame:Biblioteca Digital de Teses e Dissertações da PUC_PR, 2005. http://www.biblioteca.pucpr.br/tede/tde_busca/arquivo.php?codArquivo=461.
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Dissertação (mestrado) - Pontifícia Universidade Católica do Paraná, Curitiba, 2005<br>Inclui bibliografia<br>Pode se dizer que a geração de trajetórias é o mote principal da robótica móvel. Um robô, incapaz de percorrer uma trajetória livre de obstáculo, de forma a atingir um objetivo pré-definido, poderia inclusive deixar de ser chamado de robô móvel. A geração
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Lorenczyk, Jiří. "Matematický popis trajektorie pohybu vozidla." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-445453.
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The goal of this thesis is to nd types of curves which would allow for the construction of a path that could be traversed by a vehicle. It seems that a minimal constraint for such a path is the continuity of curve's curvature. This leads to a closer look at the three types of curves: Clothoids, which are able to smoothly connect straights with arcs of a constant curvature, interpolation quintic splines, which are C2 smooth in the interpolation nodes and -splines, these belong to the family of quintic polynomial curves too, however, they are characterised by the vector of parameters which modies the shape of the curve. The thesis is accompanied by an application allowing for manual construction of the path composed of spline curves.
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Corbin, Max. "Surface fitting head scan data sets." Ohio : Ohio University, 1999. http://www.ohiolink.edu/etd/view.cgi?ohiou1175886726.
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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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Junger, Jean-Claude. "Modélisation et réalisation d'une prothèse de genou." Vandoeuvre-les-Nancy, INPL, 1993. http://www.theses.fr/1993INPL052N.
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La complexité du mouvement des os de l'articulation du genou requiert une étude anatomique pour construire une prothèse de genou. Une bonne prothèse repose sur des surfaces permettant tous les mouvements du genou. Le nouveau type de prothèse présenté ici, est le résultat de cette approche scientifique. Dans un premier temps, nous mesurons les surfaces des condyles et de la trochlée d'une population significative d'os humains en utilisant une machine triaxiale. Puis, nous déterminons une surface moyenne servant de base à la réalisation de notre prothèse. Ensuite, en utilisant les techniques des fonctions b-splines, nous étudions les paramètres permettant de reconstruire la surface des condyles tout en respectant la cinématique ligamentaire et la transmission des contraintes. Notre prothèse respecte la position de la rotule sur les condyles et la trochlée et présente une forme proche de la forme anatomique. En relation avec cette étude, nous avons développé de nouveaux types de tiges intramédullaires ainsi que la technique de pose associée
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QUADRI, NICOLA. "THEORETICAL STUDY OF PERTURBATIVE AND NON-PERTURBATIVE PHOTOIONIZATION." Doctoral thesis, Università degli Studi di Trieste, 2018. http://hdl.handle.net/11368/2918470.
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Photoionization processes have been examined from a theoretical perspective with the aim of increasing the number of the describable phenomena involved in such processes. This aim has been achieved by the implementation of several algorithms based on the use of B-splines as basis functions to treat both correlation effects and non-perturbative photoionization regime.
The first part of the thesis is dedicated to correlation effects within the bound states. Since a standard DFT method does not permit to study any correlation effect, we present a single channel approach that uses Configuration Interaction (CI) to describe both the neutral initial state and ionic final state. More specifically, this method applies a Complete Active Space Self-Consistent Field (CASSCF) procedure to treat such correlation effects. Ionization potentials are further improved by n-electron valence state perturbation theory (NEVPT2). Dyson orbitals are used in this context to calculate the dipole transition moments. The most frequent evidence of electron correlation is the presence of additional bands, called satellite bands, in the photoelectron spectra. The structure and the position of satellite bands in some diatomic molecules has been studied. For all the considered molecules, dynamical photoionization observables have been calculated for the first ionization states, by comparing the results so obtained to those ones got by standard DFT method, Dyson orbital approach and HF method. The formalism has been also applied to the O_3 molecule within a collaboration that aimed to obtain the time-resolved photoelectron spectrum of this molecule.
In the second part of the thesis, the implementation of an algorithm to calculate two-electron integrals in the LCAO B-spline basis with the aim to treat all the many-electron effects is illustrated. This has been done to fully express the final wavefunction within the so called Close-Coupling (CC) formalism that permits to also describe correlation effects involving continuum states. In particular, two-electron integrals have been calculated by solving the Poisson equation relative to the first charge density and integrating the resulting potential with the second charge density. The results are compared to the corresponding integrals obtained by using MOLPRO quantum chemistry package.
The third part of the thesis presents a method to treat the non-perturbative phenomena by solving Time-Dependent Schrödinger Equation (TDSE). In this method, time-evolution is discretized in subintervals sufficiently small so that the Hamiltonian approximately becomes time-independent. The final wavepacket, derived by time propagation, is then projected onto the continuum states calculated with the DFT method. Photoelectron spectra and MFPADs are obtained for several systems, such as hydrogen atom, H_2^+, NH_3 and H_2 O.
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Wang, Xijun. "Geometric Trimming and Curvature Continuous Surface Blending for Aircraft Fuselage and Wing Shapes." Thesis, Virginia Tech, 2001. http://hdl.handle.net/10919/31664.
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Most of the work accomplished on surface blending is based on visual trimming. In the process of visual trimming, the unwanted portion of a surface is only hidden but not removed. Geometric trimming provides a complete mathematical description of the wanted portion of the trimming surface, and generates a new mathematical surface or sets of surface patches. The new surface is intended to resemble closely the corresponding portion of the original surface. A robust procedure is developed to geometrically trim the intersecting surfaces and blend the trimmed surface patches into one new surface. This research generates a filleting algorithm for surface blending of an aircraft fuselage shape and a wing shape at a closed trimming intersection curve, and verifies the properties of the newly created surface. In order to distinguish how well the new surface approximates the original, an error comparison tool developed in MATLAB has been employed.<br>Master of Science
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Nguyen, Tan Khoi. "Surfaces polyédriques et surfaces paramétriques : une reconstruction par approximation via les surfaces de subdivision." Thesis, Aix-Marseille 2, 2010. http://www.theses.fr/2010AIX22055/document.
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La Conception Assistée par Ordinateur (C.A.O) qui permet de concevoir des objets physiques à partir de modèles mathématiques est utilisée dans de nombreux secteurs de l’industrie.On constate actuellement une volonté généralisée de tirer parti de deux approches jusqu’à présent plutôt antagonistes : la modélisation géométrique continue qui crée des objets continus représentant par la modélisation à partir de surfaces B-splines ou NURBS) et la modélisation géométrique discrète qui qu’il s’agisse de maillages ou de surfaces de subdivision.Cette dualité d’approche a de nombreuses applications industrielles potentielles et présente donc un intérêt scientifique important. Les surfaces polyédriques et en particulier les surfaces de subdivision offrent intrinsèquement la discrétisation, sont d’une manipulation très simple, mais elles ne remplacent pas les surfaces B-splines ou NURBS. Les travaux présentés dans la thèse et qui ont abouti au passage réciproque d’une surface paramétrique à une surface polyédrique. Nous nous intéressons plus particulière aux surfaces de subdivision considérant comme une liaison entre la surface polyédriquee et la surface paramétrique parce qu’après quelques étapes de subdivision, le polyèdre caractéristique converge à une surface paramétrique correspondant. Nous y proposons des schémas de la subdivision inverse permettent de récréer les surface polyédrique grossier de subdivision précédent. Nous avons donc développé deux méthodes pour la reconstruction d’une courbe/surface paramétrique en utilisant le schéma de subdivision inverse uniforme et le schéma de subdivision inverse non-uniforme. Pour améliorer les résultats de reconstruction par la subdivision inverse, nous associons à ces méthodes une possibilité d’ajustement d’approximation qui permet de diminuer grandement l’erreur de reconstruction. Les résultats obtenus ont été comparés à une méthode bien connu de reconstruction sens au sens des moindres carrés. Nos méthodes sont très prometteuses en termes d’approximation et de compression<br>Computer Aided Geometric Design (CAGD) which allows us to design the physical objects from mathematical models is used in many sectors of industry. It is currently a general wish to take advantage of the two these approaches rather than the antagonists : The goal that the continuous geometric model creates the continuous objects represented by the modelof the surfaces B-splines or NURBS) and the discreet geometric model made by eitherthe meshes or the subdivision surfaces. This duality of the approach has many potential industrial applications and therefore submits interesting significant science. The polyhedral surfaces and the subdivision surfaces in particular which offer the intrinsically discretization,are a very simple manipulation, but they do not replace the surfaces B-splines or NURBS.The works presented in this thesis aim to the reciprocal passage from a parametric surfaceto a polyhedral surface. We are more specialy interested to subdivisions surfaces considering as a liaison between the polyhedral surface and the parametric surface, because after a few steps of subdivision, the polyhedron characteristic converges to a parametric surface corresponding.We have proposed the schemas of the inverse subdivision allowing recreating the polyhedral surface coarse of subdivision precedent. We thus presented two methods for there construction of a parametric curve/surface : one for using the schema of uniform inverse subdivision and the other for non-uniform inverse subdivision. To improve the results of reconstruction by the inverse subdivision methods, we associate these methods with the process of adjustment the approximation which allows reducing the error of reconstruction.The results obtained have been compared with a well-known least squares method. Our methods are very promising in terms of approximation and compression
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Cervera, Eva. "Evolutionary structural optimisation based on boundary element representation of B-spline geometry." Thesis, Durham University, 2003. http://etheses.dur.ac.uk/2004/.
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Evolutionary Structural Optimisation (ESO) has become a well-established technique for determining the optimum shape and topology of a structure given a set of loads and constraints. The basic ESO concept that the optimum topology design evolves by slow removal and addition of material has matured over the last ten years. Nevertheless, the development of the method has almost exclusively considered finite elements (FE) as the approach for providing stress solutions. This thesis presents an ESO approach based on the boundary element method. Non-uniform rational B-splines (NURBS) are used to define the geometry of the component and, since the shape of these splines is governed by a set of control points, use can be made of the locations of these control points as design variables. The developed algorithm creates internal cavities to accomplish topology changes. Cavities are also described by NURBS and so they have similar behaviour to the outside boundary. Therefore, both outside and inside are optimised at the same time. The optimum topologies evolve allowing cavities to merge between each other and to their closest outer boundary. Two-dimensional structural optimisation is investigated in detail exploring multi-load case and multi-criteria optimisation. The algorithm is also extended to three-dimensional optimisation, in which promising preliminary results are obtained. It is shown that this approach overcomes some of the drawbacks inherent in traditional FE-based approaches, and naturally provides accurate stress solutions on smooth boundary representations at each iteration.
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Tsao, Yu-Ming, and 曹育銘. "Continuity Adjustment of B-spline Surfaces." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/28350937295413573584.
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碩士<br>國立臺灣大學<br>機械工程學研究所<br>98<br>With the pursuit of automatic and efficiently industrial development, computer aided design has been played an important role in the industry. In response to the requirements of the work of imitation, reverse engineering is generated. Measuring the shape of products and a series of calculation including segmentation, surface reconstruction and surface adjustment are the steps of the reverse engineering process. Finally, we can reconstruct and analyze the CAD model of products and plan the product’s manufacture procedure.
This research focus on continuity adjustment of surfaces in reverse engineering. In order to reach the smoothness of adjacent surfaces, the output of surface reconstruction has been adjusted and modified. This research implements the optimal continuity adjustment of surfaces by using the numerical methods and discussing the basic information of B-spline surfaces which are the main adjust target of the research. The final goal is to export surfaces, that fit G1 and G2 continuity.
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Hong-Weng, Wu, and 吳宏文. "Automated Construction of Three Dimensional Discontinuous B-Spline SurfacesAutomated Construction of Three Dimensional Discontinuous B-Spline Surfaces." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/49546679540175057473.
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碩士<br>國立高雄應用科技大學<br>模具工程系碩士班<br>96<br>This study is to construct the discontinuous B-Spline surfaces of three dimensions by using the reverse software we had developed. In some curves or surfaces of industrial products, we need to alter the B-Spline curves by handed manner in the reverse software in order to create the geometric feature line. That feature line with discontinuity (Positional continuity) is represented on some specific surfaces or regions, and the other unmodified surfaces remain the continuity (Slope continuity). However, it takes a lot of time to construct the feature line by hand. Therefore, we use the proposal algorithm to alter the B-Spline curves or surfaces.
In this research, the 3D metrology system is used to get the 3D cloud data from the reflector surfaces of the automotive headlamp in order to construct the B-Spline curves in the fitting process. The vertices of the curve were coincided the control points of the curve vertices position, which automatically searched by the developed reverse software programs and turned the knots into the open uniform. It makes the curve’s smooth areas produce the discontinuity with above statements to create IGES files. Finally, The discontinuity B-Spline curves of three dimensions has shown in the reverse software systems from the IGES files. In this method, it can construct the curves into the free-form surfaces as well as check its quality. The producers could manufacture the headlamp’s reflector surfaces by CAM /RP systems after analysing by CAE.
The results show that the feature lines of the reflector surfaces were established rapidly in the modified areas that we expected. The results of this study are also applied to the other alteration of the modeling surfaces to save the research and development (R&D) time for the engineers.
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Liu, Yan-Ze, and 劉彥澤. "Offset Compensation of Trimmed b-spline Surfaces." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/21438189630972219210.
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碩士<br>國立臺灣大學<br>機械工程學研究所<br>102<br>With the development of the computer science, computer aided software is applied in several areas. Especially, the computer aided design is applied on many industries. For example, the CNC machining is important in the manufacture of the product. In the progress of the NC tool path simulation, it should have the inseparable geometry association of offset curve and offset surface.
The research focuses on the improvement of the surface offset method, by combining the advantages of using the data point and the control point for the construction of the offset surface. After the mutually application, finding the start position of the critical point, and using the golden search for the optimum local maximum and minimum is the key achievement of the proposed thesis. From the topological structure of the boundary curve and the base surface, the proposed method can be extended to the offset of the trimmed surface.
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Kuo, Kun-Yu, and 郭坤裕. "Geometric Local Modification with B-Spline Surface." Thesis, 1999. http://ndltd.ncl.edu.tw/handle/63141598728905880389.
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碩士<br>國立交通大學<br>機械工程系<br>87<br>The aim of this thesis study is to apply the B-Spline surfaces to modify geometric modeling locally. The reason for using the B-Spline surfaces is for very strong and simply geometric attribute, consequently provide intuition sense for designer.
First, we build the base of geometric modeling with Hermite surface. After the conversion of parameter surface, the characteristic grid of B-Spline surface can be obtained. We must plan the modified range and then move the chosen control points in this range appropriately. After the move of control points, the replacing surfaces must satisfy the original set of continuity conditions on the patch boundaries, a versatile geometric modeling module can be accomplished with a reasonable amount of effort.
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蘇德修. "B-Spline齒形之研究". Thesis, 2004. http://ndltd.ncl.edu.tw/handle/11080705267296586897.
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碩士<br>國立高雄應用科技大學<br>模具工程系碩士班<br>92<br>The purpose of this research is to design the tooth profile by using B-Spline curve, and to investigate geometric properties and meshing characteristics of the conjugate tooth profiles. Firstly the tooth geometric tooth profiles of the rack cutter are defined by the specified control points, the order of spline function and knot vectors. Then using the meshing theory and coordinate matrix transformation, the mathematical models of the generated conjugate tooth profiles are derived. Finally the geometric properties and meshing characteristics are explored by the theories of differential geometry and kinematics. By the multi degrees of freedoms of the design parameters that are the control points, order of spline functions and knot vectors, is used to study the variation of tooth geometries and meshing characteristics such as pressure angle, specific sliding, contact ratio and relative curvature, etc. A computer program is developed for the design and analysis of B-Spline tooth profiles that can be used for the creation of 3D solid model. It is hoped that the 3D solid model can be applied for manufacture by CAM software and the analysis and motion simulation with CAE software.
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Archer, Katrina Marie. "Craniofacial reconstruction using hierarchical B-Spline interpolation." Thesis, 1997. http://hdl.handle.net/2429/6373.
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Craniofacial forensic reconstruction is often the only means of determining a deceased
individual's appearance. Current manual methods of estimating the appearance of the individual
from his or her skull are extremely expensive and time-consuming. Normally a single facial
estimate is produced and publicized. As a result, the success rate for identification resulting from
facial reconstruction is on the order of only 50%. A software tool that produces multiple three-dimensional
likenesses that more completely cover the range of likely appearances due to factors
such as body fat content, and nose and lip appearance would improve this success rate. The
application should closely simulate the artist's technique of generating a base facial shape with
rough details that are later refined. The prototype generates a generic hierarchical B-spline
surface around a 3D scan of the skull. Sparse data points representing tissue thickness are first
placed at landmarks about the scan. The generic surface is subsequently automatically placed in
order to smoothly and evenly interpolate the data points. This thesis presents a new interpolation
method that is well adapted to fitting a hierarchical surface to sparse data points. A reasonable
facial approximation is produced from a minimal amount of data using this technique. Multiple
facial base shapes are easily created by using the appropriate tissue depths for race, age, sex and
body fat content. Facial details such as the eyes, nose and lips can be edited after interpolation.
These basic techniques are appropriate for use in an eventual commercial 3D forensic
reconstruction tool.
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Chen, Chien-Yi, and 陳見宜. "Automated G2 Continuity Adjustment of B-spline Surface." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/53071578178371809425.
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碩士<br>國立臺灣大學<br>機械工程學研究所<br>96<br>Computer aided design and reverse engineering are used wildly in industrial and played an important role for surface modeling。Continuity is the pivot factor for pursuing the beauty of product and the convenience of manufacturing process whether the surface data are derived from surface modeling or reverse engineering.The purpose for this research is to promote the efficiency of surface-continuity adjustment by automatic process.
This research attempts to build an automatic process by getting the geometry and topology data from surface and tries to construct the reference of patches.After the automated contunuity adjustment, G2 condition of class-A quality of surface can be obtained more easily.
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陳秀娘. "New Vectorization for Solving B-spline Curve Fitting." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/36894965925908020381.
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碩士<br>國立臺灣科技大學<br>管理研究所資訊管理學程<br>81<br>Curve fitting is important in computer - aided design, graphics, pattern recognition, and picture processing. Using the matrix diagonalization method, this thesis gives a new and fast vectorized algorithm for solving the open B - spline curve fitting. The application of our result to solve the closed B - spline curve fitting is also investigated. Given a set of random points, we demon - strate the good performance of our algorithms on the CRAY X - MP EA / 16se supercomputer. Furthermore, we compare the performance of our algorithms (Fortran codes) with the ones using the subroutine 'folrc' (Assembly codes) in MATH LIBRARY ROUTINES and the ones using the subroutine 'sptsv' (Fortran codes) in LAPACK, respectively.
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Teoh, Hok Sin. "Computer integrated manufacture of optimal B-spline cams." 1989. http://hdl.handle.net/2097/22650.
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Yeh, Shih-Yu, and 葉時有. "Hand-Shape Recognition Based on B-Spline Curves." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/26787024552931776373.
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碩士<br>國立暨南國際大學<br>電機工程學系<br>96<br>With an increasing emphasis on security, personal authentication based on biometrics has been receiving extensive attention over the past decade. Among many different biometric technologies, this thesis examines hand-shape technique for personal identification and develops a good performance recognition system based on human hand features. It is implemented and tested on VIP-CCL Lab. Hand image database. The proposed system includes four modules: image acquisition, image pre-processing, feature extraction, and recognition modules. First, the system captures a hand image using digital camera, then uses some image processing algorithms to localize the hand-geometry from the hand image via image pre-processing module. In the feature extraction module, we use 4 B-Spline curves to fit with fingers (except thumb) from a single hand image for a single person. Then we store these control points and curvatures of the B-Spline curves as well as other geometry measurements (the width of fingers) of the hand as the features of that person into the database. Finally, the system applies these features for matching in recognition module.
Experimental results show that the system has an encouraging performance on the VIP-CC Lab. Database (including 600 images from 100 classes). The proposed system uses the control points 、the curvatures and the width of fingers to generate the features, we attain the recognition rates up to 95.55%(128bytes)、85.7%(32bytes)and 96.84%(96bytes) (according to equal error rate, EER), respectively. This thesis analyzes the experimented results and verifies the related inferences of the proposed system for providing useful information for further research.