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...

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); Pós-graduação em Ciências Cartográficas - FCT; A representação do relevo ou terreno é uma componente fundamental no processo cartográfico e dentre essas representações as que têm por objetivo analisar as diferentes curvaturas de uma vertente, ou seja, classificar as vertentes de um determinado terreno em retilíneas, côncavas ou convexas tem apresentado grande aplicabilidade em áreas como a agricultura, a construção civil, o estudo de microbacias entre outros. Assim, o desenvolvimento de algoritmos que classifiquem essas formas do relevo pode contribuir muito para a produção de informações relevantes à tomada de decisões em diversas áreas do conhecimento. Alguns algoritmos com esse intuito foram anteriormente desenvolvidos, porém apresentam claras necessidades de melhoria por classificarem apenas áreas pré-estabelecidas, não podendo ser utilizados para outras regiões. Visando sanar a necessidade de implementações mais completas este trabalho apresenta a metodologia utilizada na elaboração de um algoritmo para classificação de vertentes através de ferramentas matemáticas até então pouco utilizadas nas Ciências Cartográficas: a Thin Plate Spline (TPS) que será utilizada para adensar os dados de vertentes do município de Presidente Prudente...

Signal Processing, Vol. 83, nº 11; A new de(nition of a symmetric fractional B-spline is presented. This generalises the usual integer order B-spline, that becomes a special case of the new one.

In this study, vibration behavior of orthotropic cylindrical shells with variable thickness is investigated. Based on linear shell theory and applying energy method and using spline functions, free vibration relations are derived for shell with variable thickness and curvature. Frequency parameter and mode shapes are found after solving the frequency Eigenvalue equation. Effects of variable thickness along axial and circumferential directions of the shell on its frequency parameter are studied and compared against each other. Shell thickness is assumed to be varied in a parabolic profile along both directions. Also, frequency parameters for both circular and parabolic curvatures along circumferential direction are investigated and results are compared together. In addition, effect of variable thickness on the mode shapes is studied.

This paper presents an encoding scheme adapted for Fiber Bragg Grating (FBG) optimization using metaheuristics. The proposed encoding scheme uses spline approximations in order to build softened refractive index profiles from few encoded parameters. This approach is suitable for Fiber Bragg Grating (FBG) synthesis because it ensures both the reduction of the problem dimensionality and the respect of important restrictions associated to the FBG manufacture. Simulations are shown where an ES using the spline encoding was able to converge faster and produce more interesting filters, when compared with conventional encoding schemes.

In this work we have elaborated a spline-based method of solution of inicial value problems involving ordinary differential equations, with emphasis on linear equations. The method can be seen as an alternative for the traditional solvers such as Runge-Kutta, and avoids root calculations in the linear time invariant case. The method is then applied on a central problem of control theory, namely, the step response problem for linear EDOs with possibly varying coefficients, where root calculations do not apply. We have implemented an efficient algorithm which uses exclusively matrix-vector operations. The working interval (till the settling time) was determined through a calculation of the least stable mode using a modified power method. Several variants of the method have been compared by simulation. For general linear problems with fine grid, the proposed method compares favorably with the Euler method. In the time invariant case, where the alternative is root calculation, we have indications that the proposed method is competitive for equations of sifficiently high order.; Coordenação de Aperfeiçoamento de Pessoal de Nível Superior; Neste trabalho desenlvolvemos um método de resolução de problemas de valor inicial com equações diferenciais ordinárias baseado em splines...

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. ______________________________________________________________________________ ABSTRACT; 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...

ABSTRACT: This paper presents an encoding scheme adapted for Fiber Bragg Grating (FBG) optimization using metaheuristics. The proposed encoding scheme uses spline approximations in order to build softened refractive index profiles from few encoded parameters. This approach is suitable for Fiber Bragg Grating (FBG) synthesis because it ensures both the reduction of the problem dimensionality and the respect of important restrictions associated to the FBG manufacture. Simulations are shown where an ES using the spline encoding was able to converge faster and produce more interesting filters, when compared with conventional encoding schemes.

Las funciones spline constituyen en la actualidad una herramienta b??sica en la teor??a de aproximaci??n. Desde su introducci??n en la d??cada de los cuarenta del siglo pasado hasta la actualidad han ido ocupando parcelas cada vez m??s amplia, tanto cient??ficas como t??cnicas. Un problema b??sico en el que juegan un papel fundamental es la aproximaci??n de datos emp??ricos y de funciones de una y varias variables. La construcci??n de aproximantes spline puede llevarse a cabo de muy diversas formas, entre las que la m??s conocidas son la interpolaci??n y el ajuste por m??nimos cuadrados. Son t??cnicas computacionalmente costosas, pues dan lugar a sistemas de ecuaciones lineales. Esto es especialmente relevante cuando se aplica en varias variables. Los quasi-interpolantes spline surgen con el ??nimo de conseguir buenos aproximantes con un coste moderado. El procesamiento en tiempo real de gran cantidad de datos requiere que el aproximante spline sea construido conforme se dispone de la informaci??n, por lo que es necesario dise??ar m??todos de tipo local que, adem??s, tengan un alto orden de aproximaci??n. El estudio es una variable y con nodos uniformemente espaciados se remonta a los trabajos de I.J. Schoenberg, quien consider?? como quasi-interpolantes series B-spline en cuyos coeficientes intervienen valores de funci??n o derivadas. El siguiente paso fue emplear nodos no uniformemente espacios y los correspondientes B-splines. En lo que respecta al caso multivariado...

This paper modifies the Cornwell, Schmidt and Sickles [CSS (J Econom 46:185–200, 1990)] time-varying specification of technical efficiency to allow for switching patterns in temporal changes, which may occur more than once during the sample period. For this purpose, we move from the (second-order) polynomial specification of the standard CSS to a spline function setup, while keeping CSS’s flexibility regarding the cross-sectional dimension. The spline function specification of the temporal pattern of technical efficiency can accommodate more than one turning point and thus can be non-monotonic. This allows the modeler to account for firm or individual efficiency gains that can occur relatively quickly, for example, changes related to regulation or policy changes, as well as those related to ownership/organization changes (e.g., merger or acquisitions).

In the context of coordinate metrology and reverse engineering, freeform curve reconstruction from unorganized data points still offers ways for improvement. Geometric convection is the process of fitting a closed shape, generally represented in the form of a periodic B-Spline model, to data points [WPL06]. This process should be robust to freeform shapes and convergence should be assured even in the presence of noise. The convection's starting point is a periodic B-Spline polygon defined by a finite number of control points that are distributed around the data points. The minimization of the sum of the squared distances separating the B-Spline curve and the points is done and translates into an adaptation of the shape of the curve, meaning that the control points are either inserted, removed or delocalized automatically depending on the accuracy of the fit. Computing distances is a computationally expensive step in which finding the projection of each of the data points requires the determination of location parameters along the curve. Zheng et al [ZBLW12] propose a minimization process in which location parameters and control points are calculated simultaneously. We propose a method in which we do not need to estimate location parameters...

O Método Spline Modificado foi desenvolvido para o alisamento de dados experimentais com incertezas em todas as variáveis medidas. Este método é uma extensão do Método Spline Estendido e é baseado no acoplamento do Método Spline ao Método da Máxima Verossimilhança. O Método Spline Estendido acopla o Método Spline cúbico ao Método dos Mínimos Quadrados. Este método foi desenvolvido anteriormente por Klaus Van-Ness[7]. São apresentadas diversas aplicações a dados Termodinâmicos como dados de equilíbrio líquido-vapor ( diagrama XversusY ), temperatura de ebulição como função da concentração de um sistema binário ( diagrama TversusX ) e calor de mistura de certos sistemas com álcoois ( ?H / X1 . X2versusX1 ). Em todos os casos o Método Spline Modificado mostra melhores resultados do que o Método Spline Estendido. Programas computacionais foram desenvolvidos nas linguagens BASIC e PASCAL incluindo o Método Spline cúbico e o Método Spline Estendido como casos particulares do Método Spline Modificado; The Modified Spline fit Technique has been developed for the smoothing of experimental data with uncertanties in all measured variables. This method is a new fit technique and is an extension of the Extended Spline fit Technique and it is based on the coupling of the Maximun Likelihood Principle to the Spline fit Technique. The Extended Spline fit Technique couples the cubic Spline fit Technique to the Least Square Method. It was developed before by Klaus Van-Ness 17]. Several applications to thermodynamic data such as vapor-liquid equilibrium of a binary system ( X versusY diagram )...

En este documento se presenta la descripción y los resultados de la estimación de la estructura a plazos de las tasas de interés en Colombia utilizando el método de funciones B-spline cúbicas. Adicionalmente, se llevan a cabo comparaciones entre los resultados obtenidos a través de esta metodología y los presentados por Arango, Melo y Vásquez (2002) respecto a los métodos de Nelson y Siegel, y de la Bolsa de Valores de Colombia. Se observa que el desempeño del método de estimación de funciones Bspline cúbicas es similar al de Nelson y Siegel, y estos dos métodos superan al de la Bolsa de Valores de Colombia.  

Milk yield records (305d, 2X, actual milk yield) of 123,639 registered first lactation Holstein cows were used to compare linear regression (y = β0 + β1X + e) ,quadratic regression, (y = β0 + β1X + β2X2 + e) cubic regression (y = β0 + β1X + β2X2 + β3X3 + e) and fixed factor models, with cubic-spline interpolation models, for estimating the effects of inbreeding on milk yield. Ten animal models, all with herd-year-season of calving as fixed effect, were compared using the Akaike corrected-Information Criterion (AICc). The cubic-spline interpolation model with seven knots had the lowest AICc, whereas for all those labeled as "traditional", AICc was higher than the best model. Results from fitting inbreeding using a cubic-spline with seven knots were compared to results from fitting inbreeding as a linear covariate or as a fixed factor with seven levels. Estimates of inbreeding effects were not significantly different between the cubic-spline model and the fixed factor model, but were significantly different from the linear regression model. Milk yield decreased significantly at inbreeding levels greater than 9%. Variance component estimates were similar for the three models. Ranking of the top 100 sires with daughter records remained unaffected by the model used.

Este trabajo esencialmente propone extender apropiadamente el esquema de la transformada discreta asociada a onditas spline ortogonales, de modo de posibilitar eficientes estrategias de análisis tiempo-escala-frecuencia. Con este propósito, se desarrollan variadas familias de funciones elementales spline. Las mismas son organizadas en bibliotecas de bases ortonormales. Asimismo, se propone una adecuada alternativa para la aproximación de las citadas onditas spline ortogonales por funciones spline de soporte compacto. En conexión con este propósito se diseñan algoritmos, métodos y técnicas para su aplicación al análisis de señales.; The essential objetive of this work is to extend, in an appropriate way, the scheme of the discrete transfor associated with orthogonal spline wavelets, so that efficient strategies of time-scale-frequency analysis may be obtained. To this purpose, several families of elemental spline functions are developped. These families are arranged in libraries of orthonormal bases. In addition to this, this work proposes a suitable alternative to the approximation of the above mentioned orthogonal spline wavelets, by means of compactly supported spline functions. As far as this is concerned, algorithms...

Este trabajo esencialmente propone extender apropiadamente el esquema de la transformada discreta asociada a onditas spline ortogonales, de modo de posibilitar eficientes estrategias de análisis tiempo-escala-frecuencia. Con este propósito, se desarrollan variadas familias de funciones elementales spline. Las mismas son organizadas en bibliotecas de bases ortonormales. Asimismo, se propone una adecuada alternativa para la aproximación de las citadas onditas spline ortogonales por funciones spline de soporte compacto. En conexión con este propósito se diseñan algoritmos, métodos y técnicas para su aplicación al análisis de señales.

One important area of Computer-Aided Geometric Design (CAGD) is concerned with the approximation and representation of the surfaces of solid objects. Accurately describing the shape of an object so that the description is useful to designers who must decide how to manipulate it is an important problem. B-spline techniques promise greater versatility in describing complex surfaces than other techniques, thus the B-spline surface is highlighted in the field of constructive solid geometric modeling. A method for drawing complex surfaces by using B-spline techniques is presented. The tensor product surface scheme is developed for constructing sculptured surfaces. Also, the basic principle of multivariate B-splines, i.e., nontensor product surfaces, the light of tomorrow in CAGD, is introduced.

The issue of vibration isolation challenges engineers' designs across the engineering spectrum. From an engineering standpoint, vibration control impacts the fields of transportation, manufacturing, construction and mechanical design. Dynamic systems produce vibrations for various reasons i.e. rotating unbalanced masses (high speed turbines); inertia of reciprocating components (internal combustion engines); irregular rolling contact (automobiles) or induced eddy current (locomotives) vibrations. In most cases, vibrations cause only physical discomfort and/or loss of accuracy. But in extreme cases, transmitted forces may cause a body to undergo high amplitude resonant vibrations, leading to high cyclic stresses and imminent fatigue failure resulting in a catastrophic occurrence and possible loss of life. Therefore, isolating the vibration's source from other system components becomes essential. Deploying a parallel underdamped spring-damper arrangement achieves this required isolation by suspending the component's mass. The frequency response function (FRF) of a second order under-damped suspension model suggests that for a given excitation frequency, suspensions with lower natural frequencies benefits vibration isolation. Lowering the natural frequency requires springs with low stiffness. Using soft springs is not always plausible as it significantly reduces the suspension's load carrying capacity. Therefore...

Engineers are researching solutions to resolve many of today's technical challenges. Numerical techniques are used to solve the mathematical models that arise in engineering problems. A numerical technique that is increasingly being used to solve mathematical models in engineering research is called the B-spline Collocation Method. The B-spline Collocation Method has a few distinct advantages over the Finite Element and Finite Difference Methods. The main advantage is that the B-spline Collocation Method efficiently provides a piecewise-continuous, closed form solution. Another advantage is that the B-spline Collocation Method procedure is very simple and easy to apply to many problems involving partial differential equations. The current research involves developing, and extensively documenting, a comprehensive, step-by-step procedure for applying the B-spline Collocation Method to the solution of Boundary Value problems. In addition, the current research involves applying the B-spline Collocation Method to solve the mathematical model that arises in the deflection of a geometrically nonlinear, cantilevered beam. The solution is then compared to a known solution found in the literature.

This paper demonstrates the use of shape-preserving exponential spline interpolation in a characteristic based numerical scheme for the solution of the linear advective-diffusion equation. The results from this scheme are compared with results from a number of numerical schemes in current use using test problems in one and two dimensions. These test cases are used to assess the merits of using shape-preserving interpolation in a characteristic based scheme. The evaluation of the schemes is based on accuracy, efficiency, and complexity. The use of the shape-preserving interpolation in a characteristic based scheme is accurate, captures discontinuities, does not introduce spurious oscillations, and preserves the monotonicity and positivity properties of the exact solution. However, fitting exponential spline interpolants to the nodal concentrations is computationally expensive. Exponential spline interpolants were also fitted to the integral of the concentration profile. The integral of the concentration profile is a smoother function than the concentration profile. It requires less computational effort to fit an exponential spline interpolant to the integral than the nodal concentrations. By differentiating the interpolant, the nodal concentrations are obtained. This results in a more efficient and more accurate numerical scheme.