A Tool For Teaching Spline Methods In A Computer Graphics Course

The specialized mathematics knowledge covered in a computer graphics course is usually presented to students in an abstract way. Albeit, computer graphics is an application of this (abstract) mathematics, students may find it hard to link them together. In particular one of the most difficult topics to present in a pedagogical manner to junior students in a computer graphics course is spline methods (mathematical method for data smoothing) used for curve/surface modelling. This topic involves mainly the mathematics of parametric functions, piecewise functions, derivatives, matrices, and parametric/geometric continuities. Usually a student has a vague picture of the actual output of the application of this mathematics. Many educators have experienced that students may fully understand splines application, if and when they are assigned a software project to implement splines, and this understanding could still remain vague until the very last stages of the implementation. As an alternative, static pictures may be presented in class to provide an intuitive understanding of splines. This approach is, in effect, similar to viewing a picture in a textbook. A better alternative is for the educator to demonstrate real-time spline generation, since a picture is worth ten thousand words but a moving picture (animation) is worth ten thousand static ones. This paper presents an interactive software program which is used as a tool to introduce important concepts and algorithms of spline methods to computer science and computer engineering students. The software is specially developed for educational purposes, and generates spline curves

Semantic discovery and reuse of business process patterns

Patterns currently play an important role in modern information systems (IS) development and their use has mainly been restricted to the design and implementation phases of the development lifecycle. Given the increasing significance of business modelling in IS development, patterns have the potential of providing a viable solution for promoting reusability of recurrent generalized models in the very early stages of development. As a statement of research-in-progress this paper focuses on business process patterns and proposes an initial methodological framework for the discovery and reuse of business process patterns within the IS development lifecycle. The framework borrows ideas from the domain engineering literature and proposes the use of semantics to drive both the discovery of patterns as well as their reuse

3D modeling for determination of lenght of electrical arcs using stereo images

Orientador: Maria Cristina Dias TavaresTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: O comprimento do arco elétrico é um parâmetro importante para a modelagem matem ática do arco elétrico. O perfil da variação do comprimento do arco atualmente é estimado pela análise da tensão medida entre os terminais do arco e da corrente do arco. Porém esses resultados não são conclusivos, pois não apresentam uma medição (escala métrica) do eixo-médio tridimensional do arco elétrico. Por outro lado, as imagens da evolução do arco podem fornecer informação suficiente à reconstrução do seu eixo tridimensional e à estimativa do comprimento do arco a cada instante, determinando uma curva de variação do comprimento. A principal contribuição deste trabalho, portanto, reside na obtenção da estimativa do comprimento do arco e, por conseguinte, do alongamento de arcos elétricos baseada na aplicação do modelo snake-3D na reconstrução tridimensional dos eixos longitudinais de arcos elétricos gerados artificialmente. Foram realizados diferentes experimentos para avaliar a proposta de aplicação da snake-3D. Inicialmente, algumas características geométricas dos arcos foram reproduzidas em curvas paramétricas cujas projeções, sobre seções de planos, formaram as sequências de pares de imagens e determinaram os conjuntos de casos experimentais. Em seguida os resultados obtidos através da aplicação da snake-3D foram analisados comparativamente a outros métodos de reconstrução 3D frente aos valores verdadeiros dos comprimentos das curvas. Também foram realizados experimentos com um objeto concreto, nesse caso, um neon flexível manipulado defronte a um par de câmeras reais. As matrizes de calibração foram determinadas por meio de procedimento específico, o comprimento verdadeiro do objeto foi estimado por meio de medição direta e comparado aos resultados obtidos através da aplicação da snake-3D e outro método de reconstrução 3D. Em seguida a snake-3D foi aplicada a imagens de arcos elétricos reais cuja evolução foi capturada utilizando câmeras reais. Nesses casos as estimativas dos comprimentos por meio de snake-3D foram contrapostas aos estudos baseados na análise dos sinais de tensão e de corrente medidos nas extremidades do arco em evolução. Os comprimentos obtidos com a abordagem proposta foram semelhantes aos obtidos através de medidas elétricas, o que valida o uso da metodologia desenvolvida para este tipo de aplicaçãoAbstract: The electrical arc length is an important parameter for the arc mathematical modeling. Nowadays the profile of the arc length variation is estimated by the analysis of the voltage measured at the extremities of the arc and the current of the arc. But these results are not conclusive because they do not present a metrical measurement of the three-dimensional medial-axis of the arc. On the other hand, the images of the spatial evolution of the arc can provide enough resources for recovering the 3D longitudinal axis for estimation of the arc length as well as for obtaining the curve of length variation along the time. The main contribution of this work therefore lies in the estimation of the arc length, and consequently the elongation of electric arcs based on the application of the model (3D-snake) for the three-dimensional reconstruction of the longitudinal axes of artificially generated electrical arcs. Different experiments were conducted to evaluate the proposed application of the 3D-snake. Initially, some geometrical characteristics of the arcs were reproduced in parametric curves whose projections formed sequences of image pairs and determined the sets of test cases. Then the results obtained by applying the 3D-snake were analyzed in comparison to other 3D reconstruction methods against the true values of the lengths of curves. Also experiments were performed with a concrete object, in this case, a flexible neon manipulated in front of a pair of real cameras. The calibration matrices were determined by specific procedure, the length of the real object was estimated by direct measurement and compared to results obtained by applying the 3D-snake and other 3D reconstruction method. Next the 3D-snake was applied to real images of arcs whose evolutions were captured using real cameras. In these cases the estimation of measurement through 3D-snake were opposed to results based on arc current and arc voltage measured at arc terminals. The lengths obtained with the proposed model were similar to those obtained through electrical measurements, which validates the use of the method developed for this type of applicationDoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétric

A Tool for Teaching Curve Design

This paper describes a tool for teaching curve design. This tool is a component of the software tools to be used in a computing with geometry course [3, 4] that is being developed under the support of National Science Foundation. Curve design is important in computer graphics, animation, and computer aided design. Unfortunately, curve design requires very involved mathematics even though many curve design concepts are intuitive. As a result, it has been a challenging job for instructors teaching curves and surfaces in computer graphics, computer aided design, and other related courses. During past years, there have not been very many e#orts dedicated to curve design tool development. Yen [7] produced a well-received video program explaining important concepts of B-spline curves and surfaces and Rockwood and Chambers [6] published a multimedia tutorial on computer aided geometric design. The former only provides a one-way communication, while the latter restricts users to a predefined environment with very limited interaction for users to carry out experiments. To fill this gap, our tool provides students with a fully interactive environment in which they are free to design, modify, and manipulate curved objects and perform experiments without constraint