B-splajn dijelovi koji pristaju na plohe i triangularne mreže

In this paper a technique for the construction of quartic polynomial B-spline patches fitting on analytical surfaces and triangle meshes is presented.The input data are curvature values and principal directions at a given surface point which can be computed directly, if the surface is represented by a vector function. In the case of discrete surface representation, i.e. on a triangle mesh the required input data are computed from a circular neighborhood of a specified triangle face. Such a surface patch may replace a well defined region of the mesh, and can be used e.g. in re-triangulation, mesh-simplification and rendering algorithms.U ovom se radu prikazuje metoda za konstrukciju kvartnog polinoma B-splajn dijela podesnog za analitičke plohe i mreže trokuta. Ulazni podaci su vrijednosti zakrivljenosti i glavni smjerovi u danoj točki plohe, koji se mogu izravno računati za plohu zadanu vektorskom funkcijom. Za slučaj diskretne reprezentacije plohe, tj. za triangularnu mrežu, odgovarajući ulazni podaci računaju se iz kružne okoline određ-enog trokuta mreže. Takvi dijelovi mogu zamijeniti dobro definirano područje mreže, i mogu se upotrijebiti npr. u retriangulaciji, simplifikaciji mreže i renderiranju

Optimal Outsourcing for Intellectual Property Protection and Production Cost Minimization

This paper presents a methodology for optimal outsourcing of products. Outsourcing of products can have the advantage of reducing the production cost, but often causes a risk that important technology may leak and get used by competitors. To help reduce the risk of intellectual property (IP) leakage, a model proposed in this paper assumes that it is possible to separate some of the important geometrical features on some of the product parts that are outsourced, and then manufacture them in-house. The model estimates the fraction of IP-value that is subject to risk of leakage based on patent claims and how they relate to the outsourced parts and/or features. Production cost is modelled by assuming a base cost for manufacturing parts in-house, and then a discount rate is applied if the decision to outsource is made. Separation of geometrical features from manufactured parts introduces additional cost, which is modelled as an overhead if the decision to separate features is made. The outsourcing management process is then viewed as a two-objective problem, with the objectives being the minimization of both the fraction of IP-value at risk of leakage, as well as the production cost. A case study of an auto-slide-hinge mechanism is presented, in which the two-objective optimization problem is transformed into a single-objective constrained problem. Genetic algorithm is then applied iteratively on the problem in order generate the Pareto-plot that visualizes the trade-offs between the two objectives.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87272/4/Saitou56.pd

Three-Dimensional Object Registration Using Wavelet Features

Recent developments in shape-based modeling and data acquisition have brought three-dimensional models to the forefront of computer graphics and visualization research. New data acquisition methods are producing large numbers of models in a variety of fields. Three-dimensional registration (alignment) is key to the useful application of such models in areas from automated surface inspection to cancer detection and surgery. The algorithms developed in this research accomplish automatic registration of three-dimensional voxelized models. We employ features in a wavelet transform domain to accomplish registration. The features are extracted in a multi-resolutional format, thus delineating features at various scales for robust and rapid matching. Registration is achieved by using a voting scheme to select peaks in sets of rotation quaternions, then separately identifying translation. The method is robust to occlusion, clutter, and noise. The efficacy of the algorithm is demonstrated through examples from solid modeling and medical imaging applications

Математична модель та метод розв’язання задачі віртуального базування

Розглянуто задачу віртуального базування, яка є характерною для випадку числового програмного керування (ЧПК) оброблення при виготовленні деталей з заготовок близької геометричної форми. Показано, що для таких випадків замість закріплення заготовки в теоретично заданому положенні ефективною є корекція ЧПК програми під її поточне положення. Розглянуто існуючі алгоритми розв’язання задачі віртуального базування, яка зводиться до встановлення параметрів розміщення CAD моделі деталі всередині хмари точок, отриманих скануванням поверхні заготовки. Показано, що їх основним недоліком є використання критеріїв не чутливих до взаємного положення CAD моделі деталі та сканованих точок. Як альтернативу запропоновано використовувати алгоритм, що базується на використанні методу phi-функцій, який повністю усуває вказаний недолік. Описано стратегію розв’язання задачі віртуального базування на базі запропонованого алгоритму та наведено приклади розв’язання кількох тестових задач, які підтверджують його ефективність

Utilisation des surfaces pour l'alignement et le balancement des pièces

L'alignement des pièces en utilisant les surfaces constitue le sujet principal traité dans ce travail. L'idée consiste à reconstruire les surfaces de la pièce réelle à partir de points relevés sur celle-ci par une méthode appropriée. Par la suite, ces surfaces sont subdivisées en des entités surfaciques distinctes pour être alignées avec une pièce nominale. Cela est rendu possible par l'intégration de l'algorithme dans le logiciel de CAO CATIA V5. Le développement de cette technique se base essentiellement sur la résolution d'un problème d'optimisation qui respecte un certain nombre de contraintes et de préférences. La méthode d'optimisation Simplex est utilisée pour solutionner ce problème. Finalement, le test de cette nouvelle technique avec quelques exemples, nous a permis de constater son efficacité lors de l'alignement de surfaces à géométries assez complexes. Cela se traduit par une baisse considérable du nombre de points nécessaire pour arriver à un résultat acceptabl

CONTENT BASED SEARCH OF MECHANICAL ASSEMBLIES

The increased use of 3D CAD systems by product development organizations has resulted in large databases of assemblies; this explosion of assembly data will continue in the future. Currently, there are no effective content-based techniques to search these databases. Ability to perform content-based searches on these databases is expected to help the designers in the following two ways. First, it can facilitate reuse of existing assembly designs, thereby reducing the design time. Second, a lot of useful Design for Manufacturing and Assembly (DFMA) knowledge is embedded in existing assemblies. Therefore a capability to locate existing assemblies and examine them can be used as a learning tool by the designers to learn from the existing assembly designs and hence transfer the best DFMA practices to new designers. This thesis describes a system for performing content-based searches on assembly databases. It lists the templates identified for comprehensive search definitions and describes algorithms to perform content-based searches for mechanical assemblies. The characteristics of mechanical assemblies were identified and categorized based on their similarity and computational complexity to perform comparison. The characteristics were extracted from the CAD data to prepare a CAD independent signature of the assembly. The search methodology consists of exact and approximate string matching, number matching and computing graph compatibility. Various research groups have solved the former two problems. This thesis describes a new algorithm to solve graph compatibility problem using branch and bound search. The performance of this algorithm has been experimentally characterized using randomly generated graphs. This search software provides a CAD format independent tool to perform content based search of assemblies based on the form of assemblies. The capabilities of the search software have been illustrated in this thesis through several examples. This search tool can contribute to significantly reduce the design time and reuse of the knowledge in existing designs

Medição óptica, comparação e sinalização de superfícies com forma livre de grande extensão

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro de Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2010Muitas superfícies, como cascos de navio, "carenagens" de automóveis e aeronaves, assim como pás de rotores de turbinas hidráulicas ou de aerogeradores são típicos exemplos de superfícies com forma livre. Como qualquer peça produzida pela industria, peças que contenham superfícies livres também devem ser medidas para realizar seu controle geométrico, garantindo assim que a função do produto seja realizada de forma satisfatória. Sistemas ópticos de medição são cada vez mais utilizados para a medição de superfícies livres. Isto se deve ao fato de medições por princípios ópticos possuírem diversas vantagens: (a) medição sem contato; (b) rapidez de medição, onde milhões de pontos podem ser medidos em poucos segundos; (c) relativa portabilidade e (d) incertezas de medição comparáveis a sistemas de medição com contato. Um sistema óptico portátil, capaz de realizar a medição de superfícies livres de grande extensão, compará-las com superfície de referência e ainda sinalizar localmente parâmetros de interesse através da projeção de mapas de cores na própria superfície, foi desenvolvido no âmbito da tese. O sistema funde os princípios de visão estéreo passiva e ativa. Alvos circulares são utilizados para concatenar nuvens de pontos tridimensionais em relação a um sistema de coordenadas global. Algoritmos desenvolvidos realizam o cálculo destas nuvens de pontos de forma intrinsecamente estruturada em uma única malha regular, possibilitando ainda utilizar um número qualquer de câmeras e um projetor de luz estruturada. A calibração do projetor, como uma câmera invertida do ponto de vista da óptica geométrica, possibilita calcular e projetar um mapa de cores na própria superfície auxiliando o controle dimensional e o acompanhamento de intervenções. Avaliações experimentais, utilizando diversos tipos de padrões geométricos e superfícies livres calibradas, demonstram a viabilidade e as vantagens de utilização dos métodos propostos.Many surfaces, such as ship hulls, fairing of automobiles and rotors of water or wind turbines are typical examples of free form surfaces. Like any pieces produced by industry, parts that contain free form surfaces should also be measured, to ensure that the product function is performed satisfactorily. Optical measuring systems are increasingly used for the measurement of free form surfaces. Measurement by optical principles have several advantages: (a) non-contact measuring, (b) speed of measurement, where millions of points can be measured in seconds, (c) high portability and (d) measurement uncertainties are comparable to contact measurement systems. A portable optical system, capable of measuring free form surfaces over large areas, comparing them with reference surfaces and locally project color maps on the surface to signal parameters of interest, was developed within the thesis. The system merges passive and active stereo vision. Circular targets are used to concatenate three-dimensional point clouds for a global coordinate system. Algorithms perform the calculation of these point clouds intrinsically structured into a single regular mesh, allowing also the use of any number of cameras and a structured light projector. The calibration of the projector, as an inverted camera, allows to calculate and design a color map, to signalize the surface, helping the dimensional control and monitoring of interventions. Experimental evaluations, using diferent kinds of geometric patterns and calibrated free form surfaces demonstrate the feasibility and the advantages of using the proposed methods

A feature-based shape similarity assessment framework

The popularity of 3D CAD systems is resulting in a large number of CAD models being generated. Availability of these CAD models is opening up new ways in which information can be archived, analyzed, and reused. 3D geometric information is one of the main components of CAD models. Therefore shape similarity assessment is a fundamental geometric reasoning problem that finds several different applications. In many design and manufacturing applications, the gross shape of the 3D parts does not play an important role in the similarity assessment. Instead certain attributes of part features play a dominant role in determining the similarity between two parts. Different feature-based models are usually created using their own coordinate systems. Therefore, feature-based shape similarity assessment involves finding the optimal alignment transformations for two sets of feature vectors. The optimal alignment corresponds to the minimum value of a distance function that is computed between the two sets of feature vectors being aligned. In order to compute the distance function the closest neighbor to each feature vector needs to be identified. We have developed optimal feature alignment algorithms based on the partitioning of the transformation space into regions such that the closest neighbors are invariant within each region. These algorithms can work with customizable distance functions. We have shown that they have polynomial time complexity. For higher dimension transformation spaces it is harder to design algorithms based on the partitioning of transformation spaces because the data structures involved are very complex. In those cases, feature alignment algorithms based on iterative strategies have been developed. Iterative strategies make use of optimal feature alignment algorithms based on the partitioning of lower dimension transformation spaces. Extensive experiments have been carried out to provide empirical evidence that iterative strategies can find the optimal solution for feature alignment problems. A feature-based shape similarity analysis framework has been built based on the feature alignment algorithms. This framework has been demonstrated with the two following applications. A machining feature based alignment algorithm has been developed to automatically search databases for parts that are similar to a newly designed part in terms of machining features. We expect that the retrieved parts can be used as a basis to perform cost estimation of the newly designed part. A surface feature based alignment algorithm has been developed to automatically search databases for parts that are similar to a newly designed part in terms of surface features. We expect that the retrieved parts can be used as a basis to choose the most appropriate tool maker for the newly designed part. We believe that the feature-based shape similarity assessment algorithms developed in this thesis will provide the foundations for designing new feature-based shape similarity algorithms that will enable designers to efficiently retrieve archived geometric information. We expect that these tools will facilitate information reuse and therefore decrease product development time and cost