211 research outputs found

    A mathematical framework for contact detection between quadric and superquadric surfaces

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    The calculation of the minimum distance between surfaces plays an important role in computational mechanics, namely, in the study of constrained multibody systems where contact forces take part. In this paper, a general rigid contact detection methodology for non-conformal bodies, described by ellipsoidal and superellipsoidal surfaces, is presented. The mathematical framework relies on simple algebraic and differential geometry, vector calculus, and on the C2 continuous implicit representations of the surfaces. The proposed methodology establishes a set of collinear and orthogonal constraints between vectors defining the contacting surfaces that, allied with loci constraints, which are specific to the type of surface being used, formulate the contact problem. This set of non-linear equations is solved numerically with the Newton-Raphson method with Jacobian matrices calculated analytically. The method outputs the coordinates of the pair of points with common normal vector directions and, consequently, the minimum distance between both surfaces. Contrary to other contact detection methodologies, the proposed mathematical framework does not rely on polygonal-based geometries neither on complex non-linear optimization formulations. Furthermore, the methodology is extendable to other surfaces that are (strictly) convex, interact in a non-conformal fashion, present an implicit representation, and that are at least C2 continuous. Two distinct methods for calculating the tangent and binormal vectors to the implicit surfaces are introduced: (i) a method based on the Householder reflection matrix; and (ii) a method based on a square plate rotation mechanism. The first provides a base of three orthogonal vectors, in which one of them is collinear to the surface normal. For the latter, it is shown that, by means of an analogy to the referred mechanism, at least two non-collinear vectors to the normal vector can be determined. Complementarily, several mathematical and computational aspects, regarding the rigid contact detection methodology, are described. The proposed methodology is applied to several case tests involving the contact between different (super)ellipsoidal contact pairs. Numerical results show that the implemented methodology is highly efficient and accurate for ellipsoids and superellipsoids.Fundação para a Ciência e a Tecnologia (FCT

    Registration techniques for computer assisted orthopaedic surgery

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    The registration of 3D preoperative medical data to patients is a key task in developing computer assisted surgery systems. In computer assisted surgery, the patient in the operation theatre must be aligned with the coordinate system in which the preoperative data has been acquired, so that the planned surgery based on the preoperative data can be carried out under the guidance of the computer assisted surgery system.The aim of this research is to investigate registration algorithms for developing computer assisted bone surgery systems. We start with reference mark registration. New interpretations are given to the development of well knowm algorithms based on singular value decomposition, polar decomposition techniques and the unit quaternion representation of the rotation matrix. In addition, a new algorithm is developed based on the estimate of the rotation axis. For non-land mark registration, we first develop iterative closest line segment and iterative closest triangle patch registrations, similar to the well known iterative closest point registration, when the preoperative data are dense enough. We then move to the situation where the preoperative data are not dense enough. Implicit fitting is considered to interpolate the gaps between the data . A new ellipsoid fitting algorithm and a new constructive implicit fitting strategy are developed. Finally, a region to region matching procedure is proposed based on our novel constructive implicit fitting technique. Experiments demonstrate that the new algorithm is very stable and very efficient

    Lunar Crater Identification in Digital Images

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    It is often necessary to identify a pattern of observed craters in a single image of the lunar surface and without any prior knowledge of the camera's location. This so-called "lost-in-space" crater identification problem is common in both crater-based terrain relative navigation (TRN) and in automatic registration of scientific imagery. Past work on crater identification has largely been based on heuristic schemes, with poor performance outside of a narrowly defined operating regime (e.g., nadir pointing images, small search areas). This work provides the first mathematically rigorous treatment of the general crater identification problem. It is shown when it is (and when it is not) possible to recognize a pattern of elliptical crater rims in an image formed by perspective projection. For the cases when it is possible to recognize a pattern, descriptors are developed using invariant theory that provably capture all of the viewpoint invariant information. These descriptors may be pre-computed for known crater patterns and placed in a searchable index for fast recognition. New techniques are also developed for computing pose from crater rim observations and for evaluating crater rim correspondences. These techniques are demonstrated on both synthetic and real images

    Spherical Harmonics Models and their Application to non-Spherical Shape Particles

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    The dissertation investigates spherical harmonics method for describing a particle shape. The main object of research is the non-spherical shape particles. The purpose of this dissertation is to create spherical harmonics model for a non-pherical particle. The dissertation also focuses on determining the suitability of the lowresolution spherical harmonics for describing various non-spherical particles. The work approaches a few tasks such as testing the suitability of a spherical harmonics model for simple symmetric particles and applying it to complex shape particles. The first task is formulated aiming to test the modelling concept and strategy using simple shapes. The second task is related to the practical applications, when complex shape particles are considered. The dissertation consists of introduction, 4 chapters, general conclusions, references, a list of publications by the author on the topic of the dissertation, a summary in Lithuanian and 5 annexes. The introduction reveals the investigated problem, importance of the thesis and the object of research, describes the purpose and tasks of the thesis, research methodology, scientific novelty, the practical significance of results and defended statements. The introduction ends in presenting the author’s publications on the topic of the dissertation, offering the material of made presentations in conferences and defining the structure of the dissertation. Chapter 1 revises the literature: the particulate systems and their processes, shapes of the particles and methods for describing the shape, shape indicators. At the end of the chapter, conclusions are drawn and the tasks for the dissertation are reconsidered. Chapter 2 presents the modelling approach and strategies for the points of the particle surface, spherical harmonics, the calculation of the expansion coefficients, integral parameters and curvature and also the conclusions. Chapters 3 and 4 analize the modelling results of the simple and complex particles. At the end of the both chapters conclusions are drawn. 5 articles focusing on the topic of the dissertation have been published: two articles – in the Thomson ISI register, one article – in conference material and scientific papers in Thomson ISI Proceedings data base, one article – in the journal quoted by other international data base, one article – in material reviewed during international conference. 8 presentations on the subject of the dissertation have been given in conferences at national and international levels

    Scientific visualization of stress tensor information with applications to stress determination by X-ray and neutron diffraction

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    Includes bibliographical references (leaves 232-249).The visual analysis of mechanical stress facilitates physical understanding of the tensor quantity which is concealed in scalar and vector methods. In this study, the principles and techniques of scientific visualization are used to develop a visual analysis of mechanical stresses. Scientific visualization is not only applied to the final tensorial quantity obtained from the diffraction measurements, but the visual methods are developed from, and integrated into current residual stress analysis practices by relating the newly developed visual techniques to the conventional techniques, highlighting its advantages. This study consists of the mathematical analysis of the tensor character of mechanical stresses, discussion of the principles and techniques of scientific visualization (visual data analysis) in physical research, and tensor determination, visual analysis and presentation of residual stresses obtained from diffraction measurements

    Solid rocket booster thermal radiation model, volume 1

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    A solid rocket booster (SRB) thermal radiation model, capable of defining the influence of the plume flowfield structure on the magnitude and distribution of thermal radiation leaving the plume, was prepared and documented. Radiant heating rates may be calculated for a single SRB plume or for the dual SRB plumes astride the space shuttle. The plumes may be gimbaled in the yaw and pitch planes. Space shuttle surface geometries are simulated with combinations of quadric surfaces. The effect of surface shading is included. The computer program also has the capability to calculate view factors between the SRB plumes and space shuttle surfaces as well as surface-to-surface view factors

    Guidance, flight mechanics and trajectory optimization. Volume 1 - Coordinate systems and time measure

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    Coordinate measuring system for flight control, and trajectory optimizatio

    Surface and Volumetric Segmentation of Complex 3-D Objects Using Parametric Shape Models

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    The problem of part definition, description, and decomposition is central to the shape recognition systems. In this dissertation, we develop an integrated framework for segmenting dense range data of complex 3-D scenes into their constituent parts in terms of surface and volumetric primitives. Unlike previous approaches, we use geometric properties derived from surface, as well as volumetric models, to recover structured descriptions of complex objects without a priori domain knowledge or stored models. To recover shape descriptions, we use bi-quadric models for surface representation and superquadric models for object-centered volumetric representation. The surface segmentation uses a novel approach of searching for the best piecewise description of the image in terms of bi-quadric (z = f(x,y)) models. It is used to generate the region adjacency graphs, to localize surface discontinuities, and to derive global shape properties of the surfaces. A superquadric model is recovered for the entire data set and residuals are computed to evaluate the fit. The goodness-of-fit value based on the inside-outside function, and the mean-squared distance of data from the model provide quantitative evaluation of the model. The qualitative evaluation criteria check the local consistency of the model in the form of residual maps of overestimated and underestimated data regions. The control structure invokes the models in a systematic manner, evaluates the intermediate descriptions, and integrates them to achieve final segmentation. Superquadric and bi-quadric models are recovered in parallel to incorporate the best of the coarse-to-fine and fine-to-coarse segmentation strategies. The model evaluation criteria determine the dimensionality of the scene, and decide whether to terminate the procedure, or selectively refine the segmentation by following a global-to-local part segmentation approach. The control module generates hypotheses about superquadric models at clusters of underestimated data and performs controlled extrapolation of the part-model by shrinking the global model. As the global model shrinks and the local models grow, they are evaluated and tested for termination or further segmentation. We present results on real range images of scenes of varying complexity, including objects with occluding parts, and scenes where surface segmentation is not sufficient to guide the volumetric segmentation. We analyze the issue of segmentation of complex scenes thoroughly by studying the effect of missing data on volumetric model recovery, generating object-centered descriptions, and presenting a complete set of criteria for the evaluation of the superquadric models. We conclude by discussing the applications of our approach in data reduction, 3-D object recognition, geometric modeling, automatic model generation. object manipulation, and active vision
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