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Non-Uniform Rational B-Splines (NURBS) curve has acquired great significance in the field of Computer Aided Design and Machining due to their ability to draw a large variety of shapes in an interactive computer graphics environment. A biarc curve is a composition of two circular arcs such that they are tangent continuous at the point of join. Biarcs have replaced traditionally used line segments in approximating curves and surfaces for generating tool paths of Computerised cutting machines called CNC (Computerised Numerical Controlled) machines. This is due to their ability to be at a greater proximity to the original curve with fewer number of segments. Since most of the machining tools can move only in straight lines and circular arcs, it is desirable that the tool paths be composed of biarcs and/or straight line segments. Shape preserving interpolation is a technique of drawing a curve through a set of points such that the shape represented by the data points are preserved. Both NURBS and biarc curves are not essentially shape preserving curves; however, if certain constraints are imposed on them, they are able to preserve the shape represented by the data points. This work proposes a technique that incorporates both NURBS and biarcs to perform the interpolation. The advantages are twofold; it acts as a common platform for the two techniques to operate together, which is novel, and the fitted NURBS curve can be approximated by biarcs, which has applications in the machining industry.

Non-Uniform Rational B-Splines (NURBS) curve has acquired great significance in the field of Computer Aided Design and Machining due to their ability to draw a large variety of shapes in an interactive computer graphics environment. A biarc curve is a composition of two circular arcs such that they are tangent continuous at the point of join. Biarcs have replaced traditionally used line segments in approximating curves and surfaces for generating tool paths of Computerised cutting machines called CNC (Computerised Numerical Controlled) machines. This is due to their ability to be at a greater proximity to the original curve with fewer number of segments. Since most of the machining tools can move only in straight lines and circular arcs, it is desirable that the tool paths be composed of biarcs and/or straight line segments. Shape preserving interpolation is a technique of drawing a curve through a set of points such that the shape represented by the data points are preserved. Both NURBS and biarc curves are not essentially shape preserving curves; however, if certain constraints are imposed on them, they are able to preserve the shape represented by the data points. This work proposes a technique that incorporates both NURBS and biarcs to perform the interpolation. The advantages are twofold; it acts as a common platform for the two techniques to operate together, which is novel, and the fitted NURBS curve can be approximated by biarcs, which has applications in the machining industry.

This report treats the implementation of collision detection algorithms for Boundary representations (BREPs) consisting of connected trimmed surfaces, mainly Non Uniform Rational Basis Spline (NURBS) surfaces. Using the OpenNurbs software package, complicated geometries created in CAD program Space Claim were imported to the physics engine AgX, where dynamic simulations were carried out. Collision detection algorithms for the geometry pairs BREP-line, BREP-plane and BREP-sphere have been developed and investigated. In the case of BREP-sphere collision detection, experiments have been carried out which show that BREP-shape representation exceeds trimesh-shape representation both in computational performance and in collision accuracy. The conclusion is that BREP representation has the potential to replace trimesh representation for some complex geometries with higher computational performance and more accurate simulations as a result.

Ces travaux de thèse sont dédiés à la mesure de formes 3D, de champs cinématiques 3D surfaciques et à l'identification de paramètres mécaniques à partir de mesures par corrélation d'images. Cette méthode optique se base sur l'utilisation de caméras comme support de la mesure. Pour cette raison, une étude des différents modèles de caméra classiquement utilisés est effectuée, puis le passage d'un formalisme continu pour la description des images à une approche discrète utilisant la notion de pixel est décrit. Une attention particulière est portée aux distorsions optiques et une approche utilisant la corrélation d'images pour les évaluer est développée. Une nouvelle méthode de mesure de forme 3D et de champs de déplacements 3D surfaciques par stéréo-corrélation d'images est introduite. Elle utilise un modèle numérique de l'objet observé comme support pour la corrélation. Cette méthode mène à une formulation globale de la stéréo-corrélation. Elle peut être écrite dans le cas général et particularisée à des surfaces NURBS (non-uniform rational B-splines). Le champ de déplacement est également exprimé dans un formalisme NURBS complètement cohérent avec le modèle géométrique utilisé pour définir la forme observée. Des mesures sont validées en utilisant des mouvements imposés à un carreau de Bézier usiné. La faisabilité de la technique dans plusieurs cas industriels est également étudiée avec, par exemple, la mesure des déplacements d'une pièce composite de train d'atterrissage chargée mécaniquement. Enfin, à partir de cette formulation isogéométrique de la mesure de champs, une étude de la caractérisation de propriétés élastiques est effectuée. Deux méthodes inspirées d'approches existantes sont ainsi proposées, utilisant des mesures de champs et des calculs numériques dans un formalisme isogéométrique pour identifier des paramètres de loi de comportement élastique isotrope sur un cas test numérique et pour un essai de traction uniaxiale. / This thesis is dedicated to measurement of 3D shapes, 3D kinematic fields on surfaces and identification of mechanical properties from digital image correlation measurements. This optical method uses cameras as measurement tools. For this reason, a study of the classical camera models used is performed and the description of the digitalization of an image from a continuous to a discrete formalism using the pixel is described. A specific work is dedicated to optical distortions and a method based on digital image correlation to evaluate these distortions is developped.A new method for 3D shapes and 3D displacement fields on surfaces using stereo-correlation is introduced. A numerical description of the observed object is used as a support to perform the correlation. This method lead to a global approach to stereo-correlation. It can be rewrite in a generic case or in particular to be applied to NURBS (Non-Uniform Rational B-Splines) surfaces. The displacement fields is therefore expressed in a NURBS formalism which is completely consistent with the geometrical model used to described the observed shape. Measurements are validated using prescribed motions on a Bezier patch. The feasibility of such a technique in several industrial cases is then studied with for example the measurement of the displacement of a composite part of a landing gear under mechanical loading.Finally, from this isogeometric formulation of full-field measurement, a study of the identification of elastic properties is performed. Two methods inspired from existing approaches are proposed, using full-field measurement and numerical simulations in a common isogeometric formalism to identify parameters of an isotropic linear elastic constitutive law on a both a numerical test case and a uniaxial tensile test.

EEG has been used to explore the electrical activity of the brain for manydecades. During that time, different components of the EEG signal have been iso-lated, characterized, and associated with a variety of brain activities. However, nowidely accepted model characterizing the spatio-temporal structure of the full-brainEEG signal exists to date.Modeling the spatio-temporal nature of the EEG signal is a daunting task. Thespatial component of EEG is defined by the locations of recording electrodes (rang-ing between 2 to 256 in number) placed on the scalp, while its temporal componentis defined by the electrical potentials the electrodes detect. The EEG signal is gen-erated by the composite electrical activity of large neuron assemblies in the brain.These neuronal units often perform independent tasks, giving the EEG signal ahighly dynamic and non-linear character. These characteristics make the raw EEGsignal challenging to work with. Thus, most research focuses on extracting andisolating targeted spatial and temporal components of interest. While componentisolation strategies like independent component analysis are useful, their effective-ness is limited by noise contamination and poor reproducibility. These drawbacks tofeature extraction could be improved significantly if they were informed by a globalspatio-temporal model of EEG data.The aim of this thesis is to introduce a novel data-surface reconstruction (DSR)technique for EEG which can model the integrated spatio-temporal structure of EEGdata. To produce physically intuitive results, we utilize a hyper-coordinate transfor-mation which integrates both spatial and temporal information of the EEG signalinto a unified coordinate system. We then apply a non-uniform rational B spline(NURBS) fitting technique which minimizes the point distance from the computedsurface to each element of the transformed data. To validate the effectiveness of thisproposed method, we conduct an evaluation using a 5-state classification problem;with 1 baseline and 4 meditation states comparing the classification accuracy usingthe raw EEG data versus the surface reconstructed data in the broadband rangeand the alpha, beta, delta, gamma and higher gamma frequencies. Results demon-strate that the fitted data consistently outperforms the raw data in the broadbandspectrum and all frequency spectrums.

New methods are employed to develop an anatomically accurate, analysis-ready isogeometric model of skeletal muscles. Current modeling techniques for the analysis of skeletal muscles include the utilization of finite element meshing, which inherently poses a few well-known problems that provide motivation for isogeometric analysis. In addition to those issues, standard FEA meshing cannot preserve smooth geometries, therefore the accuracy of the foregoing model and analysis is reduced. Moreover, there is no easy means to characterize fiber direction in the FEA framework due to discontinuities at element boundaries. Additionally, material property distributions such as the transition of the muscle-tendon complex along the longitudinal axis through FEA are prescribed on an element by element basis, leading to abrupt, unrealistic property changes at element boundaries. The current research builds on the idea of an isogeometric tensor-product rod using harmonic coordinates and NURBS [1]. Through a direct comparison between a meshed, FEA model and the tensor-product rod model, it can be shown that the tensor-product rod model preserves smoothness, enhancing the geometric representation passed through to analysis while reducing the total DOF of the model. Muscle fibers can be easily implemented as parametric lines with muscle-specific orientations along the muscles' longitudinal axis that match distinct fiber orientations existent within common skeletal muscles. This technique not only allows for the representation of perfectly parallel-fibered structures, but also those that do not directly follow the longitudinal axis such as a helical twist. Utilizing this geometric method also provides the framework for implementing material properties using an interpolative-style scheme. Varying properties at specific longitudinal control point cross-sections near muscle termination areas can be designated to more accurately represent the muscle-tendon complex. These new techniques allow for the creation of an analysis-ready, realistic skeletal muscle model of the male human arm. The model contains 28 muscles complete with muscle-specific geometric, fiber, and heterogeneous property characterizations all compiled into a complete "digital muscle library."

In machining complex dies, molds, aerospace and automotive parts, or biomedical components, it is crucial to minimize the cycle time, which reduces costs, while preserving the quality and tolerance integrity of the part being produced. To meet the demands for high quality finishes and low production costs in machining parts with complex geometry, computer numerical control (CNC) machine tools must be equipped with spline interpolation, feedrate modulation, and feedrate optimization capabilities. This thesis presents the development of novel trajectory generation algorithms for Non Uniform Rational B-Spline (NURBS) toolpaths that can be implemented on new low-cost CNC's, as well as, in conjunction with existing CNC's. In order to minimize feedrate fluctuations during the interpolation of NURBS toolpaths, the concept of the feed correction polynomial is applied. Feedrate fluctuations are reduced from around 40 % for natural interpolation to 0.1 % for interpolation with feed correction. Excessive acceleration and jerk in the axes are also avoided. To generate jerk-limited feed motion profiles for long segmented toolpaths, a generalized framework for feedrate modulation, based on the S-curve function, is presented. Kinematic compatibility conditions are derived to ensure that the position, velocity, and acceleration profiles are continuous and that the jerk is limited in all axes. This framework serves as the foundation for the proposed heuristic feedrate optimization strategy in this thesis. Using analytically derived kinematic compatibility equations and an efficient bisection search algorithm, the command feedrate for each segment is maximized. Feasible solutions must satisfy the optimization constraints on the velocity, control signal (i.e. actuation torque), and jerk in each axis throughout the trajectory. The maximized feedrates are used to generate near-optimal feed profiles that have shorter cycle times, approximately 13-26% faster than the feed profiles obtained using the worst-case curvature approach, which is widely used in industrial CNC interpolators. The effectiveness of the NURBS interpolation, feedrate modulation and feedrate optimization techniques has been verified in 3-axis machining experiments of a biomedical implant.

In machining complex dies, molds, aerospace and automotive parts, or biomedical components, it is crucial to minimize the cycle time, which reduces costs, while preserving the quality and tolerance integrity of the part being produced. To meet the demands for high quality finishes and low production costs in machining parts with complex geometry, computer numerical control (CNC) machine tools must be equipped with spline interpolation, feedrate modulation, and feedrate optimization capabilities. This thesis presents the development of novel trajectory generation algorithms for Non Uniform Rational B-Spline (NURBS) toolpaths that can be implemented on new low-cost CNC's, as well as, in conjunction with existing CNC's. In order to minimize feedrate fluctuations during the interpolation of NURBS toolpaths, the concept of the feed correction polynomial is applied. Feedrate fluctuations are reduced from around 40 % for natural interpolation to 0.1 % for interpolation with feed correction. Excessive acceleration and jerk in the axes are also avoided. To generate jerk-limited feed motion profiles for long segmented toolpaths, a generalized framework for feedrate modulation, based on the S-curve function, is presented. Kinematic compatibility conditions are derived to ensure that the position, velocity, and acceleration profiles are continuous and that the jerk is limited in all axes. This framework serves as the foundation for the proposed heuristic feedrate optimization strategy in this thesis. Using analytically derived kinematic compatibility equations and an efficient bisection search algorithm, the command feedrate for each segment is maximized. Feasible solutions must satisfy the optimization constraints on the velocity, control signal (i.e. actuation torque), and jerk in each axis throughout the trajectory. The maximized feedrates are used to generate near-optimal feed profiles that have shorter cycle times, approximately 13-26% faster than the feed profiles obtained using the worst-case curvature approach, which is widely used in industrial CNC interpolators. The effectiveness of the NURBS interpolation, feedrate modulation and feedrate optimization techniques has been verified in 3-axis machining experiments of a biomedical implant.

During the latest ten years, development in the industry of machine tools has been growing rapidly in our country. Since industry automation is highly demanded, the study about CNC is therefore extensively proceeded. Owing to request for higher quality, the machine tool must achieve the high speed and high precision. There are three factors in precise motion control : the accuracy of reference command, the design of servo control structure, and machine structure. However the part of machine structure attains to maturity. The design of the control system need to include good motion control and correct reference command. NURBS can represent analytic curves and free-form curves accurately and easily. Cross-coupled control is able to adjust the dynamic system of each axis to reduce the contour errors. It is expected to improve control performance in terms of contour errors by combine NURBS reference command and the cross-coupled control framework. Keywords¡Gmachine tool, NURBS, cross-coupled control