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Geometric Algebra Applications Vol. II: Robot Modelling and Control
by Eduardo Bayro-CorrochanoThis book presents a unified mathematical treatment of diverse problems in the general domain of robotics and associated fields using Clifford or geometric alge- bra. By addressing a wide spectrum of problems in a common language, it offers both fresh insights and new solutions that are useful to scientists and engineers working in areas related with robotics. It introduces non-specialists to Clifford and geometric algebra, and provides ex- amples to help readers learn how to compute using geometric entities and geomet- ric formulations. It also includes an in-depth study of applications of Lie group theory, Lie algebra, spinors and versors and the algebra of incidence using the universal geometric algebra generated by reciprocal null cones. Featuring a detailed study of kinematics, differential kinematics and dynamics using geometric algebra, the book also develops Euler Lagrange and Hamiltoni- ans equations for dynamics using conformal geometric algebra, and the recursive Newton-Euler using screw theory in the motor algebra framework. Further, it comprehensively explores robot modeling and nonlinear controllers, and discusses several applications in computer vision, graphics, neurocomputing, quantum com- puting, robotics and control engineering using the geometric algebra framework. The book also includes over 200 exercises and tips for the development of future computer software packages for extensive calculations in geometric algebra, and a entire section focusing on how to write the subroutines in C++, Matlab and Maple to carry out efficient geometric computations in the geometric algebra framework. Lastly, it shows how program code can be optimized for real-time computations. An essential resource for applied physicists, computer scientists, AI researchers, roboticists and mechanical and electrical engineers, the book clarifies and demon- strates the importance of geometric computing for building autonomous systems to advance cognitive systems research.
Geometric Algebra Applications Vol. III: Integral Transforms, Machine Learning, and Quantum Computing
by Eduardo Bayro-CorrochanoThe goal of Geometric Algebra Applications Vol. III: Integral Transforms, Machine Learning, and Quantum Computing is to present a unified mathematical treatment of diverse problems in the general domain like Clifford Fourier Transforms, Deep Learning and Geometric Algebra Convolutional Neural Networks, Quaternion Quantum Fourier Transform and Geometric Quantum Computing. Topics and features · Introduces nonspecialists to Clifford, or geometric algebra and by example encourages the reader to learn to compute using geometric entities and geometric formulations. · A study in depth for applications of Lie group theory, Lie algebra, projective geometry, and the algebra of incidence using the conformal geometric algebra. · Features the computing frameworks of the linear model n-dimensional affine plane and the nonlinear model of Euclidean space known as the horosphere, and addresses the relationships of these models to conformal, affine, and projective geometries. · Includes a thorough study of Integral transforms: Quaternion and Clifford Transforms, quaternion analytic signal, monogenic signals, Hilbert transform, Riesz transform, Clifford Fourier Transform, Quaternion Wavelet transforms, Quaternion Quantum Fourier Transform, 3D Radon Transform and Hough-Transform in geometric algebra. · Color image processing using the color model HSV, Quaternion Split rotors and motors, and the space-time Lorentz transform. · Geometric neural computing using Split Quaternions, Geometric Algebra neural networks, Clifford Support Vector Machine and Neuro Control. · Thorough discussion of several tasks of computer vision, graphics, neurocomputing, and robotics. machine learning, Deep Learning and CNNs, and Geometric Quantum Computing using the geometric algebra framework. · 130 exercises and hints for the development of future computer software packages for extensive calculations in geometric algebra. An entire section is dedicated to explaining how one should write the subroutines in C++, Phyton, Matlab, and Maple to carry out efficient geometric computations in the geometric algebra framework. Furthermore, it is shown how program code can be optimized for real-time computations. The book is an essential resource for applied mathematicians, physicists, computer scientists, graphics engineering, AI and Machine Learning researchers, roboticists and mechanical and electrical engineers, neurocomputing researchers, neuroscientists, and quantum computing specialists. It clarifies and demonstrates the importance of geometric computing for building autonomous systems and pushes forward advances in geometric cybernetics research.
Geometric and Electronic Properties of Graphene-Related Systems: Chemical Bonding Schemes
by Ngoc Thanh Tran Shih-Yang Lin Chiun-Yan Lin Ming-Fa LinDue to its physical, chemical, and material properties, graphene has been widely studied both theoretically and experimentally since it was first synthesized in 2004. This book explores in detail the most up-to-date research in graphene-related systems, including few-layer graphene, sliding bilayer graphene, rippled graphene, carbon nanotubes, and adatom-doped graphene, among others. It focuses on the structure-, stacking-, layer-, orbital-, spin- and adatom-dependent essential properties, in which single- and multi-orbital chemical bondings can account for diverse phenomena. <P><P>Geometric and Electronic Properties of Graphene-Related Systems: Chemical Bonding Schemes is excellent for graduate students and researchers, but understandable to undergraduates. The detailed theoretical framework developed in this book can be used in the future characterization of emergent materials.
Geometric and Engineering Drawing
by Ken Morling Stéphane DanjouThis introduction to descriptive geometry and contemporary drafting guides the student through the essential principles to create engineering drawings that comply with international standards of technical product specification. This heavily updated new edition now applies to CAD as well as conventional drawing. Extensive new coverage is given of: • International drafting conventions • Methods of spatial visualisation such as multi-view projection • Types of views • Dimensioning • Dimensional and geometric tolerancing • Representation of workpiece and machine elements • Assembly drawings Comprehensible illustrations and clear explanations help the reader master drafting and layout concepts for creating professional engineering drawings. The book provides a large number of exercises for each main topic. This edition covers updated material and reflects the latest ISO standards. It is ideal for undergraduates in engineering or product design, students of vocational courses in engineering communication and technology students covering the transition of product specification from design to production.
Geometric and Engineering Drawing 3E
by K. MorlingThe new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed by anyone preparing or interpreting drawings or designs with plenty of exercises to practice these principles.
A Geometric Approach to the Unification of Symbolic Structures and Neural Networks (Studies in Computational Intelligence #910)
by Tiansi DongThe unification of symbolist and connectionist models is a major trend in AI. The key is to keep the symbolic semantics unchanged. Unfortunately, present embedding approaches cannot. The approach in this book makes the unification possible. It is indeed a new and promising approach in AI. -Bo Zhang, Director of AI Institute, TsinghuaIt is indeed wonderful to see the reviving of the important theme Nural Symbolic Model. Given the popularity and prevalence of deep learning, symbolic processing is often neglected or downplayed. This book confronts this old issue head on, with a historical look, incorporating recent advances and new perspectives, thus leading to promising new methods and approaches. -Ron Sun (RPI), on Governing Board of Cognitive Science SocietyBoth for language and humor, approaches like those described in this book are the way to snickerdoodle wombats. -Christian F. Hempelmann (Texas A&M-Commerce) on Executive Board of International Society for Humor Studies
Geometric Continuum Mechanics (Advances in Mechanics and Mathematics #42)
by Marcelo Epstein Reuven SegevThis contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include:Global stress and hyper-stress theoriesApplications of de Rham currents to singular dislocationsManifolds of mappings for continuum mechanicsKinematics of defects in solid crystalsGeometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.
Geometric Continuum Mechanics and Induced Beam Theories
by Simon R. EugsterThis research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
Geometric Control of Fracture and Topological Metamaterials (Springer Theses)
by Noah MitchellThis thesis reports a rare combination of experiment and theory on the role of geometry in materials science. It is built on two significant findings: that curvature can be used to guide crack paths in a predictive way, and that protected topological order can exist in amorphous materials. In each, the underlying geometry controls the elastic behavior of quasi-2D materials, enabling the control of crack propagation in elastic sheets and the control of unidirectional waves traveling at the boundary of metamaterials. The thesis examines the consequences of this geometric control in a range of materials spanning many orders of magnitude in length scale, from amorphous macroscopic networks and elastic continua to nanoscale lattices.
Geometric Design of Roads Handbook
by Keith WolhuterExplore the Art and Science of Geometric DesignThe Geometric Design of Roads Handbook covers the design of the visible elements of the road-its horizontal and vertical alignments, the cross-section, intersections, and interchanges. Good practice allows the smooth and safe flow of traffic as well as easy maintenance. Geometric design is covered in d
Geometric Dimensioning and Tolerancing: Applications and Techniques for Use in Design, Manufacturing, and Inspection (Mechanical Engineering #96)
by James D. MeadowsExplaining the symbology of dimensioning and tolerancing and introducing a step-by-step system for geometric definition, this book provides examples for the application of geometric controls. The author breaks down the language of geometric product definition into a series of steps that consist of significant questions to be asked at any point in the product definition. He addresses functional requirements and manufacturing techniques, measurement, inspection, and gaging procedures. The book illustrates how symbology is best utilized, in what order it should be applied, and how each geometric control anticipates, integrates, and complements all other geometric controls on a part and in an assembly.
Geometric Dimensioning and Tolerancing: Workbook and Answerbook (Mechanical Engineering #112)
by James D. MeadowsGeometric Dimensioning and Tolerancing: Workbook and Answerbook offers a host of effective examples that utilize the concepts discussed in the reference/text--covering all facets of geometric dimensioning and tolerancing, measurement, inspection, and gauging applicable in any on-the-job situation. The Workbook and Answerbook is a companion to Geometric Dimensioning and Tolerancing: Applications for use in Design, Manufacturing, and Inspection (ISBN: 0-8247-9309-9) and follows the reference text chapter by chapter.
Geometric Feature-Based Fiber Optic Surface Plasmon Resonance Sensors (Springer Tracts in Electrical and Electronics Engineering)
by Sanjeev Kumar Raghuwanshi Santosh Kumar Ritesh KumarThis book focuses on the surface plasmon resonance (SPR) technique covering fibre optic sensor research. It highlights recent advancements in geometric feature-based fibre optic SPR sensors for chemical/biochemical/biosensor applications. The contents also discuss the principle of the SPR sensing technique as well as various designs of fibre optic SPR probes for improving sensor sensitivity. It also includes numerous examples of SPR-based fibre optic sensors with various geometric (such as U-type, taper type, D-type, and interferometric-based) sensors. This volume will be a useful reference to those in academia and industry especially researchers with useful information focusing on fibre optic SPR sensors.
Geometric Mechanics and Its Applications
by Weipeng Hu Chuan Xiao Zichen DengTo make the content of the book more systematic, this book mainly briefs some related basic knowledge reported by other monographs and papers about geometric mechanics. The main content of this book is based on the last 20 years’ jobs of the authors. All physical processes can be formulated as the Hamiltonian form with the energy conservation law as well as the symplectic structure if all dissipative effects are ignored. On the one hand, the important status of the Hamiltonian mechanics is emphasized. On the other hand, a higher requirement is proposed for the numerical analysis on the Hamiltonian system, namely the results of the numerical analysis on the Hamiltonian system should reproduce the geometric properties of which, including the first integral, the symplectic structure as well as the energy conservation law.
Geometric Method for Type Synthesis of Parallel Manipulators (Springer Tracts in Mechanical Engineering)
by Qinchuan Li Jacques M. Hervé Wei YeThis book focuses on the synthesis of lower-mobility parallel manipulators, presenting a group-theory-based method that has the advantage of being geometrically intrinsic. Rotations and translations of a rigid body as well as a combination of the two can be expressed and handled elegantly using the group algebraic structure of the set of rigid-body displacements. The book gathers the authors’ research results, which were previously scattered in various journals and conference proceedings, presenting them in a unified form. Using the presented method, it reveals numerous novel architectures of lower-mobility parallel manipulators, which are of interest to those in the robotics community. More importantly, readers can use the method and tool to develop new types of lower-mobility parallel manipulators independently.
Geometric Methods in Signal and Image Analysis
by Hamid Krim A. Ben HamzaThis comprehensive guide offers a new approach for developing and implementing robust computational methodologies that uncover the key geometric and topological information from signals and images. With the help of detailed real-world examples and applications, readers will learn how to solve complex signal and image processing problems in fields ranging from remote sensing to medical imaging, bioinformatics, robotics, security, and defence. With an emphasis on intuitive and application-driven arguments, this text covers not only a range of methods in use today, but also introduces promising new developments for the future, bringing the reader up-to-date with the state of the art in signal and image analysis. Covering basic principles as well as advanced concepts and applications, and with examples and homework exercises, this is an invaluable resource for graduate students, researchers, and industry practitioners in a range of fields including signal and image processing, biomedical engineering, and computer graphics.
Geometric Modeling and Mesh Generation from Scanned Images (Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Series #6)
by Yongjie Jessica ZhangCutting-Edge Techniques to Better Analyze and Predict Complex Physical Phenomena Geometric Modeling and Mesh Generation from Scanned Images shows how to integrate image processing, geometric modeling, and mesh generation with the finite element method (FEM) to solve problems in computational biology, medicine, materials science, and engineering. Based on the author’s recent research and course at Carnegie Mellon University, the text explains the fundamentals of medical imaging, image processing, computational geometry, mesh generation, visualization, and finite element analysis. It also explores novel and advanced applications in computational biology, medicine, materials science, and other engineering areas. One of the first to cover this emerging interdisciplinary field, the book addresses biomedical/material imaging, image processing, geometric modeling and visualization, FEM, and biomedical and engineering applications. It introduces image-mesh-simulation pipelines, reviews numerical methods used in various modules of the pipelines, and discusses several scanning techniques, including ones to probe polycrystalline materials. The book next presents the fundamentals of geometric modeling and computer graphics, geometric objects and transformations, and curves and surfaces as well as two isocontouring methods: marching cubes and dual contouring. It then describes various triangular/tetrahedral and quadrilateral/hexahedral mesh generation techniques. The book also discusses volumetric T-spline modeling for isogeometric analysis (IGA) and introduces some new developments of FEM in recent years with applications.
Geometric Modeling and Reasoning of Human-Centered Freeform Products
by Charlie C. WangThe recent trend in user-customized product design requires the shape of products to be automatically adjusted according to the human body's shape, so that people will feel more comfortable when wearing these products. Geometric approaches can be used to design the freeform shape of products worn by people, which can greatly improve the efficiency of design processes in various industries involving customized products (e.g., garment design, toy design, jewel design, shoe design, and design of medical devices, etc.). These products are usually composed of very complex geometric shapes (represented by free-form surfaces), and are not driven by a parameter table but a digital human model with free-form shapes or part of human bodies (e.g., wrist, foot, and head models). Geometric Modeling and Reasoning of Human-Centered Freeform Products introduces the algorithms of human body reconstruction, freeform product modeling, constraining and reconstructing freeform products, and shape optimization for improving the manufacturability of freeform products. Based on these techniques, the design automation problem for human-centered freeform products can be fundamentally solved. Researchers and developers working on problems of automatic designing individually customized products can use this book as a reference, and it can also be used in courses in computer-aided product design at the graduate level.
Geometric Modeling of Fractal Forms for CAD
by Christian Gentil Gilles Gouaty Dmitry SokolovDesigning and controlling complex shapes like porous volumes and rough surfaces is a challenge. Fractal geometry is an interesting approach which considerably simplify the problem. Even though underlying concepts reduce the set possible shapes, they generate a surprising variety of shapes. In this book we present a formalism to design such complex objects for geometric aided geometry design applications. The goal of this formalism is to provide to the end user the possibility to manipulate fractal objects as a standard euclidean object with standard tools of CAD system. This formalism encompass curves, surfaces, volumes, as well as NURBS and subdivision surfaces. All theoretical and practical aspects are developed, from the design up to 3D printing.
Geometric Nonlinearity in Structural Behavior: Evaluating Analytical Processes (Synthesis Lectures on Engineering, Science, and Technology)
by Anthony James DeLuzioThis book provides a fundamental understanding of the analytic process involved in solving complex problems, such as the influence of geometric nonlinearity on buckling, vibration, and second-order displacements. Because the book assumes linear behavior the solution can be evaluated using matrix math. Computer software, however, must be used to account for possible nonlinear material behavior due to the local yielding of the members that would result in changes to the elements of the stiffness matrix. Hence the computer solution must be iterative. The number of iterations and the iteration interval may be set manually by the user or internally by the software which can affect the solution.
Geometric Optics
by Antonio Romano Roberto CavaliereThis book--unique in the literature--provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica®. Replete with workout examples and exercises, Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. The work may be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica, or geometric optics.
Geometric Optimal Control
by Urszula Ledzewicz Heinz SchättlerThis book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.
Geometric Procedures for Civil Engineers
by Elias C. Tonias Constantine N. ToniasThis book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice. A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.
Geometric Structures of Information (Signals and Communication Technology)
by Frank NielsenThis book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.
Geometric Tolerancing of Products: Integration Of Functionality:selected Conference Papers Of The 7th Cirp International Seminar On Computer-aided Tolerancing, Held At The École Normale Supérieure De Cachan, France, 24-25 April 2001 (Wiley-iste Ser.)
by François Villeneuve Luc MathieuThis title describes the various research results in the field of geometric tolerancing of products, an activity that highlights the difficult scientific locks. The collection is of great importance for further innovation in the development of industrial products.