Gerald Farin - Böcker

The Geometry Toolbox takes a novel and particularly visual approach to teaching the basic concepts of two- and three-dimensional geometry. It explains the geometry essential for today's computer modeling, computer graphics, and animation systems. While the basic theory is completely covered, the emphasis of the book is not on abstract proofs but rather on examples and algorithms. The Geometry Toolbox is the ideal text for professionals who want to get acquainted with the latest geometric tools. The chapters on basic curves and surfaces form an ideal stepping stone into the world of graphics and modeling. It is also a unique textbook for a modern introduction to linear algebra and matrix theory.

Putting the G into CAGD, the authors provide a much-needed practical and basic introduction to computer-aided geometric design. This book will help readers understand and use the elements of computer-aided geometric design, curves and surfaces, without the mathematical baggage that is necessary only for more advanced work. Though only minimal background in mathematics is needed to understand the bookís concepts, the book covers an amazing array of topics such as Bezier and B-spline curves and their corresponding surfaces, subdivision surfaces, and NURBS (Non-Uniform Rational B-Splines). Also included are techniques such as interpolation and least squares methods.

Linear algebra is growing in importance. 3D entertainment, animations in movies and video games are developed using linear algebra. Animated characters are generated using equations straight out of this book. Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology.The Fourth Edition of this popular text introduces linear algebra in a comprehensive, geometric, and algorithmic way. The authors start with the fundamentals in 2D and 3D, then move on to higher dimensions, expanding on the fundamentals and introducing new topics, which are necessary for many real-life applications and the development of abstract thought. Applications are introduced to motivate topics.The subtitle, A Geometry Toolbox, hints at the book’s geometric approach, which is supported by many sketches and figures. Furthermore, the book covers applications of triangles, polygons, conics, and curves. Examples demonstrate each topic in action.This practical approach to a linear algebra course, whether through classroom instruction or self-study, is unique to this book.New to the Fourth Edition:Ten new application sectionsA new section on change of basis. This concept now appears in several placesChapters 14-16 on higher dimensions are notably revisedA deeper look at polynomials in the gallery of spacesIntroduces the QR decomposition and its relevance to least squaresSimilarity and diagonalization are given more attention, as are eigenfunctionsA longer thread on least squares, running from orthogonal projections to a solution via SVD and the pseudoinverseMore applications for PCA have been addedMore examples, exercises, and more on the kernel and general linear spacesA list of applications has been added in Appendix AThe book gives instructors the option of tailoring the course for the primary interests of their students: mathematics, engineering, science, computer graphics, and geometric modeling.

This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coordinate systems, an introduction to facets (planes and triangle meshes) and an introduction to computer graphics. The scientific computing part of the book covers topics in numerical linear algebra (basics, solving linear system, eigen-problems, SVD, and PCA) and numerical calculus (basics, data fitting, dynamic processes, root finding, and multivariate functions). The visualization component of the book is separated into three parts: empirical data, scalar values over 2D data, and volumes.

Linear algebra is growing in importance. 3D entertainment, animations in movies and video games are developed using linear algebra. Animated characters are generated using equations straight out of this book. Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology.The Fourth Edition of this popular text introduces linear algebra in a comprehensive, geometric, and algorithmic way. The authors start with the fundamentals in 2D and 3D, then move on to higher dimensions, expanding on the fundamentals and introducing new topics, which are necessary for many real-life applications and the development of abstract thought. Applications are introduced to motivate topics.The subtitle, A Geometry Toolbox, hints at the book’s geometric approach, which is supported by many sketches and figures. Furthermore, the book covers applications of triangles, polygons, conics, and curves. Examples demonstrate each topic in action.This practical approach to a linear algebra course, whether through classroom instruction or self-study, is unique to this book.New to the Fourth Edition:Ten new application sectionsA new section on change of basis. This concept now appears in several placesChapters 14-16 on higher dimensions are notably revisedA deeper look at polynomials in the gallery of spacesIntroduces the QR decomposition and its relevance to least squaresSimilarity and diagonalization are given more attention, as are eigenfunctionsA longer thread on least squares, running from orthogonal projections to a solution via SVD and the pseudoinverseMore applications for PCA have been addedMore examples, exercises, and more on the kernel and general linear spacesA list of applications has been added in Appendix AThe book gives instructors the option of tailoring the course for the primary interests of their students: mathematics, engineering, science, computer graphics, and geometric modeling.

This fifth edition has been fully updated to cover the many advances made in CAGD and curve and surface theory since 1997, when the fourth edition appeared. Material has been restructured into theory and applications chapters. The theory material has been streamlined using the blossoming approach; the applications material includes least squares techniques in addition to the traditional interpolation methods. In all other respects, it is, thankfully, the same. This means you get the informal, friendly style and unique approach that has made Curves and Surfaces for CAGD: A Practical Guide a true classic.

The book's unified treatment of all significant methods of curve and surface design is heavily focused on the movement from theory to application. The author provides complete C implementations of many of the theories he discusses, ranging from the traditional to the leading-edge. You'll gain a deep, practical understanding of their advantages, disadvantages, and interrelationships, and in the process you'll see why this book has emerged as a proven resource for thousands of other professionals and academics.

Provides authoritative and accessible information for those working with or developing computer-aided geometric design applications Covers all significant CAGD curve and surface design techniques-from the traditional to the experimental Includes a new chapter on recursive subdivision and triangular meshes Presents topical programming exercises useful to professionals and students alike

The Geometry Toolbox takes a novel and particularly visual approach to teaching the basic concepts of two- and three-dimensional geometry. It explains the geometry essential for today's computer modeling, computer graphics, and animation systems. While the basic theory is completely covered, the emphasis of the book is not on abstract proofs but rather on examples and algorithms. The Geometry Toolbox is the ideal text for professionals who want to get acquainted with the latest geometric tools. The chapters on basic curves and surfaces form an ideal stepping stone into the world of graphics and modeling. It is also a unique textbook for a modern introduction to linear algebra and matrix theory.

Non-Uniform Rational B-Splines have become the de facto standard in CAD/CAM and computer graphics. This well-known book covers NURBS from their geometric beginnings to their industrial applications. The second edition incorporates new results and a chapter on Pythagorean curves, a development that shows promise in applications such as NC machining or robot motion control. Includes more than fifty new figures.

Putting the G into CAGD, the authors provide a much-needed practical and basic introduction to computer-aided geometric design. This book will help readers understand and use the elements of computer-aided geometric design, curves and surfaces, without the mathematical baggage that is necessary only for more advanced work. Though only minimal background in mathematics is needed to understand the bookís concepts, the book covers an amazing array of topics such as Bezier and B-spline curves and their corresponding surfaces, subdivision surfaces, and NURBS (Non-Uniform Rational B-Splines). Also included are techniques such as interpolation and least squares methods.

This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coordinate systems, an introduction to facets (planes and triangle meshes) and an introduction to computer graphics. The scientific computing part of the book covers topics in numerical linear algebra (basics, solving linear system, eigen-problems, SVD, and PCA) and numerical calculus (basics, data fitting, dynamic processes, root finding, and multivariate functions). The visualization component of the book is separated into three parts: empirical data, scalar values over 2D data, and volumes.

In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing,modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applicationsinclude CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany.Topics treated are: curve and surface modelling - non-manifold modelling in CAD - multiresolution analysis of complex geometric models - surface reconstruction - variational design - computational geometry of curves and surfaces - 3D meshing - geometric modelling for scientific visualization - geometric models for biomedical applications

In this volume experts from university and industry are presenting new technologies for solving industrial problems as well as important and practicable impulses for new research.The following topics are treated:- solid modelling- geometry processing- feature modelling- product modelling- surfaces over arbitrary topologies- blending methods- scattered data algorithms- smooting and fairing algorithms- NURBS 21 articles are giving a state-of-the-art survey of the relevant problems and issues in the rapidly growing area of geometric modelling.

19 papers presented by international experts give a state-of-the-art survey of the relevant problems and issues in modeling, CAD/CAM, scientific visualization, and computational geometry. The following topics are treated: - surface design and fairing - subdivision schemes - variational design - NURBS - reverse engineering - physically-based modelling - medical imaging.

This book emerged from a DoE/NSF-sponsored workshop, held in Tahoe City, California, October 2000. About fifty invited participants presented state-of-the-art research on topics such as: - terrain modeling- multiresolution subdivision- wavelet-based scientific data compression- topology-based visualization- data structures, data organization and indexing schemes for scientific data visualization.All invited papers were carefully refereed, resulting in this collection. The book will be of great interest to researchers, graduate students and professionals dealing with scientific visualization and its applications.