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| Author | : Charles A. Micchelli |
| Publisher | : SIAM |
| Total Pages | : 263 |
| Release | : 1995-01-01 |
| Genre | : Mathematics |
| ISBN | : 0898713315 |
Examines concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies them.
| Author | : Nikolay Golovanov |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 0 |
| Release | : 2014-12-24 |
| Genre | : Computer-aided design |
| ISBN | : 9781497473195 |
"The book outlines methods used to construct curves, surfaces, and solids. It describes composition, principles of manipulation, and applications of geometric models. It has been written for university students and specialists in computer-aided design."--Abstract, p. 3.
| Author | : Michael E. Mortenson |
| Publisher | : |
| Total Pages | : 552 |
| Release | : 1997-02-05 |
| Genre | : Computers |
| ISBN | : |
A comprehensive, up-to-date presentation of the indispensable core concepts of geometric modeling Now completely updated to include the most recent developments in the field, Geometric Modeling, Second Edition presents a comprehensive discussion of the core concepts of this subject. It describes and compares all the important mathematical methods for modeling curves, surfaces, and solids, and shows how to transform and assemble these elements into complex models. Written in a style free of the jargon of special applications, this unique book focuses on the essence of geometric modeling and treats it as a discipline in its own right. It integrates the three important functions of geometric modeling: to represent elementary forms (i.e., curves, surfaces, and solids), to shape and assemble these into more complex forms, and to determine concomitant derivative geometric elements (i.e., intersections, offsets, and fillets). With more than 300 illustrations, Geometric Modeling, Second Edition appeals to the reader's visual and intuitive skills in a way that makes it easier to understand its more abstract concepts. An extensive bibliography lists many supporting works, directing the reader to more specialized treatments of this subject. Geometric Modeling, Second Edition serves as an invaluable guide to computer graphics and CAD/CAM specialists, applications designers, scientific programmers, teachers, and students.
| Author | : Charles A. Micchelli |
| Publisher | : SIAM |
| Total Pages | : 265 |
| Release | : 1995-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970067 |
This monograph examines in detail certain concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies these ideas. The two principal themes of the text are the use of piecewise polynomial representation (this theme appears in one form or another in every chapter), and iterative refinement, also called subdivision. Here, simple iterative geometric algorithms produce, in the limit, curves with complex analytic structure. In the first three chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield algorithm for computing cardinal splines is tied into stationary subdivision. This ultimately leads to the construction of prewavelets of compact support. The remainder of the book deals with concepts of "visual smoothness" of curves, along with the intriguing idea of generating smooth multivariate piecewise polynomials as volumes of "slices" of polyhedra. The final chapter contains an evaluation of polynomials by finite recursive algorithms. Each chapter contains introductory material as well as more advanced results.
| Author | : Jean H. Gallier |
| Publisher | : Morgan Kaufmann |
| Total Pages | : 512 |
| Release | : 2000 |
| Genre | : Computers |
| ISBN | : 9781558605992 |
"Curves and Surfaces in Geometric Modeling: Theory and Algorithms offers a theoretically unifying understanding of polynomial curves and surfaces as well as an effective approach to implementation that you can apply to your own work as a graduate student, scientist, or practitioner." "The focus here is on blossoming - the process of converting a polynomial to its polar form - as a natural, purely geometric explanation of the behavior of curves and surfaces. This insight is important for more than just its theoretical elegance - the author demonstrates the value of blossoming as a practical algorithmic tool for generating and manipulating curves and surfaces that meet many different criteria. You'll learn to use this and other related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more." "It will be an essential acquisition for readers in many different areas, including computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision, and motion planning."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
| Author | : Mohamed Elkadi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 252 |
| Release | : 2006-11-02 |
| Genre | : Mathematics |
| ISBN | : 3540332758 |
This book spans the distance between algebraic descriptions of geometric objects and the rendering of digital geometric shapes based on algebraic models. These contrasting points of view inspire a thorough analysis of the key challenges and how they are met. The articles focus on important classes of problems: implicitization, classification, and intersection. Combining illustrative graphics, computations and review articles this book helps the reader gain a firm practical grasp of these subjects.
| Author | : G. Farin |
| Publisher | : Elsevier |
| Total Pages | : 849 |
| Release | : 2002-08-13 |
| Genre | : Computers |
| ISBN | : 0444511040 |
This book provides a comprehensive coverage of the fields Geometric Modeling, Computer-Aided Design, and Scientific Visualization, or Computer-Aided Geometric Design. Leading international experts have contributed, thus creating a one-of-a-kind collection of authoritative articles. There are chapters outlining basic theory in tutorial style, as well as application-oriented articles. Aspects which are covered include: Historical outline Curve and surface methods Scientific Visualization Implicit methods Reverse engineering. This book is meant to be a reference text for researchers in the field as well as an introduction to graduate students wishing to get some exposure to this subject.
| Author | : Nickolas S. Sapidis |
| Publisher | : SIAM |
| Total Pages | : 330 |
| Release | : 1994-01-01 |
| Genre | : Computers |
| ISBN | : 9781611971521 |
This state-of-the-art study of the techniques used for designing curves and surfaces for computer-aided design applications focuses on the principle that fair shapes are always free of unessential features and are simple in design. The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee fairness, and assist the user in identifying and removing shape aberrations in a surface model without destroying the principal shape characteristics of the model. Aesthetic aspects of geometric modeling are of vital importance in industrial design and modeling, particularly in the automobile and aerospace industries. Any engineer working in computer-aided design, computer-aided manufacturing, or computer-aided engineering will want to add this volume to his or her library. Researchers who have a familiarity with basic techniques in computer-aided graphic design and some knowledge of differential geometry will find this book a helpful reference. It is essential reading for statisticians working on approximation or smoothing of data with mathematical curves or surfaces.
| Author | : Guido Brunnett |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 473 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 3662074435 |
Geometric Modeling and Scientific Visualization are both established disciplines, each with their own series of workshops, conferences and journals. But clearly both disciplines overlap; this observation led to the idea of composing a book on Geometric Modeling for Scientific Visualization.
| Author | : Max K. Agoston |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 960 |
| Release | : 2005-01-04 |
| Genre | : Computers |
| ISBN | : 9781852338183 |
Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modeling, this two-volume work covers implementation and theory in a thorough and systematic fashion. It covers the computer graphics part of the field of geometric modeling and includes all the standard computer graphics topics. The CD-ROM features two companion programs.
