Mathematical Aspects of Geometric Modeling

Mathematical Aspects of Geometric Modeling
Title Mathematical Aspects of Geometric Modeling PDF eBook
Author Charles A. Micchelli
Publisher SIAM
Pages 263
Release 1995-01-01
Genre Mathematics
ISBN 0898713315

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Examines concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies them.

Mathematical Aspects of Geometric Modeling

Mathematical Aspects of Geometric Modeling
Title Mathematical Aspects of Geometric Modeling PDF eBook
Author Charles A. Micchelli
Publisher SIAM
Pages 265
Release 1995-01-01
Genre Mathematics
ISBN 9781611970067

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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.

Geometric Modeling

Geometric Modeling
Title Geometric Modeling PDF eBook
Author Michael E. Mortenson
Publisher
Pages 536
Release 2006
Genre Computers
ISBN

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Completely updated to include the most recent developments in the field, the third edition like the two previous editions, emphasizes clarity and thoroughness in the mathematical development of its subjects. It is written in a style that is free of jargon of special applications, while integrating the three important functions of geometric modeling: to represent elementary forms (curves, surfaces, and solids), to shape and assemble these into complex forms, and to determine geometric properties and relationships. With hundreds of illustrations, this unique book appeals to the readers visual and intuitive skills in a way that makes it easier to understand its more abstract concepts. Upper-division and graduate students, teachers, and professionals studying, teaching or practicing geometric modeling, 3D modeling, computational geometry, computer graphics applications, animation, CAD/CAM, and related subjects will find this to be a very valuable reference. Introduction. Curves. Hermite Curves. Bezier Curvers. B-Spline Curves. Surfaces. Bicubic Hermite Surfaces. Bezier Surfaces. B-Spline Surfaces. Solids. Complex Model Construction. Geometric Properties. Answers to Selected Exercises. Index.

Curves and Surfaces in Geometric Modeling

Curves and Surfaces in Geometric Modeling
Title Curves and Surfaces in Geometric Modeling PDF eBook
Author Jean H. Gallier
Publisher Morgan Kaufmann
Pages 512
Release 2000
Genre Computers
ISBN 9781558605992

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"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

Geometric Modeling

Geometric Modeling
Title Geometric Modeling PDF eBook
Author Nikolay Golovanov
Publisher Createspace Independent Publishing Platform
Pages 0
Release 2014-12-24
Genre Computer-aided design
ISBN 9781497473195

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"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.

Geometric Modeling for Scientific Visualization

Geometric Modeling for Scientific Visualization
Title Geometric Modeling for Scientific Visualization PDF eBook
Author Guido Brunnett
Publisher Springer Science & Business Media
Pages 512
Release 2003-11-17
Genre Mathematics
ISBN 9783540401162

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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.

Algebraic Geometry and Geometric Modeling

Algebraic Geometry and Geometric Modeling
Title Algebraic Geometry and Geometric Modeling PDF eBook
Author Mohamed Elkadi
Publisher Springer Science & Business Media
Pages 252
Release 2006-11-02
Genre Mathematics
ISBN 3540332758

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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.