Curves and surfaces in geometric modeling : theory and algorithms
著者
書誌事項
Curves and surfaces in geometric modeling : theory and algorithms
（The Morgan Kaufmann series in computer graphics and geometric modeling）
Morgan Kaufmann, c2000
大学図書館所蔵 件 / 全27件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
この図書・雑誌をさがす
注記
Includes bibliographical references (p. 467-471) and index
内容説明・目次
内容説明
"Curves and Surfaces for Geometric Design" offers both a theoretically unifying understanding of polynomial curves and surfaces and an effective approach to implementation that you can bring to bear on your own work whether you're a graduate student, scientist, or practitioner. Inside, the focus 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 far more than its theoretical elegance, for the author proceeds to demonstrate 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 related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more.The product of groundbreaking research by a noteworthy computer scientist and mathematician, this book is destined to emerge as a classic work on this complex subject.
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. This book achieves a depth of coverage not found in any other book in this field.It offers a mathematically rigorous, unifying approach to the algorithmic generation and manipulation of curves and surfaces; covers basic concepts of affine geometry, the ideal framework for dealing with curves and surfaces in terms of control points; details (in Mathematica) many complete implementations, explaining how they produce highly continuous curves and surfaces; presents the primary techniques for creating and analyzing the convergence of subdivision surfaces (Doo-Sabin, Catmull-Clark, Loop), and contains appendices on linear algebra, basic topology, and differential calculus.
目次
1 Introduction 2 Basics of Affine Geometry 3 Introduction to the Algorithmic Geometry of Polynomial Curves 4 Multiaffine Maps and Polar Forms 5 Polynomial Curves as Be'zier Curves 6 B-Spline Curves 7 Polynomial Surfaces 8 Subdivision Algorithms for Polynomial Surfaces 9. Polynomial Spline Surfaces and Subdivision Surfaces 10 Embedding an Affine Space in a Vector Space 11 Tensor Products and Symmetric Tensor Products 12 Appendix 1: Linear Algebra 13 Appendix 2: Complements of Affine Geometry 14 Appendix 3: Topology 15 Appendix 4: Differential Calculus
「Nielsen BookData」 より
