Curves and Surfaces in Computer Aided Geometric Design

Softcover Nachdruck of the original 1. Auflage 1988
ISBN: 978-3-642-48954-9
Verlag: Springer

Buch, Englisch, 378 Seiten, Paperback, Format (B × H): 170 mm x 244 mm, Gewicht: 681 g

ThIS IS an English verSIOn of the book m two volumes, entitled "KeiJo Shon Kogaku (1), (2)" (Nikkan Kogyo Shinbun Co.) written in Japanese. The purpose of the book is a umfied and systematic exposition of the wealth of research results m the field of mathematical representation of curves and surfaces for computer aided geometric design that have appeared in the last thirty years. The material for the book started hfe as a set of notes for computer aided geometnc design courses which I had at the graduate schools of both computer SCIence, the umversity of Utah m U.S.A. and Kyushu Institute of Design in Japan. The book has been used extensively as a standard text book of curves and surfaces for students, practtcal engmeers and researchers. With the aim of systematic expositIOn, the author has arranged the book in 8 chapters: Chapter 0: The sIgmficance of mathemattcal representations of curves and surfaces is explained and histoncal research developments in this field are revIewed. Chapter 1: BasIc mathematical theones of curves and surfaces are reviewed and summanzed. Chapter 2: A classical mterpolation method, the Lagrange interpolation, is discussed. Although its use is uncommon in practice, this chapter is helpful in understanding Chaps. 4 and 6. Chapter 3: This chapter dIscusses the Coons surface in detail, which is one of the most important contributions in this field. Chapter 4: The fundamentals of spline functions, spline curves and surfaces are discussed in some detail.

Zielgruppe

Research

Autoren/Hrsg.

Yamaguchi, Fujio

Fachgebiete

• Mathematik | Informatik EDV | Informatik Technische Informatik
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Grafikprogrammierung
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Software Engineering
• Technische Wissenschaften Technik Allgemein Konstruktionslehre und -technik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

0. Mathematical Description of Shape Information.- 0.1 Description and Transmission of Shape Information.- 0.2 Processing and Analysis of Shapes.- 0.3 Mathematical Description of Free Form Shapes.- 0.4 The Development of Mathematical Descriptions of Free Form Curves and Surfaces.- References.- 1. Basic Theory of Curves and Surfaces.- 1.1 General.- 1.2 Curve Theory.- 1.3 Theory of Surfaces.- References.- 2. Lagrange Interpolation.- 2.1 Lagrange Interpolation Curves.- 2.2 Expression in Terms of Divided Differences.- References.- 3. Hermite Interpolation.- 3.1 Hermite Interpolation.- 3.2 Curves.- 3.3 Surfaces.- References.- 4. Spline Interpolation.- 4.1 Splines.- 4.2 Spline Functions.- 4.3 Mathematical Representation of Spline Functions.- 4.4 Natural Splines.- 4.5 Natural Splines and the Minimum Interpolation Property.- 4.6 Smoothing Splines.- 4.7 Parametric Spline Curves.- 4.8 End Conditions on a Spline Curve.- 4.9 Cubic Spline Curves Using Circular Arc Length.- 4.10 B-Splines.- 4.11 Generation of Spline Surfaces.- References.- 5. The Bernstein Approximation.- 5.1 Curves.- 5.2 Surfaces.- References.- 6. The B-Spline Approximation.- 6.1 Uniform Cubic B-Spline Curves.- 6.2 Uniform Bi-cubic B-Spline Surfaces.- 6.3 B-Spline Functions and Their Properties (1).- 6.4 B-Spline Functions and Their Properties (2).- 6.5 Derivation of B-Spline Functions.- 6.6 B-Spline Curve Type (1).- 6.7 B-Spline Curve Type (2).- 6.8 Recursive Calculation of B-Spline Functions.- 6.9 B-Spline Functions and Their Properties (3).- 6.10 B-Spline Curve Type (3).- 6.11 Differentiation of B-Spline Curves.- 6.12 Geometrical Properties of B-Spline Curves.- 6.13 Determination of a Point on a Curve by Linear Operations.- 6.14 Insertion of Knots.- 6.15 Curve Generation by Geometrical Processing.- 6.16 Interpolation of a Sequence of Points with a B-Spline Curve.- 6.17 Matrix Expression of B-Spline Curves.- 6.18 Expression of the Functions C0,0(t), C0,1(t), C1,0(t) and C1,1(t) by B-Spline Functions.- 6.19 General B-Spline Surfaces.- References.- 7. The Rational Polynomial Curves.- 7.1 Derivation of Parametric Conic Section Curves.- 7.2 Classification of Conic Section Curves.- 7.3 Parabolas.- 7.4 Circular Arc Formulas.- 7.5 Cubic/Cubic Rational Polynomial Curves.- 7.6 T-Conic Curves.- References.- Appendix A: Vector Expression of Simple Geometrical Relations.