Multivariate Spline Functions and Their Applications

2001
ISBN: 978-0-7923-6967-7
Verlag: Springer Netherlands

Buch, Englisch, 512 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 2010 g

Reihe: Mathematics and Its Applications

As is known, the book named "Multivariate spline functions and their applications" has been published by the Science Press in 1994. This book is an English edition based on the original book mentioned 1 above with many changes, including that of the structure of a cubic - interpolation in n-dimensional spline spaces, and more detail on triangu lations have been added in this book. Special cases of multivariate spline functions (such as step functions, polygonal functions, and piecewise polynomials) have been examined math ematically for a long time. I. J. Schoenberg (Contribution to the problem of application of equidistant data by analytic functions, Quart. Appl. Math., 4(1946), 45 - 99; 112 - 141) and W. Quade & L. Collatz (Zur Interpo lations theories der reellen periodischen function, Press. Akad. Wiss. (PhysMath. KL), 30(1938), 383- 429) systematically established the the ory of the spline functions. W. Quade & L. Collatz mainly discussed the periodic functions, while I. J. Schoenberg's work was systematic and com plete. I. J. Schoenberg outlined three viewpoints for studing univariate splines: Fourier transformations, truncated polynomials and Taylor ex pansions. Based on the first two viewpoints, I. J. Schoenberg deduced the B-spline function and its basic properties, especially the basis func tions. Based on the latter viewpoint, he represented the spline functions in terms of truncated polynomials. These viewpoints and methods had significantly effected on the development of the spline functions.

Zielgruppe

Research

Fachgebiete

• Technische Wissenschaften Technik Allgemein Konstruktionslehre und -technik
• Mathematik | Informatik EDV | Informatik Informatik
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Grafikprogrammierung
• Geisteswissenschaften Design Produktdesign, Industriedesign
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Spiele-Programmierung, Rendering, Animation
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik

Inhaltsverzeichnis

1 Introduction to Multivariate Spline Functions.- 2 Multivariate spline spaces.- 3 Other methods for studying multivariate spline functions.- 4 Higher-dimensional spline spaces.- 5 Rational spline functions.- 6 Piecewise algebraic curves and surfaces.- 7 Applications of multivariate spline functions in finite element method and CAGD.- References.