Spline functions on triangulations / Ming-Jun Lai and Larry L. Schumaker.

Format:

Book

Author/Creator:

Lai, Ming-Jun, author.

Schumaker, Larry L., 1939- author.

Series:

Encyclopedia of mathematics and its applications ; v. 110.

Encyclopedia of mathematics and its applications ; volume 110

Language:

English

Subjects (All):

Spline theory.

Physical Description:

1 online resource (xv, 592 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2007.

Language Note:

English

Summary:

Spline functions are universally recognized as highly effective tools in approximation theory, computer-aided geometric design, image analysis, and numerical analysis. The theory of univariate splines is well known but this text is the first comprehensive treatment of the analogous bivariate theory. A detailed mathematical treatment of polynomial splines on triangulations is outlined, providing a basis for developing practical methods for using splines in numerous application areas. The detailed treatment of the Bernstein-Bézier representation of polynomials will provide a valuable source for researchers and students in CAGD. Chapters on smooth macro-element spaces will allow engineers and scientists using the FEM method to solve partial differential equations numerically with new tools. Workers in the geosciences will find new tools for approximation and data fitting on the sphere. Ideal as a graduate text in approximation theory, and as a source book for courses in computer-aided geometric design or in finite-element methods.

Contents:

Bivariate polynomials

Bernstein-Bézier methods for bivariate polynomials

B-patches

Triangulations and quadrangulations

Bernstein-Bézier methods for Spline spaces

C¹ macro-element spaces

C² macro-element spaces

Cr macro-element spaces

Dimension of Spline spaces

Approimation power of Spline spaces

Stable local minimal determining sets

Bivariate box Splines

Spherical Splines

Approximation power of spherical Splines

Trivariate polynomials

Tetrahedral partitions

Trivariate Splines

Trivariate macro-element spaces.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88341-0

1-107-38407-9

1-107-38758-2

0-511-88947-X

1-107-39891-6

0-511-72158-7

1-107-39050-8

1-107-39530-5

OCLC:

862614509