Rational Bases and Generalized Barycentrics: Applications to Finite Elements and Graphics

✍ Scribed by Eugene Wachspress (auth.)

• Publisher: Springer International Publishing
• Year: 2016
• Tongue: English
• Leaves: 302
• Edition: 1
• Category: Library

✦ Synopsis

This three-part volume explores theory for construction of rational interpolation functions for continuous patchwork approximation. Authored by the namesake of the Wachspress Coordinates, the book develops construction of basis functions for a broad class of elements which have widespread graphics and finite element application. Part one is the 1975 book “A Rational Finite Element Basis” (with minor updates and corrections) written by Dr. Wachspress. Part two describes theoretical advances since 1975 and includes analysis of elements not considered previously. Part three consists of annotated MATLAB programs implementing theory presented in Parts one and two.

✦ Table of Contents

Front Matter....Pages i-xxi
Front Matter....Pages 1-1
Patchwork Approximation in Numerical Analysis....Pages 3-21
The Quadrilateral....Pages 23-36
Rational Wedges for Selected Polycons....Pages 37-60
Algebraic Geometry Foundations....Pages 61-82
Rational Wedge Construction for Polycons and Polypols....Pages 83-113
Approximation of Higher Degree....Pages 115-132
Three-Dimensional Approximation....Pages 133-157
A Rational Solution to an Irrational Problem....Pages 159-170
Finite Element Discretization....Pages 171-205
Two-Level Computation....Pages 207-211
Front Matter....Pages 213-213
Two Dimensions....Pages 215-233
Higher Dimensions....Pages 235-240
Forty Years After....Pages 241-242
Front Matter....Pages 243-243
Computer Programs....Pages 245-279
Back Matter....Pages 281-292

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering; Algebraic Geometry; Partial Differential Equations; Computer Graphics