Rational Bases and Generalized Barycentrics

Applications to Finite Elements and Graphics

  • Eugene Wachspress

Table of contents

  1. Front Matter
    Pages i-xxi
  2. A Rational Finite Element Basis

    1. Front Matter
      Pages 1-1
    2. Eugene Wachspress
      Pages 3-21
    3. Eugene Wachspress
      Pages 23-36
    4. Eugene Wachspress
      Pages 37-60
    5. Eugene Wachspress
      Pages 61-82
    6. Eugene Wachspress
      Pages 115-132
    7. Eugene Wachspress
      Pages 133-157
    8. Eugene Wachspress
      Pages 159-170
    9. Eugene Wachspress
      Pages 171-205
    10. Eugene Wachspress
      Pages 207-211
  3. Advances in Theory

    1. Front Matter
      Pages 213-213
    2. Eugene Wachspress
      Pages 215-233
    3. Eugene Wachspress
      Pages 235-240
    4. Eugene Wachspress
      Pages 241-242
  4. Computer Programs

    1. Front Matter
      Pages 243-243
    2. Eugene Wachspress
      Pages 245-279
  5. Back Matter
    Pages 281-292

About this book


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.


Applied Algebraic Geometry Barycentric Coordinates Finite Elements Mean Value Coordinates Polytope basis Functions Rational Basis Functions Wachspress Coordinates

Authors and affiliations

  • Eugene Wachspress
    • 1
  1. 1.Department of Civil Engineering and Engineering MechanicsColumbia UniversityNew YorkUSA

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-21613-3
  • Online ISBN 978-3-319-21614-0
  • Buy this book on publisher's site