Rational Bases and Generalized Barycentrics

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.

Stands as the only monograph examining theory for constructing interpolation functions for a general class of elements Provides mathematicians working in algebraic geometry applications of deep concepts in that field Reinforces understanding of basic concepts in approximation related to patchwork representation of physical systems Serves as a reference for students in associated research areas, such as finite elements, animation, algebraic geometry, approximation theory, generalized barycentric coordinates Maximizes reader knowledge of existing tools such as basis functions for standard finite element and graphics triangle and rectangle elements

Inhalt

Part I.- Theorems and lemmas.- Chapter 1 Patchwork approximation in numerical analysis.- Chapter 2 The quadrilateral.- Chapter 3 Rational wedges for selected polycons.- Chapter 4. Algebraic geometry foundations.- Chapter 5 Rational wedge construction for polycons and polypols.- Chapter 6 Approximation of higher degree.- Chapter 7 Three-dimensional approximation.- Chapter 8 A rational solution to an irrational problem.- Chapter 9 Finite element discretization.- Chapter 10 Two-level computation.- Part II.- Chapter 11. Two dimensions.- Chapter 12. Higher dimensions.- Chapter 13. Forty years after.- Part III.- Chapter 14. Computer programs.