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