Multivariate Spline FunctionsandTheirApplications

This book deals with the algebraic geometric method of studying multivariate splines. Topics treated include: the theory of multivariate spline spaces, higher dimensional spline, rational spline, piecewise algebraic variety (including piecewise algebraic curve and surface) and applications in the finite element method and computer aided geometric design. Many new results are given. .
This volume will be of interest to researchers and graduate students whose work involves approximations and expansions, numerical analysis, computational geometry, image processing and CAD/CAM. ...

Chapter 1 Introduction to Multivariate Spline Functions
1.1 Basic frame of multivariate spline functions.
1.2 Generalized truncated power function and general representation of multivariate spline functions
1.3 Interpolation by multivariate spline functions
1.4 Weighted Spline and splines with different smoothness
1.5 Introduction to multivariate rational splines
1.6 N-Dimensional Spline Functions
Chapter 2 Multivariate spline spaces
2.1 Multivariate spline spaces on cross-cut partitions
2.2 Spline spaces on rectangular and simple cross-cut partitions
2.3 Spline spaces on type-1 triangulations
2.4 Spline spaces on type-2 triangulations
2.5 Spline spaces on some non-uniform triangulations
2.6 Spline spaces with boundary conditions on uniform type-1 and type-2 triangulations
2.7 Spline spaces with boundary conditions on non-uniform type-2 triangulations
2.8 Dimension of spline space Skμ(Δ) on triangulations
2.9 Decomposition method for studying multivariate splines
2.9.1 Examples
Chapter 3 Other methods for studying multivariate spline functions

As is known, the book named "Multivariate spline functions and their applications" has been published by the Science Press in 1994. . This book is an English edition based on the original book mentioned above with many changes, including that of the structure of a cubic C1-interpolation in n-dimensional spline spaces, and more detail on triangulations have been added in this book. Special cases of multivariate spline functions (such as step functions, polygonal functions, and piecewise polynomials) have been examined mathematically for a ..