Multivariate splines

Charles K. Chui9780898712261, 0898712262

The subject of multivariate splines has become a rapidly growing field of mathematical research. The author presents the subject from an elementary point of view that parallels the theory and development of univariate spline analysis. To compensate for the missing proofs and details, an extensive bibliography has been included. There is a presentation of open problems with an emphasis on the theory and applications to computer-aided design, data analysis, and surface fitting. Applied mathematicians and engineers working in the areas of curve fitting, finite element methods, computer-aided geometric design, signal processing, mathematical modelling, computer-aided design, computer-aided manufacturing, and circuits and systems will find this monograph essential to their research.

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Table of contents :
Multivariate Splines……Page 1
Contents……Page 5
Preface……Page 7
CHAPTER 1 Univariate Splines……Page 9
CHAPTER 2 Box Splines and Multivariate Truncated Powers……Page 23
CHAPTER 3 Bivariate Splines on Three- and Four-Directional Meshes……Page 35
CHAPTER 4 Bivariate Spline Spaces……Page 49
CHAPTER 5 Bezier Representation and Smoothing Techniques……Page 65
CHAPTER 6 Finite Elements and Vertex Splines……Page 79
CHAPTER 7 Computational Algorithms……Page 101
CHAPTER 8 Quasi-lnterpolation Schemes……Page 121
CHAPTER 9 Multivariate Interpolation……Page 137
CHAPTER 10 Shape-Preserving Approximation and Other Applications……Page 165
APPENDIX A Computational Scheme for Interpolation……Page 179
Bibliography……Page 185