Chapter 1 Mathematical Foundations of Computational Geometry 1.1 Weierstrass Theorem 1.2 Uniform Approximation 1.2.1 Borel Existence Theorem 1.2.2 Best Approximation Theorem 1.2.3 Tchebysherv Polynomials and Their Applications 1.3 Square Approximation 1.3.1 The Method of Least Squares 1.3.2 Spatial L2ρ(χ) 1.3.3 Orthogonal Functions and Generalized Fourier Series 1.4 Polynomial Interpolation 1.4.1 Lagrange Interpolation Formula 1.4.2 Newton Interpolation Formula 1.4.3 Interpolation Remainder 1.4.4 Hermite Interpolation Formula 1.4.5 Introduction to Multivariate Polynomial Interpolation 1.5 Univariate Spline 1.5.1 Trigonometric Spline Function Interpolation 1.5.2 Spline Function and Its Properties 1.6 Introduction to Multivariate Spline 1.6.1 Basic Theorem of Multivariate Spline Space 1.6.2 Dimension of Multivariate Spline Space 1.6.3 Multivariate B-Spline and Quasi-Interpolation Operator Exercise 1 Chapter 2 Basic Theory of Curves and Surfaces 2.1 Vectors and Vector Functions 2.2 Representation of Curves and Surfaces 2.2.1 Parametric Representation of Curves and Surfaces 2.2.2 Algebraic Representation of Curves and Surfaces Chapter 3 Bezier Curves and Surfaces Chapter 4 B-Spline Curves and Surfaces Chapter 5 Rational Bezier Curves and Surfaces and NURBS Methods Chapter 6 Subdivision Methods Chapter 7 Radial Basis Functions References
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