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Polynomial splines ➤ is a polynomial spline of degree n with knots iff • Piecewise polynomial (of degree n) within each interval • Higher-order continuity at the knots of ➤ Effective degrees of freedom is 1 ➤ “Cardinal splines”: • Unit spacing: • ∞ number of knots 4
Polynomial B-splines ➤ B-spline of degree n ➤ Symmetric B-spline ➤ Key properties • compact support • piecewise polynomial • positivity • smoothness (continuity) [Schoenberg, 1946] 5
Page 1 and 2: Point Lattices in Computer Graphics
Page 3: Notations ➤ one-sided ➤ Fourier
Page 7 and 8: Fundamental B-spline properties ➤
Page 9 and 10: B-spline differential property “p
Page 11 and 12: Spline fitting ➤ How to find the
Page 13 and 14: Spline interpolation ➤ Discrete B
Page 15 and 16: Spline interpolation ➤ Interpolat
Page 17 and 18: Spline fitting: (2) smoothing splin
Page 19 and 20: Spline fitting: (3) least-square sp
Page 21 and 22: Least-square spline ➤ Special cas
Page 23 and 24: Quantitative approximation quality
Page 25 and 26: High-quality image interpolation pe
Page 27 and 28: High-quality isosurface rendering
Page 29 and 30: Wavelets ➤ Admissible scaling fun
Page 31 and 32: Haar wavelet transform revisited +
Page 33 and 34: Wavelets ➤ Wavelets act as differ
Page 35 and 36: Hexagonal lattices r 2 Voronoi cell
Page 37 and 38: Hex-splines ➤ Basis functions for
Page 39 and 40: Hex-splines ➤ Basis functions for
Page 41 and 42: Hex-splines versus B-splines ➤ Ke
Page 43 and 44: Hex-splines versus B-splines ➤ Cl
Page 45: And finally ➤ Many thanks go to M

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