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Overview ➤ B-splines: <strong>the</strong> right tool for interpolation • fundamental properties • spline fitting • interpolation; smoothing; least-squares • quantitative approximation quality ➤ A primer to <strong>the</strong> wavelet transform • multi-resolution, semi-orthogonal wavelets ➤ 2-D extension: hex-splines on any regular periodic lattice • hexagonal versus Cartesian lattice 2
Notations ➤ one-sided ➤ Fourier transform ➤ Z-transform 3
Page 1: Point Lattices in Computer Graphics
Page 5 and 6: Polynomial B-splines ➤ B-spline o
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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