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Multi-resolution approximation ➤ m-scale relation ➤ Pyramid or tree algorithms ( ) • fast evaluation of binomial filter n=1 • for high n ~ Gaussian filter 28
Wavelets ➤ Admissible scaling function (“father wavelet”) • Riesz basis conditions • partition of unity • two-scale relation ➤ B-splines are perfect candidates ➤ Then there exists a wavelet such that forms a Riesz basis of L 2 [Mallat-Meyer 1989] 29
Page 1 and 2: Point Lattices in Computer Graphics
Page 3 and 4: Notations ➤ one-sided ➤ Fourier
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: High-quality isosurface rendering
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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