Interpolation and Curve Fitting

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Blending Functions of Bezier <strong>Curve</strong>s • Also known as degree 3 Bernstein polynomials • Weighted sum of Bernstein polynomials (infinite series) converges uniformly to any continuous function on the interval [0,1] P( u) 3 (1 u ) p 2 3 u(1 u ) p i 2 3u (1 u ) p i 3 u p i T i 1 2 3 Numerical Methods © Wen-Chieh Lin 18
Composing Bezier <strong>Curve</strong>s • Control points at consecutive segments need be collinear to avoid a discontinuity of slope Numerical Methods © Wen-Chieh Lin 19
Page 1 and 2: Interpolation and Curve Fitting Pie
Page 3 and 4: Global vs. Local Control • Does a
Page 5 and 6: Interpolation in Parametric Form
Page 7 and 8: Cubic 3D Curves • Three cubic pol
Page 9 and 10: Hermite Curve Formation— consider
Page 11 and 12: Hermite Curve Formation (cont.) •
Page 13 and 14: Hermite Curve Formation (cont.) •
Page 15 and 16: Blending Functions of Hermite Splin
Page 17: Bezier Curves (cont.) • Variant o
Page 21 and 22: Cubic B-Splines • Basis-spline (B
Page 23 and 24: • From Solving for B-spline Coeff
Page 25 and 26: Blending Functions of Cubic B-Splin
Page 27 and 28: Composing B-splines • Given point
Page 29 and 30: Interpolating on a Surface • Bezi
Page 31 and 32: Numerical Methods © Wen-Chieh Lin
Page 33 and 34: Bezier Surfaces p ( 0,0) p 0,0) 3(
Page 35 and 36: Least Square Approximation • High
Page 37 and 38: Curve Fitting • Given m data poin
Page 39 and 40: Example: curve fitting • Fitting
Page 41 and 42: Example (cont.) • The computed ap
Page 43 and 44: Orthogonality • Space spanned by
Page 45 and 46: Pseudoinverse and Condition Number
Page 47 and 48: Sensitivity and Conditioning • Se
Page 49 and 50: Normal Equation Method • If m ×
Page 51 and 52: Example: Normal Equation Method •

Interpolation and Curve Fitting

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