B-Spline Interpolation and Approximation
B-Spline Interpolation and Approximation
Hongxin Zhang and Jieqing Feng
2006-12-18 State Key Lab of CAD&CG
Zhejiang University
Contents
? Parameter Selection and Knot Vector Generation
? Global Curve Interpolation ? Global Curve Approximation ? Global Surface Interpolation ? Global Surface Approximation ? Assignments
12/18/2006
State Key Lab of CAD&CG
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Parameter Selection and Knot Vector Generation
? Overview ? The Uniformly Spaced Method ? The Chord Length Method ? The Centripetal Method ? Knot Vector Generation ? The Universal Method ? Parameters and Knot Vectors for
Surfaces
12/18/2006
State Key Lab of CAD&CG
3
Overview Parameter Selection and Knot Vector
Generation
? B-spline interpolation
Input a set of data points D0, ..., Dn Find
A B-Spline Curve: C=C(t) n +1 parameters t0, ..., tn
Such that
Dk = C(tk) for all 0 k n.
12/18/2006
State Key Lab of CAD&CG
4
Overview Parameter Selection and Knot Vector
Generation
Examples of B-Spline Interpolation
12/18/2006
State Key Lab of CAD&CG
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