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

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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

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State Key Lab of CAD&CG

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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

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State Key Lab of CAD&CG

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