Multi-degree reduction of Bézier curves using reparameterization

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)161-169
Journal / PublicationCAD Computer Aided Design
Volume43
Issue number2
Publication statusPublished - Feb 2011

Abstract

L2-norms are often used in the multi-degree reduction problem of Bzier curves or surfaces. Conventional methods on curve cases are to minimize ∫01∥A(t)-C(t)∥2dt, where C(t) and A(t) are the given curve and the approximation curve, respectively. A much better solution is to minimize ∫01∥A(φ(t))- C(t)∥2dt, where A(φ(t)) is the closest point to point C(t), that produces a similar effect as that of the Hausdorff distance. This paper uses a piecewise linear function L(t) instead of t to approximate the function φ(t) for a constrained multi-degree reduction of Bzier curves. Numerical examples show that this new reparameterization-based method has a much better approximation effect under Hausdorff distance than those of previous methods. © 2010 Elsevier Ltd. All rights reserved.

Research Area(s)

  • Bzier curves, L2-norm, Multi degree reduction, Reparameterization

Citation Format(s)

Multi-degree reduction of Bézier curves using reparameterization. / Chen, Xiao-Diao; Ma, Weiyin; Paul, Jean-Claude.

In: CAD Computer Aided Design, Vol. 43, No. 2, 02.2011, p. 161-169.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review