Matching admissible G 2 Hermite data by a biarc-based subdivision scheme

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

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Original languageEnglish
Pages (from-to)363-378
Journal / PublicationComputer Aided Geometric Design
Issue number6
Publication statusPublished - Aug 2012


Spirals are curves with single-signed, monotone increasing or decreasing curvature. A spiral can only interpolate certain G2 Hermite data that is referred to as admissible G2 Hermite data. In this paper we propose a biarc-based subdivision scheme that can generate a planar spiral matching an arbitrary set of given admissible G2 Hermite data, including the case that the curvature at one end is zero. An attractive property of the proposed scheme is that the resulting subdivision spirals are also offset curves if the given input data are offsets of admissible G2 Hermite data. A detailed proof of the convergence and smoothness analysis of the scheme is also provided. Several examples are given to demonstrate some excellent properties and practical applications of the proposed scheme. © 2012 Elsevier B.V. All rights reserved.

Research Area(s)

  • Admissible G 2 Hermite interpolation, Geometry driven subdivision, Monotone curvature, Nonlinear subdivision scheme, Shape preserving, Spiral