Matching admissible G2 Hermite data by a biarc-based subdivision scheme

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. ► This article presents a geometry driven interpolating subdivision scheme. ► The scheme interpolates an arbitrary set of planar admissible G2 Hermite data. ► It produces a global G2 spiral spline curve. ► It easily generates an exact offset curve of the limit spiral spline curve with the same subdivision scheme.