Matching admissible image Hermite data by a biarc-based subdivision scheme Original Research Article

Spirals are curves with single-signed, monotone increasing or decreasing curvature. A spiral can only interpolate certain image Hermite data that is referred to as admissible image 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 image 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 image 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.