Matching admissible G 2 Hermite data by a biarc-based subdivision scheme (Full Version) Chongyang Deng a,b , Weiyin Ma ∗,b a Institute of Applied Mathematics and Engineering Computations, Hangzhou Dianzi University, Hangzhou 310018, China b Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Kowloon, Hong Kong, China Abstract Spirals are curves with single-signed, monotone increasing or decreasing curvature. A spiral can only interpolate certain G 2 Hermite data that is referred to as admissible G 2 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 G 2 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 G 2 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. Key words: Geometry driven subdivision; Nonlinear subdivision scheme; Admissible G 2 Hermite interpolation; Spiral; Monotone curvature; Shape preserving * Corresponding author Email addresses: dcy@hdu.edu.cn (Chongyang Deng), mewma@cityu.edu.hk (Weiyin Ma ) Preprint submitted to Computer Aided Geometric Design March 18, 2012