Curve approximation by G1 arc splines with a limited number of types of curvature and length

Abstract

A method for approximating planar curves by G1 continuous arc splines with a limited number of types of curvatures and lengths, named k-arc splines, is proposed. A k-arc spline is a particular arc spline, and it has only k types of arcs less than the total number of segments. Due to this property, k-arc splines require discrete variables that relate segments and k types of arcs for representation. Therefore k-arc spline approximation problems must deal with discrete variables in contrast to general arc spline approximation problems. The authors present a method to appropriately estimate these variables from curvature values of a target curve. The proposed method enables a formulation of the approximation problem as a continuous optimization problem that conventional optimization algorithms can solve efficiently. The estimation method also provides a suitable initial solution for the algorithms. Some examples to show the broad applicability of the proposed algorithm are shown.