Optimal Single Biarc Fitting and its Applications

AbstractThis paper proposes a new approach for fitting an optimized biarc to a given 2D polygon and its two end tangents. A biarc can be constructed which matches two end points and two end tangents, but an additional constraint is required to make the biarc unique. The conventional approach to biarc construction, which has been adopted in arc spline approximation, introduces additional constraints to uniquely determine the biarc. Instead of imposing such constraints, the proposed approach exploits the inherent freedom in the choice of the biarc to achieve a better fit minimizing the distance between the polygon and the biarc. The approach is simple in concept and acceptable in computation. When applied in arc spline approximation tasks, the approach can play an important role in reducing the number of segments in the resulting arc spline. Some experimental results demonstrate its usefulness and quality.