Spiral arc spline approximation to a planar spiral

摘要

A biarc is a one-parameter family of G1 curves that can satisfy G1 Hermite data at two points. An arc spline approximation to a smooth planar curve can be found by reading G1 Hermite data from the curve and fitting a biarc between each pair of data points. The resulting collection of biarcs forms a G1 arc spline that interpolates the entire set of G1 Hermite data. If the smooth curve is a spiral, it is desirable that the arc spline approximation also be a spiral. Several methods are described for choosing the free parameters of the biarcs so that the arc spline approximation to a smooth spiral is a spiral.