Dividing G^2 Hermite Data into Admissible G^2 Hermite Data by Biarcs

A planar spiral is a kind of curve with single-signed,monotone increasing or decreasing curvature.A spiral can only interpolate a group of admissible G^2 Hermite data(G^2 Hermite data which can be interpolated by spiral).In this paper,we present a biarc-based method for interpolating C-shaped inadmissible G^2 Hermite dataA,T A,OA;B,T B,OBby piecewise spirals.Based on the biarc matching the corresponding G1 Hermite data,one or two new points and their tangents,curvatures are inserted,so that the inadmissible data can be divided into at most three groups of admissible data.Depending on the different positions of the biarc matching G1 data,three methods are proposed.Then piecewise spirals are given to match the divided data.We can generate at most three piecewise spirals for arbitrary C-shaped inadmissible data,and thoroughly solved the problem of interpolating arbitrary data with least spiral segments.It has potential application value to highway designs,railway routes and other geometric design curves.Several examples are given to demonstrate the proposed method.