Generation & Application Of G～2-Continuity Interpolation Curve With The Arc Length As Its Parameter

In GCAD,the modeling methods of curve play the most important role. For many years, people have devoted to looking for the methods of the modeling curve, especially those for the curve interpolation are of great variety. However, most of them were merely studied interpolation curves with general parameters. As we know, the curvature and the arc length are intrinsic to the curve itself. Therefore, a method for generating the interpolation curve with the curvature as the interpolation condition and with the arc length as the parameter is actually the one solving the generated problems from the nature of the curve, which really attracts the attention of many researchers. In this paper, we begin with the linear interpolation of the curvature given at the interpolation points, with the arc length as the parameter, we get the interpolation method of the curve through constructing the linear curvature, besides, to make the total curve reach G~2-continuity, we intersect an arbitrary point into any two points, between each segment we further make a fraction linear curvature, and then with the arc length as the parameter and on condition of the given values of the interpolation points and curvatures, we obtain methods for achieving a geometric spline curve with G~2-continuity and also providing the numerical solutions. This is the very method that conveniently getting the arc length for the arbitrary segment or general of the curve, and the changing curvature. Finally, we attach to exact examples to provide some illustrations.