Interpolation by $G^2$ Quintic Pythagorean-Hodograph Curves

Gašper Jaklič
2014 Numerical Mathematics: Theory, Methods and Applications  
In this paper, the G 2 interpolation by Pythagorean-hodograph (PH) quintic curves in R d , d ≥ 2, is considered. The obtained results turn out as a useful tool in practical applications. Independently of the dimension d, they supply a G 2 quintic PH spline that locally interpolates two points, two tangent directions and two curvature vectors at these points. The interpolation problem considered is reduced to a system of two polynomial equations involving only tangent lengths of the
more » ... of the interpolating curve as unknowns. Although several solutions might exist, the way to obtain the most promising one is suggested based on a thorough asymptotic analysis of the smooth data case. The numerical algorithm traces this solution from a particular set of data to the general case by a homotopy continuation method. Numerical examples confirm the efficiency of the proposed method.
doi:10.4208/nmtma.2014.1314nm fatcat:2cgbtbphdrhynevwt5pndkyf7m