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,th...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 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.展开更多
文摘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 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.
