Presents information on a study which outlined the blossom approach to the dimension count of bivariate spline space. Smoothness conditions in blossoming form; Application of the approach to the case of Morgan-Scott p...Presents information on a study which outlined the blossom approach to the dimension count of bivariate spline space. Smoothness conditions in blossoming form; Application of the approach to the case of Morgan-Scott partition.展开更多
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
In this paper, the problem of finding the intersection of a triangular Bezier patch and a plane is studied. For the degree that one frequently encounters in practice, i.e. n = 2,3, an efficient and reliable algorithm ...In this paper, the problem of finding the intersection of a triangular Bezier patch and a plane is studied. For the degree that one frequently encounters in practice, i.e. n = 2,3, an efficient and reliable algorithm is obtained, and computational steps are presented.展开更多
基金the 973 Project on Mathematical Mechanics!G1998030600NSF and SF of National Educational Committee of China
文摘Presents information on a study which outlined the blossom approach to the dimension count of bivariate spline space. Smoothness conditions in blossoming form; Application of the approach to the case of Morgan-Scott partition.
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.
基金Supported by NSF and SF ofstate Education Commission of Chlna.Supported by the Ministry of Science and Technology of Slovenija.
文摘In this paper, the problem of finding the intersection of a triangular Bezier patch and a plane is studied. For the degree that one frequently encounters in practice, i.e. n = 2,3, an efficient and reliable algorithm is obtained, and computational steps are presented.
