In this paper? we discussed the existence and uniqueness and approximation degree of interpolation splines by S: with the type - Ⅱ triangulations on rectangular.
A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape paramet...A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape parameters. Comput. Aided Geom. Design, 28：151-163 （2011）], is proposed. Without solving a linear system, the spline curves can be used to interpolate sets of points with C2 continuity partly or entirely. The shape parameters have a predictable adjusting role on the sp[ine curves.展开更多
This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precisio...This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An approach to determining the freedom degrees is given, the continuity equations for constructing C2 quartic spline curve are discussed, and a new method for constructing C2 quartic spline surface is presented. The advantages of the new method are that the equations that the surface has to satisfy are strictly row diagonally dominant, and the discontinuous points of the surface are at the given data points. The constructed surface has the precision of quartic polynomial. The comparison of the interpolation precision of the new method with cubic and quartic spline methods is included.展开更多
文摘In this paper? we discussed the existence and uniqueness and approximation degree of interpolation splines by S: with the type - Ⅱ triangulations on rectangular.
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.20206033)湖南省自然科学基金(the Natural Science Foundation of Hunan Province of China under Grant No.06JJY4073)湖南省教育厅科研资助项目(No.06C791)
基金Supported by the National Natural Science Foundation of China(No.10871208,No.60970097)Graduate Students Scientific Research Innovation Project of Hunan Province(No.CX2012B111)+1 种基金the Postdoctoral Science Foundation of China(No.2015M571931)the Fundamental Research Funds for the Central Universities(No.2017MS121)
文摘A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape parameters. Comput. Aided Geom. Design, 28：151-163 （2011）], is proposed. Without solving a linear system, the spline curves can be used to interpolate sets of points with C2 continuity partly or entirely. The shape parameters have a predictable adjusting role on the sp[ine curves.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 60173052)Shandong Province Key Natural Science Foundation (Grant No. Z2001G01).
文摘This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An approach to determining the freedom degrees is given, the continuity equations for constructing C2 quartic spline curve are discussed, and a new method for constructing C2 quartic spline surface is presented. The advantages of the new method are that the equations that the surface has to satisfy are strictly row diagonally dominant, and the discontinuous points of the surface are at the given data points. The constructed surface has the precision of quartic polynomial. The comparison of the interpolation precision of the new method with cubic and quartic spline methods is included.
