A new method for determining knots to construct polynomial curves is presented. At each data point, a quadric curve which passes three consecutive points is constructed. The knots for constructing the quadric curve ar...A new method for determining knots to construct polynomial curves is presented. At each data point, a quadric curve which passes three consecutive points is constructed. The knots for constructing the quadric curve are determined by minimizing the internal strain energy, which can be regarded as a function of the angle. The function of the angle is expanded as a Taylor series with two terms, then the two knot intervals between the three consecutive points are defined by linear expression. Between the two consecutive points, there are two knot intervals, and the combination of the two knot intervals is used to define the final knot interval. A comparison of the new method with several existing methods is included.展开更多
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
In order to relieve the deficiency of the usual cubic Hermite spline curves,the quartic Hermite spline curves with shape parameters is further studied in this work. The interpolation error and estimator of the quartic...In order to relieve the deficiency of the usual cubic Hermite spline curves,the quartic Hermite spline curves with shape parameters is further studied in this work. The interpolation error and estimator of the quartic Hermite spline curves are given. And the characteristics of the quartic Hermite spline curves are discussed.The quartic Hermite spline curves not only have the same interpolation and continuity properties of the usual cubic Hermite spline curves, but also can achieve local or global shape adjustment and C;continuity by the shape parameters when the interpolation conditions are fixed.展开更多
基金A preliminary version of this paper appeared in Proc. the 1st Korea-China Joint Conference on Geometric and Visual Computing. Supported by the National Natural Science Foundation of China （Grant Nos. 60403036, 60573114）.
文摘A new method for determining knots to construct polynomial curves is presented. At each data point, a quadric curve which passes three consecutive points is constructed. The knots for constructing the quadric curve are determined by minimizing the internal strain energy, which can be regarded as a function of the angle. The function of the angle is expanded as a Taylor series with two terms, then the two knot intervals between the three consecutive points are defined by linear expression. Between the two consecutive points, there are two knot intervals, and the combination of the two knot intervals is used to define the final knot interval. A comparison of the new method with several existing methods is included.
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Hunan Provincial Natural Science Foundation(2017JJ3124)of Chinathe Scientific Research Fund(14B099)of Hunan Provincial Education Department of China
文摘In order to relieve the deficiency of the usual cubic Hermite spline curves,the quartic Hermite spline curves with shape parameters is further studied in this work. The interpolation error and estimator of the quartic Hermite spline curves are given. And the characteristics of the quartic Hermite spline curves are discussed.The quartic Hermite spline curves not only have the same interpolation and continuity properties of the usual cubic Hermite spline curves, but also can achieve local or global shape adjustment and C;continuity by the shape parameters when the interpolation conditions are fixed.
