CAJ | 학술논문

给出了一种带形状参数的三次三角Hermite插值样条曲线，具有标准三次Hermite插值样条曲线完全相同的性质。给定插值条件时，样条曲线的形状可通过改变形状参数的取值进行调控。在适当条件下，该样条曲线对应的Ferguson曲线可精确表示椭圆、抛物线等工程曲线。通过选择合适的形状参数，该插值样条曲线能达到C 2连续，而且其整体逼近效果要好于标准三次Hermite插值样条曲线。
급출료일충대형상삼수적삼차삼각Hermite삽치양조곡선，구유표준삼차Hermite삽치양조곡선완전상동적성질。급정삽치조건시，양조곡선적형상가통과개변형상삼수적취치진행조공。재괄당조건하，해양조곡선대응적Ferguson곡선가정학표시타원、포물선등공정곡선。통과선택합괄적형상삼수，해삽치양조곡선능체도C 2련속，이차기정체핍근효과요호우표준삼차Hermite삽치양조곡선。
A class of cubic trigonometric Hermite interpolating splines curves with shape parameters is presented in this paper, which inherits the same properties of the standard cubic Hermite interpolating splines. For given interpolating con-ditions, the shape of the proposed splines curves can be adjusted by changing the values of the parameters. In proper con-ditions, the corresponding Ferguson curve can be used to represent some engineering curves exactly, such as ellipse and parabola. By selecting proper shape parameters, the proposed interpolating splines curves could satisfy C 2 continuous and approximate the interpolated functions better than the standard cubic Hermite interpolating splines curves.