Abstract
In this paper, the quartic Hermite parametric interpolating spline curves are formed with the quartic Hermite basis functions with parameters, the parameter selections of the spline curves are investigated, and the criteria for the curve with the shortest arc length and the smoothest curve are given. When the interpolation conditions are set, the proposed spline curves not only achieve C1-continuity but also can realize shape control by choosing suitable parameters, which addressed the weakness of the classical cubic Hermite interpolating spline curves.
Highlights
In CAGD&CG, it is always an important research topic to adjust and control the shape of fitting curves
E classical cubic Hermite interpolation spline curves have been widely used in practical engineering problems in [5,6,7]
When interpolation conditions are given, the shape of the cubic Hermite interpolation spline curves could not be changed. at is to say, we need to change interpolation conditions to modify the shape of the spline curves
Summary
In CAGD&CG, it is always an important research topic to adjust and control the shape of fitting curves. The Beziertype and B-spline curves with parameters are discussed in the articles [1,2,3,4]. When interpolation conditions are given, the shape of the cubic Hermite interpolation spline curves could not be changed. To overcome the limitations of the cubic Hermite interpolation spline curves in shape adaptability, the construction of Hermite interpolation spline with parameters has attracted the attention of many scholars. Ose articles proposed several interpolation spline functions with parameters, which have similar properties to the classical cubic Hermite interpolation, and they can push the curve to the designated area by modifying the parameters. E shape of the spline curve could be adjusted by amending the parameters when the interpolation conditions are satisfied. We inspected the techniques to determine the parameters such that the quartic Hermite spline curve has the shortest arc length or has the least curve energy value and makes the quartic Hermite spline curve the smoothest or achieves the minimal sum of the arc length and the curve energy value
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