CAJ | 학술논문

文章提出带形状参数λ的n＋1（n≥2）次多项式调配函数，建立了带形状参数的分段多项式曲线生成法，分析了生成曲线及其调配函数的性质，并给出了扩展曲线 G2连续拼接的条件。通过研究发现，在控制多边形不变的情况下，可以通过改变形状参数值调整曲线的形状，随着形状参数值的增加，带形状参数的Bézier曲线将接近于控制多边形，随着曲线阶数的升高，形状参数的取值范围将扩大。实例表明，该方法应用于曲线曲面设计是有效的。
문장제출대형상삼수λ적n＋1（n≥2）차다항식조배함수，건립료대형상삼수적분단다항식곡선생성법，분석료생성곡선급기조배함수적성질，병급출료확전곡선 G2련속병접적조건。통과연구발현，재공제다변형불변적정황하，가이통과개변형상삼수치조정곡선적형상，수착형상삼수치적증가，대형상삼수적Bézier곡선장접근우공제다변형，수착곡선계수적승고，형상삼수적취치범위장확대。실례표명，해방법응용우곡선곡면설계시유효적。
A class of blending function of degree n+1(n≥2) with shape parameter λis presented in this paper .Based on the blending function ,a method of generating piecewise polynomial curves with a shape parameter is given .The properties of the curves and the blending functions are analyzed ,and the condition of G2 continuity of extension curve is discussed .It is found that with the control polygon of the constructed curve unchanged ,the shape of curve can be adjusted by changing the shape parame-ter value .With the increase of the shape parameter value ,the Bézier curves with shape parameter ap-proximate to the control polygon .With the elevation of the degree of curve ,the feasible range of the shape parameter value will be extended .Examples illustrate that this method of constructing curves and surfaces is useful in CAGD .