带两类形状参数的三次λμ-α-DP曲线的构造

构造了一种带两类形状参数的三次λμ-α-DP基函数,形状参数的引入有效地增强了DP曲线的形状控制能力。新的曲线不仅可以整体修改曲线的形状,而且具有局部可调性。分析了三次λμ-α-DP基函数以及曲线的性质,给出不同的参数取值对基函数和曲线形状的影响,以及曲线光滑连续拼接的条件:当满足一定的条件时,曲线可以达到G2连续。另给出G1连续的旋转面。利用奇异混合技术,在三次λμ-α-DP曲线中加入一类奇异混合函数,并分别对新曲线的相关性质和取不同参数时曲线的变化规律进行了论证。实例证明,改变调配参数的取值,可以调整奇异混合插值曲线与直线段的逼近程度,增强曲线的形状控制能力。

Construction of the cubic λμ-α-DP curve with two kinds of shape parameters

This paper constructs a type of cubic λμ-α-DP basic function with two kinds of shape parameters. It can effectively global or locally modify its shape. The properties of the cubic λμ-α-DP basis function and curve are analyzed. Moreover, the effect and modification ability of the basis function and the curve with different parameter values are illustrated through graphics. Smooth continuous conditions of the curve are deduced: they can meet with G2 continuous when certain conditions are met. G1 continuous rotating surfaces are also given. Furthermore, using the singular blending technique, the singular blending cubic λμ-α-DP interpolation curve with shape parameters is constructed. The properties of the curve and the influences of the curve with multiple parameters are presented. By changing the blending parameters, the approximation degree between the singular blending interpolation curve and its control polygon can be adjusted, thus enhancing the shape-control capability of the cubic λμ-α-DP interpolation curves.