Research On Generalized Cubic DP Curve With Shape Parameters

In order to improve the effects of shape control for DP curve,generalized cubic DP curve with two shape parameters is presented.First,a type of generalized cubic DP basis functions are extended.Cubic DP basis functions with two shape parameters are given.Then,based on the basis functions,cubic DP curve with shape parameters is defined.The geometrical meanings of the shape parameters are discussed.G~1,G~2 continuous conditions of the curve based on shape parameters are given.Finally,the position parameter mis introduced,which makes the tangent point of the curve can be adjusted freely and the curve can be designed more flexibly.Example results show that,generalized cubic DP curve with shape parameters not only achieveG~1,G~2 continuity,but also can realize shape control through the parameters.The main work of this paper is as follow:1.A generalized cubic DP basis functions with shape parameters are constructed by adding the shape parameters.The tension parameter?and bias parameter?are added to the first-order derivative of the cubic DP curve at the end points.From the form of the final basis functions,the cubic DP basis functions are added by the blending functions,whose sum are constant equal to zero.The properties of the basis functions are studied and analyzed.The generalized cubic DP curve with shape parameters is further defined and its properties are analyzed.Local shape adjustment of the curve can be accomplished by changing the parameter values.Not only the geometric meaning of shape parameters are discussed,but alsoG~1 andG~2 continuity conditions of the shape parameter curve are discussed.2.The position parameter m is introduced into the above basis function.The cubic DP curve with adjustable tangent point is obtained,which makes it possible for the position of the tangent point can be controlled at any place on the first or last edge of the control polygon.It is not limited at the first or the last control points.3.An application example of generalized cubic DP curve with shape parameters is given.