Construction Of PH Curve With Parameters And Its Application

In recent years,the study of PH curve is an important research topic in CAGD.PH curve is a polynomial curve.PH curve has two main characteristics.The arc length and isometric line of the curve can be expressed as polynomial or rational polynomial according to the parameters of curve.In this paper,based on the Bézier curve with parameters,the geometric characteristic conditions to be PH curve are obtained.Then a geometric curve construction method of PH curve based on control polygon is given.And a class of cubic PH curve with parameters is obtained.Based on this curve,a C-type transition curve between two circles that do not contain each other is constructed.The transition curve is aG~2 continuous curve.Under certain conditions,the internal curvature of the transition curve has a unique curvature extreme point.The full text is arranged as follows:The first part is the preliminary knowledge,which introduces the relevant research results of PH curve and transition curve.In the second part,based on a class of cubic m-Bézier curves with shape parameters,the vertex coordinates of the control polygon of m-Bézier curve are solved according to the definition of PH curve.Then the relationship between the edges and corners is obtained.The relationship between the edges and corners is the geometric characteristic condition for the curve to be PH curve.Under this condition,the geometric construction method of cubic m-PH curve is constructed by constructing the conditions of the edge and corner.The degree is low.It is easy to compute.And the introduction of shape parameters makes the adjustment of curve more flexible.In the third part,the transition curve between two circles is constructed based on the cubic m-PH curve.It is proved that the curve is continuous under certain conditions.And the curvature inside the curve has a unique curvature extreme point.