Research On The Construction Of PH Curve And Related Problems

PH curves are one of main research contents in CAGD.They are important polynomial parametric curves.The main feather is the offsets and the arc lengths are polynomial and rational polynomial representations,which is compatible with CAD system.The thesis is to develop an approximation method by PH curves with parameters.The curve can be adjusted more flexibly by adjusting shape parameters.It presents an effective method for the design of curves and surfaces.The geometric characteristic condition of PH curve is studied.And the geometric construction method of PH curve is obtained by constructing control polygon.Then the transition curve between two circles that are mutually exclusive is presented.The thesis is organized as follows.The first part is the introduction,which mainly introduces the geometric construction methods of PH curves and the construction methods of transition curves.The second part presents the definition of cubic a-Bézier curve with parameter.Based on the curve,the necessary and sufficient condition ofa-Bézier to be a PH curve is obtained by the definition of PH curve,which is the geometric characterization in terms of the leg-lengths and angles of the control polygon.?-PH curve is got,i.e.,PH curve with parameter.And the error analysis between a-Bézier curve and?-PH curve is estimated.On the basis of this,the geometric construction method is presented by constructing the control polygon.The third part describes geometric construction method of PH-DP curve based on the geometric characterization in terms of the side lengths and angles of the control polygon.The error analysis between DP curve and PH-DP curve is estimated.Then the cubic PH-DP transition curve is constructed between two circles that are mutually exclusive.