Extension And Jointing Of Disk B-Spline Curve And Its Modeling Design

In this paper,we mainly study the extension,match and shape Design of disk spline curve in Computer Aided Geometry Design(CAGD)system.According to the characteristics of B-spline curve in circular domain combined with the actual application scenarios in real life,some innovations and expansions are made.Through a series of mathematical transformations,the extension and match problems of disk spline curves are transformed into the solving optimization problems of complex functions with multiple parameters.First,as a preparation,we introduce the basic concepts and theories about the circular domain algorithm and its properties.The main research content of this paper is as follows:(1)In order to overcome the defect of unadjustable shape of traditional continuation curve,a new algorithm for cubic disk B-spline curve continuation is proposed:Two independent degrees of freedom were used to adjust the shape of the Bézier curve segment in the circular domain,and the optimal parameters were determined by minimizing the objective function of strain energy in the Bézier curve segment.Then,the whole disk curve can be expressed as disk B-spline curve by the unclipping algorithm.Repeated use of the continuation algorithm and unclipping algorithm can complete the continuation of multiple target disks.Finally,on the basis of the proposed continuation algorithm,an algorithm is proposed to splice two non-adjacent disk B-spline curves by using a hexagonal disk Bézier curve with shape adjustable.(2)In view of the above hexaxed circular Bézier curve splicing algorithm’s complexity and certain error,a hybrid continuation splicing algorithm was proposed:first,two auxiliary continuation disk Bézier curves were constructed,and the hybrid continuation splicing segment disk curves were obtained by using mixed function technique.The effect of balance factorμin mixing function on adjusting the curve shape of circular domain of mixing continuation splicing segment is analyzed,and different splicing methods are given.The hybrid continuation algorithm is compared with the hexacycle Bézier curve splicing algorithm.Numerical experiments on Matlab show that the disk curve constructed by the hybrid continuation algorithm has the advantages of low computational complexity and better parameter continuity.(3)In order to improve the shape control ability of disk spline curve,the cubic disk spline curve with shape parameters is obtained by introducing shape parameters into the basis function.The properties of cubic disk spline curve with shape parameters and the geometric significance of shape parameters are discussed and analyzed.The shape control effects of different values of parametersα,λandμon cubic disk spline curve with shape parameters are discussed and analyzed.The conditions of G~2continuity between cubic disk spline curves with shape parameters are studied and proved.In order to construct the ideal cubic combination disk spline curve with shape parameters,three optimization models of shape parameters were proposed based on the minimization of disk curve strain energy.Figure:18 table:3 reference:68...