Study On The Method Of Generating Curves And Surfaces By Constructing Blended Functions

Generate curves and surfaces has been a hot topic of CAD/CAM curves and surfaces modeling technology research for a long time, and especially curve and surface blending technology is being widely studied and applied. For the existing research work, this paper construction different blended functions to generating different curves and surfaces, which retain the original shape of the curves and surfaces nature of the connection point.First of all, a brief introduction to computer-aided geometric origin, the generating and study abroad of blending curves and surfaces, and this paper describes the application of theoretical knowledge base.Then, the focus of this paper describes in detail the structure of blending function and blending curves and surfaces, and gives examples for different blending curves and surfaces. The blended function constructed into two categories:one for the polynomial blending function, and one for the rational blending functions. First of all, we use the Hermite interpolation polynomial constructed to meet the relevant properties to generate H-Cn blended polynomial function, and then introduce a degree of freedom to get one parameter and two parameters H-Cn polynomial blended functions. On the basis of rational Bezier, we construct a B-Cn rational blending functions to satisfy theorem conditions. And through studying the properties of these two types of hybrid functions, we can find these two functions have four same properties of non-negativity, boundedness, decrement, and symmetry. The examples of blending curves and surfaces in this paper mainly about G1G2continuity.Finally, this paper using energy minimization method to smoothing polynomial blended functions and curves, combined with Newton iteration method and simultaneous equations of Newton iteration. Through energy smoothing method, we find that, when one parameter, ai=0and βj=5.88169are the answers of C1and C2continuity, respectively; when two parameters, ai=-1.285085, bj=0.642542and ai=-0.209856, bj=0.105134are the answers of c1and c2continuity, respectively; when ai=0and βj=0, the generated G1and G2curves have the minimum energy property.Some specific applications graphics presented in this article are based on this article and using Matlab programming algorithm to draw. Through examples, we can more clearly see the advantages of a better kind of hybrid approach.