Research And Implement Of Practicable Surfaces Intersection Algorithm

Surface and surface intersection (551) is one of the key tasks in CAGD. There are 6 types of 551 algorithms available, they are: geometric division, algebraic iteration, trace, lattice, analytics and trigonometry methods. But none of them has completely reached a good balance between efficiency and precision, because the research was done either from one side of versatility or merely the other side of precision.At present, trace method is considered a relatively better method with higher precision and better stability. This method is consist of three steps: first search, secondly trace and lastly sort. But the efficiency is lower, which should be improved.In this thesis, first some SSI algorithms common used are analyzed and some problems and relatively measures are pointed out. Then a better algorithm梩wodivision trace method, is put forward and implemented, which has stronger stability, higher precision and efficiency. The following is main research work:1 .Geometry characters (such as tangent plane and normal plane etc.) and differential coefficient characters are theoretically analyzed in detail, then the intersection differential coefficient system model for trace is constructed.2.A practical 551 algorithm梩wo-division trace method, is proposed, which not only combines the advantages of all of the above methods, but also has higher precision and efficiency.3.The error is estimated by the five-order Cash-Karp method caused by fourorder Runge-Kutta method in algorithm implement.4.OOP technology in programming is used. The operation platform is Windows NT Workstation and the development kits are Visual C++ and OpenGL. Some examples demonstrate availability of the algorithm.5. The proposed algorithm is further verified in subsequent practical applications such as surface trimming, surface cutting and surface transition.6.Multi-extremum SSI is also studied and the prospect about the algorithm is discussed.