Transition Surface Generation Algorithm And Surface Smoothing Technology Research

Blending surfaces generation is an extremely important part in Computer Aided Geometric Design and Computer Graphics.It's primary research objects are surfaces expression,design,display and analyze under Computer Graphics system.With the rapid development of CAD/CAM,technology of surface modeling has been used in more and more products design.At the same time,the theory and methods of blending surfaces generation is one of attractive fields.Surface fairing is also one of important topics in CAGD research.Because of its significant application in CAD/CAM domains such as aviation,space navigation,autos and shipping,this issue become a research focus.The research on surface fairing has been continued to the present because of the complexity.In this paper,firstly,we research blending surfaces generation methods,analyzed and compared all these methods on the aspects of their theories,characteristics,scope,advantages and disadvantages.The research focus on generating blending surfaces base on partial differential equations.From traditional static PDE-based and dynamic PDE-based,analyzed their theory and methods.We generated blending surface with C'continuity using Pseudo-Navier method.To solve the shortage that traditional static PDE method has,proposes dynamic PDE to generate blending surfaces.It uses iterative finite difference algorithm to solve dynamic PDE, and investigates how different user handles affect dynamic deformations of surfaces,such as parametric variables,density and damping coefficient on.The modeling samples illustrate that the new dynamic PDE method brings more and better flexibility.It is very valuable for aided geometric design.Finally,we research the theory and rule of surface fairing and several classical faring methods,moreover analyze their advantage and disadvantage.In this paper,non-uniform B-spline multi-resolution wavelet decomposition was applied to the fairing of NURBS surface. The global faring direction was determined by global faring measure of two parametrical directions,and then the global fairing of surface was realized though global decomposition of surface.This algorithm is effective,and it will be one of research focuses in the future.