Cutting Surfaces And Three-dimensional Reconstructionn Based On PDE

The surface modeling technology based on PDE has a special status andbenefits in many shapes technology.In this paper,we research the trimming PDEsurfaces and three-dimensional model reconstruction.In the trimming PDE surfaces,amethod is proposed to draw the fourth-order trimming PDE surfaces.Using thismethod to draw the trimming PDE surfaces compared with the method that HassanUgail proposed in2006,error tinier,precision higher.In the part of three-dimensionalmodel reconstruction we research the three-dimensional model that based onPDE,and uses slice patches approach to the polygon meshes,and the ideas thatproposed to solved the problems when the three-dimensional model that based onPDE has been drawn is offered.The advantages of reconstruct the three-dimensionalmodel which based on the PDE that can be obtained locally original patch closure ofthe boundary conditions,the fitting out of the patch is closer to the original patch,andtherefore better able to retain some abnormal of the rules.The first chapter introduces the research status of partial differentialequations,surface trimming and surface reconstruction,and introduces thebackground and significance of PDE, clearly the potential for PDE in the field ofsurface modeling.The second chapter describes the analytical solution of PDE andthe geometric properties of biharmonic PDE surface.The third chapter presents amethod can be widely used in cutting fourth-order PDE surfaces.The fourth chapterstudies the slice patch-based design method of PDE and propose solutions to solvetwo PDE piecewise patch design problems in the implementation.One is the normalvector degradation at the edge of PDE patch,by calculating the average normalvectors to get the normal where the normal is degradation;another deal for theproblem that we find in the application is to fold the model,we passed a creaseconcept to determine corner crease is remain or not,and we use the mean vector toeliminate the corner crease.The fifth chapter of this paper summarizes the workdescribed in this paper,and point out deficiencies and areas for improvement in thefuture.Research on this topic indicates that the PDE’s advantages in surfacemodeling techniques,the paper PDE-based surface trimming and slicing patch aregood supplement for free-surface modeling design techniques.