Research Of Swept Surface And Skinning Surface Based On PDE

Surfaces generated by using partial differential equations, as a method of surface modeling in computer graphics. play an important role in generating blend surfaces, free-form surfaces and functional surfaces modeling. The key character of this method is that it regards the surfaces as the solution to some partial differential equations. The surfaces generated by this way. usually called PDE surfaces, are naturally smooth. and suitable for artistic and functional design.The PDE method was initially proposed by Bloor and Wilson. and then has been enhanced and widely applied. For 20 years, this study achieved some success, but there are still a lot of questions, such as interpolation of scattered points, surface reconstruction; the problem of shape control of PDE surfaces:the application in the design of functional surfaces, and so on.In this paper. PDE surface is constructed based on the theory of PDE-based scanning surface construction and application of PDE masked ball on the 3D surface optimization. The main works show as follows:(1) Doing research on the method of constructing swept surfaces, bring in the concept of parameters such as line. For a given initial and boundary conditions, we only care about the parameters of its corresponding point value. not on the curve of their expression. Obtained by solving the differential equation parameters such as surface scanning lines. and then constructed by swept surface model theory.(2) Using the superposition principle of differential equation, the PDE-based swept surface is divided into two sub-surface parts of the surface to the base surface and tectonic deformation. By splitting the differential equation and boundary conditions, the solution of the homogeneous equations and non-homogeneous equation can correspond to the base surface and deformed surfaces. Experimental results show that the method of swept surface structure deformation and shape control is easy.(3) As the information of the border was not clear or strict application of surface modeling, we find that the surface can be calculated by PDE and then adjust the boundary energy function to optimize the surface. In this paper, we study about masked surface of 3D ball. analvsis the method of the masked surface construction and the application of PDE on optimizing surface. Using the energy function of masked surface as the evaluation. we step up the parameters along the opposite of the gradient of the energy function to minimal the energy function, which makes the boundary curves to converge, so as to optimize the masked surface. Experimental results show that this method can optimize the masked surface.