Research Of Trimming Partial Differential Equation Surface

Surface trimming can be broadly described as a process whereby a given surface patch is machematically re-defined subject to the condition that a given unwanted portion of the original surface be removed. This process involves the generation of new surface geometry for the trimmed pathc by means of closely approximating the corresponding portion of the surface on the original patch. Trimming surface is one of the most basic algorithm of editing operations for surface, it is a basic of surface modeling and surface processing. Trimming surface has a very wide range of application environments.This usually require efficient algorithms to calculate stable and easy to control the accuracy. However, due to complexity of the problem about surface with surface for trimming and intersection, this has not yet been a very satisfactory solution. There are many people research about trimming of B-spline curves at home and abroad, but few people study on the trimming surface base on partial differential equations. Innovative finite difference method is proposed to solve the partial differential equations surfaces, and then constitute the triming curve in the parameters domain by using implicit curves and parametric curves, the finally trim parameter domain according to the mapping mechanism with the original surface redraw the partial differential equation of the surface. At the same time because of taking advantage of this technique to trim out the PDE surface after intersection, using a modified method for computing intersection line between two PDE surface, Using the 3 points same circle convergent method to solve the defect of difficult to determine the length of pace by the original method, And then fix the error by Cross-line refinement. Experiments proved that this method is fast, high accuracy, stability and so on.The main structure layout as fallows: The first chapter recalls the main course of development of surface modeling, introduced research status about cutting surfaceand application of PDE surface; The second chapter introduces the origin of the study of partial differential equations, application background and the general equation of expression, focusing on describing how to use difference method to solve an elliptic partial differential equations, then focus on modeling methods base on partial differential equations describing, including the use of finite difference method for solving partial differential equations, constructe PDE surfaces and so on. There are many methods to solve partial differential equations, there are many advantages to use finite difference method for solving partial differential equations surface like simple, practical, easy to realize and so on. Chapter three presents a new method of cutting the surface of partial differential equations, first using finite difference method for solving approximation PDE surface, then the surface of the projection plane transform to the xy plane and generate a regular grid contour lines, indicated by the parameter or implicitly expressed by the curve in the xy plane cutting the definition of crop area, then cut left onto the grid PDE surfaces, by this achieve trimming of the PDE surface. The experimental results show that the method can quickly generate cutting surfaces PDE. Chapter four mainly uses marching method to calculate the intersection line between two PDE surfaces, and then cutting off part of the intersection, this process also improves some shortcomings caused by marching method; optimization algorithm after optimization can better adapt the partial differential equations and trimming surface with intersection. Experimental results show that cut through the above method can effectively cut off the excess after the intersection of PDE surface, the algorithm can meet the good stability, high precision, can guarantee topological consistency, and high efficiency requirements. Chapter five base on the study of partial differential equations surface, with the Visual C + + environment, combination of C + + language and OpenGL 3D graphics applications for coding, development test platform to verify the correctness of the theory proposed.