Research Of Differential Mesh Editing Algorithms

With the fast advancement of 3D scanning techniques, the information complexity of geometric models grows quickly too. Techniques of geometric processing to handle such situations have seen new progresses accordingly, for example, 3D Differential Domain Editing Method. It regards 3D geometry modals as scalar fields defined on the 3D domain meshes. Unlike its traditional counterparts, this method processes geometric models via implicitly manipulating differential properties of meshes. In this way, geometric details can be better preserved.I introduce the theoretical foundation of differential domain methods in the beginning of this dissertation. Then I analyze a series of papers on differential domain methods of recent years. I compare their efficiency, robustness, and application area to find their respective advantages and disadvantages. In the following chapter, I introduce the methods of 3D mesh smoothing proposed in recent years. Base on those, I develop a new method which called the Global Mesh Smoothing Method Based on Poisson Equation on Gradient Fields. The experimentation result shows that my method is simple, non-iterative, fast, features -preserving, adaptive, and achieves global optimized solutions. Then the dissertation analyzes applications of differential mesh editing algorithm, especially the layer based 3D mesh editing system through theory and experiments. The improved system I proposes is more practical.Finally, I list the major contributions of my dissertation here:I compare the newest 3D mesh differential domain editing algorithms.I propose a new method called the Global Mesh Smoothing Method based on Poisson Equation on Gradient Fields.I implement and improve the layer based 3D mesh editing system.