Triangle Mesh Simplification And Surface Smoothing

In recent years, with the development of computer science and 3D scanning technology, digital geometry model has become a new type of multi-media. Mesh models are one of the most popular methods to represent digital geometry model and have been widely used in many fields, such as internet, entertainment and manufacture industries. Digital geometry processing(DGP) is the main tool to deal with the type of multi-media and has become one of the most important research fields in multi-media and computer graphics. Many digital geometry processing algorithms, such as surface reconstruction, mesh simplification, mesh edit, mesh morphing, surface smoothing and mesh parameterization, have been proposed in the past two decades. Two of these algorithms, mesh simplification and surface smoothing, will be researched in the paper. Main achievements of our work are as follows:A new mesh simplification algorithm based on surface curvature estimation is proposed in the paper and it is implemented on the basis of triangle collapse. According to the discrete curvature on triangle meshes, more important features can be preserved in regions of high curvature after simplification. A method to get the new vertex after the collapse of a triangle based on discrete curvature and spherical surface estimation is also given in the paper. Experiments illustrate the efficiency of our algorithm.Triangle collapse simplification algorithm is established on the framework of multiple-choice algorithm(MCA) compared to which is implemented on the traditional framework of greedy optimization. It improves the efficiency of algorithm and confirms that MCA can be used in mesh simplification.An efficient mesh smoothing method is proposed. Our method can smooth surface quickly, while preserving features. Firstly, we smooth the normal of every triangle in the mesh and get the normal of every point in the mesh after triangle normal smoothing. Secondly, we improve the moving direction of each vertex according to the distances between current vertex and adjacent vertices, and the angles between the normal of current vertex and of adjacent vertices. Thirdly, we get the weight of each vertex in the iteration using Gaussian. We provide a series of examples to demonstrate the effectiveness of our method with fewer iteration times and less volume shrinkage.