Research And Implementation On Surfaces Reconstruction

In recent years, with the rapid development of three-dimensional(3D) data acquisition techniques, surfaces reconstruction remains a subject of intensive research in Computer Graphics(CG). This paper focused on the mesh methods of surfaces reconstruction from variational datasets. The main topics include the mesh optimization of polygonized implicit surfaces, the triangulation of implicit surfaces, the remeshing of triangular mesh and the triangulation of scattered point cloud. This presentation is divided into five chapters.In chapter 1, a survey is given about surfaces reconstruction technology. We introduce the existing methods about how to mesh the surfaces and their applications in industry and medical domains.In chapter 2, we discuss two methods about the optimization of polygonized implicit surfaces, including dynamic mesh optimization for polygonized implicit surfaces with sharp features, and triangulation optimization of polygonized implicit surfaces based on quadric error metrics, respectively; and describe the scale-adaptive surface modeling. Experimental results demonstrate that it can produce high quality triangulations which compared to those produced by traditional methods. Since the generated triangles mostly tend to equilateral and the triangles vary with the local curvature of the implicit surfaces, the output is appropriate for applications that require high quality triangulations. We have adapted the surface modeling approach to vessel surfaces reconstruction with complex topology.In chapter 3, we propose a versatile method for remeshing irregular mesh with complex topology. First, a control geometry image is generated based on the parameterization and geometry properties of the input mesh. Then, an interactive resampling is applied on the control image using halftone technique. Finally, a binary image obtained from resampling is connected to construct a planar triangular mesh using Delaunay triangulation principle, and mesh optimization is performed to achieve a high quality mesh. This method is considerably flexible and can meet user-specified demands.In chapter 4, we describe a hybrid approach to use a mesh for approximating a scattered point cloud over a piecewise smooth surface. Due to the large amounts of points obtained from 3D digital scans, it is difficult for traditional methods to triangulate those large datasets. Thus, from the view point of engineering, we design a fast and accurate approach for triangulating scattered point sets. First, an adaptive spherical cover and auxiliary corresponding to the cover elements are generated. Then the intersections between the spheres of the cover are analyzed and the auxiliary points are connected for generating mesh.Finally, we conclude in chapter 5. The main points in future works are briefly introduced.