With the development of 3D range scanning, more and more complex objects are scanned to generate their 3D geometric models,and this type of measure-based modeling has become an important trend in computer graphics. The widespread requirements of 3D geometry models push the research on digital geometry processing. In this thesis we focused on two fundamental issues on the estimation of local geometry properties and the reconstruction of cylinder surface. Based on these researches, we developed an approach to reconstruct real trees from a single scan. The main contributions of this thesis are as follows: 1.Estimating differential geometry properties from unorganized point cloud. An accurate and robust method is proposed to estimate the curvatures and Darboux frames from unorganized point clouds. This method takes into account the normal information of all neighboring points and directly computes second-order differential quantities from the variation of unit normal vectors, which improves the accuracy and robustness of curvature estimation on irregular sampled noisy data. The main advantage of the approach is that the estimation of curvatures at a point does not rely on the accuracy of the normal vector at that point, and the normal vectors can be refined in the process of normal fitting. Compared with the state-of-the-art methods for estimating curvatures and Darboux frames on both synthetic models and real point clouds, the approach is shown to be more accurate and robust for noisy and unorganized point cloud data. 2.Fast cylinder fitting. A fast cylinder fitting method is presented by using a new approximate distance between a point and the cylinder surface. The method can transform the conventional cylinder fitting with 5 parameters to a nonlinear optimization with only 2 parameters, which not only reduces the time complexity of the nonlinear optimization in cylinder fitting but also alleviate the solution dependence on the initial estimation and avoid local optimization to some extent. 3.Simple Reconstruction of Tree Branches. We present a multi-process approach that is mainly performed in 2D space to faithfully construct a 3D model of the trunk and main brunches of a real tree. The approach takes a single scan of a bare tree using a laser scanner as the input source data for modeling, and focus on the reconstruction of the branching structures and dimensions of the tree.
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