| The technique of surface reconstruction has extensive use in surface measuring modification and visualization and such fields. The technique of surface reconstruction from scattered points, for its universality, is very important both theoretically and practically.In chapter 1, a brief review is made about several relative techniques, e.g., triangulation vs. topologic reconstruction, mesh optimization or simplification, and surface modification vs. geometric reconstruction. Based on the present state of investigation, several problems are put forward about topologic reconstruction and geometric reconstruction which have been studied carefully in this dissertation .In chapter 2, surface triangulation and local feature of a surface set are considered together. Three factors are discussed which should be taken into account when sampling points from a surface set to describe its 2d manifold feature. These three factors are local bending degree of a single piece of surface, overall bending degree of a single piece of surface and vicinity degree between different surfaces. The definitions of flat surface triangulation, local separate sample and overall separate sample are given based on this discussion.In chapter 3, the local structure of a scattered point set and its classical algorithms are investigated. Two algorithms for Delaunay triangulation from scattered points are suggested, one of which is from points in plane and the other from points in space. The problem of recognizability of 2d manifold is promoted and the relationship is pointed out between such recognizability and the local structure of a scattered point set.In chapter 4, based .on the recognizability of 2d manifold, an algorithm is presented for topologic reconstruction from scattered points. The algorithm is applicable to nonself-intersectant smooth surface set of any topology, including nonorientable surfaces, and its result is optimal surface triangulation in a way. When the given point set is a local separate sample of a closed surface set or an overall separate sample with known radius of sampling hole, the algorithm will reconstruct a correct result; when the separate condition is not satisfied at some points, the algorithm will give result with corresponding holes. The algorithms and formulas are promoted for extracting the topological information from a set of triangles which are topologically compatible.In chapter 5, two new C-T algorithms are proposed for geometric reconstruction, one of which adopts B-B patches on triangles and the other Bezier patches onrectangles. The first algorithm gives unique result unaffected by the handling order of points concerned, and it calculates the control vertexes at once without estimation and correction. The originality innovation of the second algorithm is that it adopts Bezier patches on rectangles for the first time in this problem, hence can be directly adopted by most CAD/CAM software. Because the two algorithms are confined to local area, and assign redundant degrees of freedom reasonably, they are highly efficient and can give relatively smooth fitting surface.In chapter 6, the usage of Floater's algorithm on a disk is discussed which is for geometric reconstruction of surface with four edges using double cubic B-spline surface, and the algorithm is generalized to a cylinder and a Mobius. An important property of the Floter linear system is pointed out and proved, and based on this, a special solution method for it is proposed. This solution method has a linear complexity both in time and space, and its numerical stability is similar to that of overall selected host element with normalization, hence remarkably improves the efficiency of Floater's algorithm.In chapter 7, under the background of Shoe CAD software development, the surface measuring modification system therein is introduced with its main functions, implementation methods and application samples. At the same time, the algorithm in this dissertation is used to generate finite element mesh automatically.In cha...
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