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Algorithm Research on Reconstruction of Triangle Bezier Surface of Scattered Data Points

Author: YuCunGuang
Tutor: LiuRunTao
School: Harbin University of Science and Technology
Course: Applied Mathematics
Keywords: Triangular Bézier Surface fitting Delaunay triangulation Surface Reconstruction
CLC: TP391.41
Type: Master's thesis
Year: 2007
Downloads: 144
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Abstract


Surface Reconstruction technology has wide application background in the field of surface measurement modeling and visualization . Way , a systematic study on the the triangular Bézier nature and theoretical surface reconstruction from unorganized points . Based on the classical algorithm research at home and abroad to achieve arbitrary topology grid sub- G 1 continuous geometric reconstruction . Firstly, the surface reconstruction research situation analysis derived the triangular Bézier fitting application prospects , establish the thesis content . By unorganized points neighborhood structure and its classical algorithm is proposed and demonstrated the method of calculating the scattered points Delaunay triangulation , the local structures of planar point set Delaunay triangulation algorithm . Then the triangular Bézier nature comprehensive introduction, focuses on the basic principles of the triangular Bézier its splicing parameters in the continuity and geometric continuity . When more complex curved shape , the use leaflets patch and difficult to meet the requirements , and the need to connect using a variety of curved sheet , which requires that in the curved surface at the junction of the sheet reaches a certain continuity requirements . Parametric continuity gradually replaced by the geometric continuity . Along the boundary of G 1 continuous surfaces need at least four times a triangular Bézier surface . Finally, for any topological surface geometry reconstruction , two new CT segmentation algorithm : one with a the BB surface on the triangular domain , the other with a the Bézier surface on the rectangular domain . The first algorithm is characterized by the reconstruction results are not dependent on the processing order of the vertices , does not require the preliminary estimates and correction of the control points , allows the calculation of each control vertex at once . The second algorithm innovation lies on this issue for the first time with a the Bézier surface on the rectangular domain , which can be directly used by most CAD / CAM software . The two algorithms are fully localized , and a reasonable allocation of the extra degrees of freedom , and therefore has a higher efficiency , and can be constructed relatively light smooth interpolation surface .

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