基于Crust图的散乱数据点集的曲面网格重建的算法研究

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1、湖南大学硕士学位论文基于Crust图的散乱数据点集的曲面网格重建的算法研究姓名：廖鸿文申请学位级别：硕士专业：软件工程指导教师：朱理20051108苎三呈型兰里墼墼!!鍪堡皇叁墼塑塑塑丝耋塞墼塞鎏丝垒AbstractSurfacereeonstruclionfromscatterpointsisallimportantpartofcomputergeometricmodelingandplaysanessentialroleincomputergraphics．Thetechniqueofsurfacereconstructionfromscarerpointshasext

2、ensiveuseinmanyapplicationssuchasreverseengineering，medicineintageprocessing，andvirtualenvironments．Wegetonlythe3Dcoordinateofthesepointswithoutanyothercorrelativeinformation．Itisreallyahardworktogeneratethecomplexsurfacejustbythesescatterpoints．First，inordertosolvethisproblem，weselectthec

3、rust—basedsurfacereconstructionalgorithm．Itcalculatesthepolesofeverysamplepoint．thencomputestheDelaunaytriangulationwithsamplepointsandthepoles，atlast，extractsthetrianglethatincludesthethreeverticeswhichareallthesamplepoints．Thesetrianglesgeneratethecrustofthetlnknow／1surface．Additionally,

4、themeshwitllthesetrianglesisthesan-leastheoriginalsurfaceinthetopologicalstructure．Second，forgeneratingtheexactmeshofaunkrlownsurface．thelocalstructureofascatteredpointsetanditsclassicalDelaunaylxiangulationalgorithmsareinvestigated．BecausethereislocalfeatureofDelaanaytriangulation,wesugge

5、stedtwoalgorithmsforDelaunaytriangulationfromscatteredpoints，oneofwhichisfrompointsinplaneandtheotherfrompointsinspace．Last，becausethemeshofthecrustisnotalwayssatisfied．Itmayincludethetetrahedronormayappearsomeholesinthemeshsnrface，Thesedefectsareinducedbythedataorbythemethoditself．Forthes

6、ereasons，thetwofollow-upstepsareaccepted．Oneis’。minimalnormalvariationalgorithm'1．theotheris”fillingthecirclealrea”．Experimentsdemonstratetriangularmeshesgeneratedinthisthesisappeartobeingoodformandprecision．Thegenerationisalsoefficientandcapableofsatisfyingneedofapplications．Keywords：Surf

7、acereconstruction；Crust；Delaunaytriangulation；Voronoigraph；Computationalgeometry插图索引图1．1曲面重建示意图⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯l图1．2单侧曲面莫比乌斯带⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．3图1．3高度点元数据拓扑重建⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯一3图1．4截面线元数据拓扑重建⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．⋯⋯．3图I．5