NURBS中某些问题的研究

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1、大连理工大学硕士学位论文NURBS中某些问题的研究姓名：刘文海申请学位级别：硕士专业：计算数学指导教师：王仁宏20030301AbstractFromtheeights，themethodofNonUniformRationalB-spline(NURBS)hasbecomethemostpopularindesignofcurvesandsurfaces．ItisusedwidelYinCAD／CGandhasbecomethestandardofindustry．BecauseoftheadvantagesofNURBScurvesandsurfaces，

2、itisimportanttoresearchintoNURBS．Inthispaper，themainworkisaboutthemodificationofNURBScurvesandsurfaces．NURBSisoneofthemostpopularmethodfordesigningcomplexcurvesandsurfaces．AftertreatingNURBScurves／surfaces．weoftenneedtomodifythemtosatisfytheuser’sdesignrequirements．BydefinitionofNUR

3、BScurves／surfaces，therearethreewaystomodifytheshape：i)bychangingknotsvector；ii)bymovingcontrolpoints：iii)bychangingtheweights．ThispaperpresentsaunifiedapproachthatmodifiestheshapeofNURBSsurfacesbyalteringtheweightsandthelocationofthecontrolpointsSimultaneouslY，Ahomogeneouscoordinate

4、representationiSintroducedinthiSmethod．AnalgebraiCprocedureformodifyingtheshapeofNURBSsurfaceiSpFesented，whichcanovercomeshortcomingofgeometryway．ItiSnotonlyusedformodificationofonepointonthesurface，butalsousedformodifyingonepointofthesurfacebymovingseveralcontrolpoints．Furthermorei

5、tisusedfortheconditionofmodifyingseveralpointsofsurface．ThiSpaperisorganizedasfollows：thereiSabriefingofthedevelopmentofNURBSshapemodificationinthefirstchapter：thesecondintroducesthefundamentalknowledgeofNURBScuI-ves／surf8ces：Atpresents，somepeopleinvestigatesshapemodificationofNURBS

6、curves／surfacesbasedthemethodoffairingB-splinecurves／surfaces．SOthemethodsthatfairsB-splinecurves／surfacesareintroducedinthethirdchapter：TheforthpresentsseveralapproachesofmodifyingNURBScurves．ThemethodofmodifyingNURBSsurfacesiSpresentedinthelastchapter．Keyword：Shapemodification：fai

7、ring：NURBScurves／surfaces：controlpointsWeightsofcontrolpoints2NURBS中的某灶问题的lij

8、_究l绪论1．1背景曲线曲面造型是CAD／CG中最为活跃，同时也是最关键的学科分支之一，它随着CAD／CAM技术的研究发展而不断完善，渐趋成熟。曲线曲面造型技术是随着汽车，航空等现代工业的发展而出现的。工业产品的形状大致上可分为两类或由这两类组成：一类是仅由初等解析曲线曲面组成，大多数的机械零件属于这一类，可以用画法几何和机械制图完全清楚的表达和传递所包含的全部形状信息。第二类是不能由初等解析曲线曲面组成，

9、而以复杂方式自出的变化的曲线曲面即自由