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1、DiscreteSurfaceModelingusingGeometricFlowsGuoliangXu¤QingPanAcademyofMathematicsandSystemScience,ChineseAcademyofSciences,Beijing,ChinaEmail:xuguo@lsec.cc.ac.cnChandrajitL.BajajyCenterforComputationalVisualizationandInstituteforComputationalEngineering&Sciences,DepartmentofCompu
2、terScience,UniversityofTexas,Austin,TX78712Email:bajaj@cs.utexas.eduAugust17,2003AbstractWeusevariousnonlineargeometricpartialdifferentialequationstoefficientlysolveseveralsurfacemodelingproblems,includingsurfaceblending,N-sidedholefillingandfree-formsurfacefitting.Thenonlinearequati
3、onsusedincludetwosecondorderflows(meancurvatureflowandaveragemeancurvatureflow),onefourthorderflow(surfacediffusionflow)andasixthorderflow.Thesenonlinearequationsarediscretizedbasedondiscretedifferentialgeometryoperators.Theproposedapproachissimple,efficientandgivesverydesirableresults,fo
4、rarangeofsurfacemodels,possiblyhavingsharpcreasesandcorners.Keywords:GeometricPDE;DiscreteSurface;SurfaceBlending;N-sidedholefilling;Free-formSurfaceDesign.1IntroductionWeusevariouscurvaturedrivengeometricpartialdifferentialequations(GPDE)tosolveseveralsurfacemodelingproblems.TheG
5、PDEsweuseincludemeancurvatureflow,averagedmeancurvatureflow,surfacediffusionflowandevenhigherorderflows.Alltheseequationsarenonlinearandthegeometryintrinsic,i.e.,theydonotdependuponanyparticularparameterization.Theproblemswesolveincludesurfaceblending,N-sidedholefillingandfree-formsur
6、facefittingwithhighboundarycontinuity.FortheproblemsofsurfaceblendingandN-sidedholefilling,wearegiventriangularsurfacemeshesofthesurroundingarea.Triangularsurfacepatchesneedtobeconstructedtofilltheopeningsenclosedbythesurroundingsurfacemeshandinterpolateitsboundarywithsomespecifiedo
7、rderofcontinuity.Forthefree-formsurfacefittingproblem,wearepossiblygivenasetofpoints,orawireframeofcurvesthatdefinesanoutlineofthedesiredshape,orevensomesurfacepatches.Weconstructasurfacewhichinterpolatesthepointsorcurvesortheboundariesofthepatcheswithspecifiedorderofcontinuities.T
8、hefree-formsurface¤SupportinpartbyNSFCgrant1024
