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1、OptimalBoundaryTriangulationsCharlieC.L.WangDepartmentofAutomationandComputer-AidedofanInterpolatingRuledSurfaceEngineering,ChineseUniversityofHongKong,Shatin,N.T.,WeinvestigatehowtodefineatriangulatedruledsurfaceinterpolatingtwopolygonalHongKong,People’
2、sRepublicofChinadirectricesthatwillmeetavarietyofoptimizationobjectiveswhichoriginatefrommanye-mail:cwang@acae.cuhk.edu.hkCAD/CAMandgeometricmodelingapplications.Thisoptimaltriangulationproblemisformulatedasacombinatorialsearchproblemwhosesearchspacehow
3、everhasthesizetightlyfactorialtothenumbersofpointsonthetwodirectrices.Totacklethisbound,weKaiTang1introduceanovelcomputationaltoolcalledmultilayerdirectedgraphandestablishanDepartmentofMechanicalEngineering,equivalencebetweentheoptimaltriangulationandth
4、esingle-sourceshortestpathprob-HongKongUniversityofScienceandlemonthegraph.WellknowngraphsearchalgorithmssuchastheDijkstra’sarethenTechnology,employedtosolvethesingle-sourceshortestpathproblem,whicheffectivelysolvestheClearWaterBay,KLN,optimaltriangulat
5、ionprobleminOmntime,wherenandmarethenumbersofverticesHongKong,People’sRepublicofChinaonthetwodirectricesrespectively.Numerousexperimentalexamplesareprovidedtoe-mail:mektang@ust.hkdemonstratetheusefulnessoftheproposedoptimaltriangulationprobleminavarie
6、tyofengineeringapplications.DOI:10.1115/1.20528501IntroductiontionobjectiveisÒmaximaldevelopability,Ówhichseekstomaxi-mizethenumberofÒtwist-freeÓrulingsonaruledsurface,whereRuledsurfacesarewidelyusedincomputer-aideddesignandarulingistwist-freeifallthe
7、surfacenormalvectorsalongitaremanufacturingCAD/CAMandcomputergraphicsapplications.paralleltoeachotherÑincasealltherulingsaretwist-freethenForexample,theyareutilizedtoapproximatefreeformsurfacessotheruledsurfaceisdevelopable4.Theoretically,thisisavar
8、ia-thatefÞcientNCtoolpathscanbegenerated1.InRef.2ktionaloptimizationproblem7.Let0,1denotethevectormoulddraftsarecreatedonfreeformsurfacesbyapproximatingspaceofalltheclassCkreal-valuedfunctionsdeÞnedon0,1.isolinesurfa
