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1、201414thInternationalConferenceonComputationalScienceandItsApplicationsSlicingTriangleMeshes:AnAsymptoticallyOptimalAlgorithmRodrigoM.M.H.Gregori?,NeriVolpato?,RodrigoMinetto?andMuriloV.G.daSilva??DepartamentoAcademicodeInform?atica′?DepartamentoAcade
2、micodeMec?anica?FederalUniversityofTechnology–Parana(UTFPR)′Curitiba,BrazilEmail:rodrigo.gregori@gmail.com,{nvolpato,rminetto,murilo}@utfpr.edu.brAbstract—AdditiveManufacturing,popularlyknownas“3Dtoitssimplicity[1],however,sinceameshvertexcanbeprintin
3、g”,isamanufacturingprocessbasedonoverlappingsharedbymanytrianglesthismightleadtoredundancy.of?atlayersinordertobuildaphysicalobject.ThedataThemeshmustbeslicedinordertoobtainthecontourforbuildingthisobjectcomesfroma3Dmodel,usuallyinformation,andeachsli
4、ceis“printed”bytheprototyperrepresentedbyatrianglemesh.Oneofthe?rststagesinthisprocessistoslicethetrianglemesh,resultingin2.5-Dcontours,andtheoverlappingofallslicescomposesthe?nalobject.representingeachoneofthelayersoftheobject.ThereareInordertoimprov
5、ethequalityoftheprintedmodelandmanystrategiesforslicingmeshes,howevermostofthecurrentspendlesstimeintheprocess,modernslicingproceduresliteratureisconcernedwithadhocissuessuchasthequalitymakeuseslicesofvariablethickness,thisapproachisalsoofthemodel,spe
6、ci?cimprovementsintheslicingprocessandmemoryusage,whereasnoneofthemaddressestheproblemknownasadaptiveslicing.Anextensivereviewonadaptivefromanalgorithmiccomplexityperspective.Whilecurrentslicingcanbefoundin[2].222algorithmsforslicingrunonO(n+k)orO(n+n
7、lognk)Theslicingproblemhasbeenaddressedintherapidproto-forntrianglesandkplanes,thealgorithmproposedinthistypingresearchcommunity,butmostofthecurrentliteraturepaperrunsonO(nk),wherekistheaveragenumberofslicesisconcernedwithadhoc(butstillrelevant)engine
8、eringis-cuttingeachtriangle,whatisasymptoticallythebestthatcanbeachievedundercertaincommonassumptions.suessuchasthequalityofthemodel,speci?cimprovementsintheslicingprocessandmemoryusage,whereasnoneKeywords-processplanning,trianglemeshes;slicin
