Minimum bounding box - Wikipedia
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Arbitrarily oriented minimum bounding box Minimumboundingbox FromWikipedia,thefreeencyclopedia Jumptonavigation Jumptosearch Smallestboxwhichenclosessomesetofpoints Aseriesofgeometricshapesenclosedbyitsaxis-alignedminimumboundingbox(in2dimensions) Ingeometry,theminimumorsmallestboundingorenclosingboxforapointsetSinNdimensionsistheboxwiththesmallestmeasure(area,volume,orhypervolumeinhigherdimensions)withinwhichallthepointslie.Whenotherkindsofmeasureareused,theminimumboxisusuallycalledaccordingly,e.g.,"minimum-perimeterboundingbox". Theminimumboundingboxofapointsetisthesameastheminimumboundingboxofitsconvexhull,afactwhichmaybeusedheuristicallytospeedupcomputation.[1] Theterms"box"and"hyperrectangle"comefromtheirusageintheCartesiancoordinatesystem,wheretheyareindeedvisualizedasarectangle(two-dimensionalcase),rectangularparallelepiped(three-dimensionalcase),etc. Inthetwo-dimensionalcaseitiscalledtheminimumboundingrectangle. Contents 1Axis-alignedminimumboundingbox 2Arbitrarilyorientedminimumboundingbox 3Object-orientedminimumboundingbox 4Digitalimageprocessing 5Seealso 6References Axis-alignedminimumboundingbox[edit] Theaxis-alignedminimumboundingbox(orAABB)foragivenpointsetisitsminimumboundingboxsubjecttotheconstraintthattheedgesoftheboxareparalleltothe(Cartesian)coordinateaxes.ItistheCartesianproductofNintervalseachofwhichisdefinedbytheminimalandmaximalvalueofthecorrespondingcoordinateforthepointsinS. Axis-alignedminimalboundingboxesareusedtoanapproximatelocationofanobjectinquestionandasaverysimpledescriptorofitsshape.Forexample,incomputationalgeometryanditsapplicationswhenitisrequiredtofindintersectionsinthesetofobjects,theinitialcheckistheintersectionsbetweentheirMBBs.Sinceitisusuallyamuchlessexpensiveoperationthanthecheckoftheactualintersection(becauseitonlyrequirescomparisonsofcoordinates),itallowsquicklyexcludingchecksofthepairsthatarefarapart. Arbitrarilyorientedminimumboundingbox[edit] Thearbitrarilyorientedminimumboundingboxistheminimumboundingbox,calculatedsubjecttonoconstraintsastotheorientationoftheresult.Minimumboundingboxalgorithmsbasedontherotatingcalipersmethodcanbeusedtofindtheminimum-areaorminimum-perimeterboundingboxofatwo-dimensionalconvexpolygoninlineartime,andofathree-dimensionalpointsetinthetimeittakestoconstructitsconvexhullfollowedbyalinear-timecomputation.[1]Athree-dimensionalrotatingcalipersalgorithmcanfindtheminimum-volumearbitrarily-orientedboundingboxofathree-dimensionalpointsetincubictime.[2]MatlabimplementationsofthelatteraswellastheoptimalcompromisebetweenaccuracyandCPUtimeareavailable.[3] Object-orientedminimumboundingbox[edit] Inthecasewhereanobjecthasitsownlocalcoordinatesystem,itcanbeusefultostoreaboundingboxrelativetotheseaxes,whichrequiresnotransformationastheobject'sowntransformationchanges. Digitalimageprocessing[edit] Indigitalimageprocessing,theboundingboxismerelythecoordinatesoftherectangularborderthatfullyenclosesadigitalimagewhenitisplacedoverapage,acanvas,ascreenorothersimilarbidimensionalbackground. Seealso[edit] Boundingsphere Boundingvolume Minimumboundingrectangle Darbouxintegral References[edit] ^abToussaint,G.T(1983)."Solvinggeometricproblemswiththerotatingcalipers"(PDF).Proc.MELECON'83,Athens.{{citejournal}}:Citejournalrequires|journal=(help) ^JosephO'Rourke(1985),"Findingminimalenclosingboxes",ParallelProgramming,SpringerNetherlands ^Chang,Chia-Tche;Gorissen,Bastien;Melchior,Samuel(2018)."Matlabimplementationofseveralminimum-volumeboundingboxalgorithms".GitHub.. Retrievedfrom"https://en.wikipedia.org/w/index.php?title=Minimum_bounding_box&oldid=1095161342" Categories:GeometryGeometricalgorithmsHiddencategories:CS1errors:missingperiodicalArticleswithshortdescriptionShortdescriptionisdifferentfromWikidata Navigationmenu Personaltools NotloggedinTalkContributionsCreateaccountLogin Namespaces ArticleTalk English Views ReadEditViewhistory More Search Navigation MainpageContentsCurrenteventsRandomarticleAboutWikipediaContactusDonate Contribute HelpLearntoeditCommunityportalRecentchangesUploadfile Tools WhatlinkshereRelatedchangesUploadfileSpecialpagesPermanentlinkPageinformationCitethispageWikidataitem Print/export DownloadasPDFPrintableversion Inotherprojects WikimediaCommons Languages ItalianoPortuguêsРусскийУкраїнська Editlinks
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