the clipper library - version 6 · ver 6 is a major update that adds support for open path...

TheClipperLibrary-Version6LibraryOverview Changes Example FAQ Rounding Deprecated License

Classes(Hierarchy)

ClipperBaseClipper

ClipperOffsetPolyNodePolyTree

TypesCInt InitOptions JoinType PolyFillTypeClipType IntPoint Path PolyTypeEndType IntRect Paths ZFillCallback

FunctionsArea ClosedPathsFromPolyTree OffsetPaths PointInPolygonCleanPolygon MinkowskiDiff OpenPathsFromPolyTree PolyTreeToPathsCleanPolygons MinkowskiSum Orientation ReversePath

UnitsClipperLib

Copyright©2010-2014AngusJohnson-Clipper6.2.0-Helpfilebuilton1-November-2014

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Changes

v6.2.1(31October2014)

Bugfix:BugfixinClipperOffset.ExecutewherethePolytree.IsHolepropertywasreturningincorrectvalueswithnegativeoffsets

Modified:VeryminorimprovementtojoinroundinginClipperOffset

Bugfix:FixedCPPOpenGLdemo

v6.2.0(26September2014)

Bugfix:Numerousminorbugfixes-toomanytolist.(Seerevisions454-475inSourceforgeRepository.)

Modified:ParametershavechangedinthecustomcallbackfunctionthatcanbeassignedtoZFillFunction.

Modified:Deprecatedfunctionshavebeenremoved.

Modified:TheCurvesdemohasbeentemporarilyremoved.(ItneedstobeupdatedbutthatwasholdingupthislatestreleaseoftheClipperlibrary.)

v6.1.3(18January2014)

Bugfix:FixedpotentialendlessloopconditionwhenaddingopenpathstoClipper.

Bugfix:FixedmissingimplementationofSimplifyPolygonfunctioninC++code.

Bugfix:FixedincorrectupperrangeconstantforpolygoncoordinatesinDelphicode.

Added:AddedPointInPolygonfunction.

Added:OverloadedMinkowskiSumfunctiontoaccommodatemulti-contourpaths.

Modified:Documentationupdated.

v6.1.2(15December2013)

Bugfix:FixedbrokenC++headerfile.

Modified:Minorimprovementtojoiningpolygons.

Bugfix:Fixedacoupleofbugsaffectingopenpathsthatcouldraiseunhandledexceptions.

Deleted:Previouslydeprecatedcodehasbeenremoved.

Modified:TheOffsetPathsfunctionisnowdeprecatedasithasbeenreplacedbytheClipperOffsetclasswhichismuchmoreflexible.

Bugfix:SeveralminorbugshavebeenfixedincludingoccasionallyanincorrectnestingwithinthePolyTreestructure.

v6.0.0(30October2013)Ver6isaMAJORupdatethataddssupportforopenpathclipping.

Added:Openpath(polyline)clipping.Anew'Curves'demoapplicationshowcasesthis(seethe'Curves'directory).

Update:Majorimprovementinthemergingofshared/collinearedgesinclipsolutions(seeExecute).

Added:TheIntPointstructurenowhasanoptional'Z'member.(Seetheprecompilerdirectiveuse_xyz.)

Added:UserscannowforceClippertouse32bitintegers(viatheprecompilerdirectiveuse_int32)insteadofusing64bitintegers.Using32bitintegersimprovesclippingperformancebyabout20-30%.(ThishasrequiredtheintroductionofanewcIntintegertype.)Thetrade-offtothisspeedupinperformanceisaveryrestrictedvertexcoordinaterangeof±46340.

Modified:Toaccommodateopenpaths,thePolygonandPolygonsstructureshavebeenrenamedPathandPathsrespectively.TheAddPolygonandAddPolygonsmethodsoftheClipperBaseclasshavebeenrenamedAddPathandAddPathsrespectively.Severalotherfunctionshavebeensimilarlyrenamed.

Modified:ThePolyNodeClasshasanewIsOpenproperty(tosupportopenpaths).

Modified:TheClipperclasshasanewZFillFunctionproperty.

Added:MinkowskiSumandMinkowskiDifffunctionsadded.

Added:SeveralothernewfunctionshavebeenaddedincludingPolyTreeToPaths,OpenPathsFromPolyTreeandClosedPathsFromPolyTree.

Added:TheClipperconstructornowacceptsanoptionalInitOptionsparametertosimplifysettingproperties.

Bugfix:Numerousminorbugshavebeenfixed.

Deprecated:Version6isamajorupgradefrompreviousversionsandquiteanumberofchangeshavebeenmadetoexposedstructuresandfunctions.Tominimizeinconveniencetoexistinglibraryusers,somecodehasbeenretainedandsomeaddedtomaintainbackwardcompatibility.However,becausethiscodewillberemovedinafutureupdate,ithasbeenmarkedasdeprecatedandaprecompilerdirectiveuse_deprecatedhasbeendefined.

v5.1.6(23May2013)

BugFix:TheCleanPolygonfunctionwasbuggy.

Added:NewOffsetPolyLinesfunction.(ReplacedwithOffsetPathsfunctioninver6.)

Changed:Thebehaviourofthe'miter'JoinTypehasbeenchangedsothatwhensquaringoccurs,it'snolongerextendeduptothemiterlimitbutissquaredoffatexactly'delta'units.(Thisimprovesthelookofmiteringwithlargerlimitsatacuteangles.)

Update:Minorcoderefactoringandoptimisations.

v5.1.5(5May2013)

Update:ForceSimplepropertyaddedtotheClipperClass.(RenamedStrictlySimpleinver6.)

Update:Furtherimprovementstothisdocumentation.

Update:Minorcodeoptimisationsandtrivialbugfixes.

v5.1.4(24March2013)

Update:CleanPolygonfunctionenhanced.

Update:Documentationimproved.

v5.1.3(12March2013)

Bugfix:Minorbugfixes.

Update:Documentationsignificantlyimproved.

v5.1.2(26February2013)

Bugfix:PolyNodeclasswasmissingaconstructor.

Update:TheMiterLimitparameterintheOffsetPolygonsfunctionhasbeenrenamedLimitandcannowalsobeusedtolimitthenumberofverticesusedtoconstructarcswhenJoinTypeissettojtRound.

v5.1.0(17February2013)

Update:ExPolygonshasbeenreplacedwiththePolyTree/PolyNodeclassestomorefullyrepresenttheparent-childrelationshipsofthepolygonsreturnedbyClipper'sExecutemethod.

Added:NewCleanPolygonandCleanPolygonsfunctions.

Bugfix:Anotherorientationbugfixed.

Bugfix:SignificantfixesinandtidyoftheinternalInt128class(whichisusedonlywhenpolygoncoordinatevaluesaregreaterthan±0x3FFFFFFF(~1.07e9)).

Update:TheAreafunctionhasbeenupdatedwithafasteralgorithm.

Update:Documentationupdates.Thenewishbutundocumented'CheckInputs'parameteroftheOffsetPolygonsfunctionhasbeenrenamed'AutoFix'anddocumentedtoo.Thecommentsonroundinghavealsobeenimproved(ieclearerandexpanded).

v4.10.0(25December2012)

Bugfix:Orientationbugsshouldnowberesolved(finally!).

Bugfix:BuginInt128class.

Bugfix:FurtherfixestorareOrientationbug.

v4.9.7(29November2012)

Bugfix:Bugthatveryrarelyreturnedawrongpolygonorientation.

Bugfix:ObscurebugaffectingOffsetPolygonswhenusingjtRoundfortheJoinTypeparameterandwhenpolygonsalsocontainverylargecoordinatevalues.

Bugfix:Anotherobscurebugrelatedtojoiningintersections.

Bugfix:BugsinInt128classoccasionallycausingwrongorientations.

Bugfix:Furtherfixesrelatedtojoiningintersections.

v4.9.0(9October2012)

Bugfix:Obscurebugrelatedtojoiningintersections.

v4.8.9(25September2012)

Bugfix:Obscurebugrelatedtoprecisionofintersections.

v4.8.8(30August2012)

Bugfix:FixedbuginOffsetPolygonsfunctionintroducedinversion4.8.5.

v4.8.7(24August2012)

Bugfix:ReversePolygonfunctioninC++translationwasbroken.

Bugfix:Twoobscurebugsaffectingorientationfixedtoo.

v4.8.6(11August2012)

Bugfix:PotentialformemoryoverflowerrorswhenusingExPolygonsstructure.

Bugfix:Thepolygoncoordinaterangehasbeenreducedto±0x3FFFFFFFFFFFFFFF(4.6e18).

Update:ReversePolygonsfunctionwasmisnamedReversePointsinC++.

Update:SimplifyPolygonfunctionnowtakesaPolyFillTypeparameter.

v4.8.5(15July2012)

Bugfix:PotentialformemoryoverflowerrorsinOffsetPolygons().

v4.8.4(1June2012)

Bugfix:AnotherobscurebugaffectingExPolygonsstructure.

v4.8.3(27May2012)

Bugfix:Obscurebugcausingincorrectremovalofavertex.

v4.8.2(21May2012)

Bugfix:ObscurebugcouldcauseanexceptionwhenusingExPolygonstructure.

v4.8.1(12May2012)

Update:Codetidyandminorbugfixes.

v4.8.0(30April2012)

Bugfix:Occasionalerrorsinorientationfixed.

Update:Addednotesonroundingtothedocumentation.

v4.7.6(11April2012)

Bugfix:FixedabugintheOrientationfunction(affectingC#translationsonly).

Update:Minordocumentationupdate.

v4.7.5(28March2012)

Bugfix:FixedarecentlyintroducedbugthatoccasionallycausedanunhandledexceptioninC++andC#translations.

v4.7.1(3March2012)

Bugfix:RarecrashwhenJoinCommonEdgesjoinedpolygonsthat'cancelled'eachother.

Bugfix:Clipper'sinternalOrientationmethodoccasionallyreturnedwrongresult.

Update:ImprovedC#code(thankstonumeroussuggestionsfromDavidPiepgrass)

v4.7(10February2012)

Update:Improvedthejoiningofoutputpolygonssharingacommonedge.

Added:AddedSimplifyPolygonandSimplifyPolygonsfunctions.

v4.6(29October2011)

Added:SupportforPositiveandNegativepolygonfilltypes(inadditiontotheEvenOddandNonZerofilltypes).

Bugfix:TheOffsetPolygonsfunctionwasgeneratingtheoccasionalartefactwhen'shrinking'polygons.

v4.5.5(6October2011)

Bugfix:FixedanobscurebuginClipper'sJoinCommonEdgesmethod.

Update:ReplacedIsClockwisefunctionwithOrientationfunction.TheorientationissuesaffectingOffsetPolygonsshouldfinallyberesolved.

Change:TheAreafunctiononceagainreturnsthesignedarea.

v4.4.0(6August2011)

BugFix:AnumberofminorbugfixesthatmostlyaffectedthenewExPolygonsstructure.

v4.3.0(17June2011)

Added:ExPolygonsstructurethatexplicitlyassociates'hole'polygonswiththeir'outer'containerpolygons.

Added:ExecutemethodnowoverloadedsothesolutionparametercanbeeitherPolygonsorExPolygons.

Bugfix:Fixedararebugintheorientationofsolutionpolygons.

v4.2.4(26April2011)

Update:Inputpolygoncoordinatescannowcontainthefullrangeofsigned64bitintegers(ie+/-9,223,372,036,854,775,807).ThismeansthatfloatingpointvaluescanbeconvertedtoandfromClipper's64bitvertexstructure(IntPoint)andstillretainaprecisionofupto18decimalplaces.However,sincethelarge-integermaththatsupportsthisexpandedrangeimposesasmallcostonperformance(~15%),anewpropertyUseFullCoordinateRangehasbeenaddedtotheClipperclasstoallowusersthechoiceofwhetherornottousethisexpandedcoordinaterange.Ifthispropertyisdisabled,coordinatevaluesarerestrictedto+/-1,500,000,000.(Bydefault,thispropertyisenabled.)

v4.0(4April2011)

Majorupdate:Clipperisamajorrewriteofearlierversions.Thebiggestchangeisthatfloatingpointvaluesarenolongerused,exceptforthestoringofedgeslopevalues.Themainbenefitofthisistheissueofnumericalrobustnesshasbeenaddressed.DuetoothermajorcodeimprovementsClipperv4isapproximately40%fasterthanClipperv3.

Changes:TheAddPolyPolygonmethodhasbeenrenamedtoAddPolygons,andtheIgnoreOrientationpropertyhasbeenremoved.Theclipper_misclibraryhasbeenmergedbackintotheclipperlibrary.

v2.8(20November2010)

Updated:Outputpolygonswhichpreviouslysharedacommonedgearenowmerged.

Added:AddedsupportmoduleforCairoGraphicsLibrary(withaccompanyingdemo).

Added:AddedC#andC++demos.

v2.522(15October2010)

Added:AddedC#translation(thankstoOlivierLejeune)andalinktoRubybindings(thankstoMikeOwens).

v2.0(31July2010)

Majorupdate:ClippernowprocessespolygonsusingboththeEven-Odd(alternate)andNon-Zero(winding)fillingrules.

v1.4c(16June2010)

Additions:AddedDelphiandC++unitstosupporttheAGGgraphicslibrary

v1.2s(2June2010)

Additions:C++translationofDelphicode

v1.0(9May2010)-Initialpublicrelease

SeeAlsoDeprecated,Rounding,Clipper.Constructor,Clipper.Execute,Clipper.ZFillFunction,ClipperBase.AddPath,ClipperBase.AddPaths,ClipperOffset,ClipperOffset.Execute,PolyNode,PolyTree,Area,CleanPolygon,CleanPolygons,ClosedPathsFromPolyTree,MinkowskiDiff,MinkowskiSum,OffsetPaths,OpenPathsFromPolyTree,Orientation,PointInPolygon,PolyTreeToPaths,SimplifyPolygon,SimplifyPolygons,Defines,CInt,InitOptions,IntPoint,Path,Paths,PolyFillType,ZFillCallback


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Deprecated

Theprecompilerdirective'use_deprecated'allowsuserstoupdatetheClipperlibrarywithoutbeingforcedtomakeimmediatechangestocodethataccessesthelibrary.Depricatedcodewillberemovedinafutureupdate.(Enabledbydefault.)

Deprecatedtypesandfunctions:

Alldeprecatedcodehasbeenremovedfromversion6.2.0.


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DelphiCodeSample:usesgraphics32,clipper;functionGetEllipsePoints(bounds:TIntRect):TPath;begin//codetocreateanellipticalpolygonhereend;procedureDrawPolygons(polys:TPaths;color:TColor32);begin//codetodisplaythepolygonshereend;varsub,clp,sol:TPaths;begin

//setupthesubjectandclippolygons...setlength(sub,3);sub[0]:=GetEllipsePoints(IntRect(100,100,300,300));sub[1]:=GetEllipsePoints(IntRect(125,130,275,180));sub[2]:=GetEllipsePoints(IntRect(125,220,275,270));setlength(clp,1);clp[0]:=GetEllipsePoints(IntRect(140,70,220,320));

//displaythesubjectandclippolygons...DrawPolygons(sub,0x8033FFFF);DrawPolygons(clp,0x80FFFF33);//gettheintersectionofthesubjectandclippolygons...withTClipper.CreatedotryAddPaths(sub,ptSubject,true);AddPaths(clp,ptClip,true);Execute(ctIntersection,sol,pftEvenOdd,pftEvenOdd);finallyfree;end;//finallydrawtheintersectionpolygons...DrawPolygons(sol,0x40808080);

C++CodeSample:#include"clipper.hpp"...

//fromclipper.hpp...//typedeflonglongcInt;//structIntPoint{cIntX;cIntY;};//typedefstd::vectorPath;//typedefstd::vectorPaths;

usingnamespaceClipperLib;

Example

voidGetEllipsePoints(IntRect&bounds,Path&p){/*...*/}voidDrawPolygons(Paths&p,unsignedcolor){/*...*/}intmain(){//setupthesubjectandclippolygons...Pathssub(3);GetEllipsePoints(IntRect(100,100,300,300),sub[0]);GetEllipsePoints(IntRect(125,130,275,180),sub[1]);GetEllipsePoints(IntRect(125,220,275,270),sub[2]);Pathsclp(1);GetEllipsePoints(IntRect(140,70,220,320),clp[0]);//displaythesubjectandclippolygons...DrawPolygons(sub,0x8033FFFF);DrawPolygons(clp,0x80FFFF33);//gettheintersectionofthesubjectandclippolygons...Clipperclpr;clpr.AddPaths(sub,ptSubject,true);clpr.AddPaths(clp,ptClip,true);Pathssolution;clpr.Execute(ctIntersection,solution,pftEvenOdd,pftEvenOdd);//finallydrawtheintersectionpolygons...DrawPolygons(solution,0x40808080);}

C#CodeSample:...usingClipperLib;...usingPath=List;usingPaths=List;staticPathGetEllipsePoints(IntRectbounds){/*...*/}staticvoidDrawPolygons(Pathp,uintcolor){/*...*/}staticvoidMain(string[]args){Pathssubjs=newPaths(3);subjs.Add(GetEllipsePoints(newIntRect(100,100,300,300)));subjs.Add(GetEllipsePoints(newIntRect(125,130,275,180)));subjs.Add(GetEllipsePoints(newIntRect(125,220,275,270)));Pathsclips=newPaths(1);clips.Add(GetEllipsePoints(newIntRect(140,70,220,320)));DrawPolygons(subjs,0x8033FFFF);DrawPolygons(clips,0x80FFFF33);Pathssolution=newPaths();

Clipperc=newClipper();c.AddPaths(subjs,PolyType.ptSubject,true);c.AddPaths(clips,PolyType.ptClip,true);c.Execute(ClipType.ctIntersection,solution);DrawPolygons(solution,0x40808080);}


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FAQ

WhydoesClipperuseintegercoordinates,notfloats?Thishasbeendonetopreservenumericalrobustness.Earlyversionsofthelibrarydidusefloatingpointcoordinates,butitbecameapparentthatfloatingpointimprecisionwasalwaysgoingtocauseoccasionalerrors.

HowdoIusefloatingpointcoordinateswithClipper?It'sasimpletasktomultiplyyourfloatingpointcoordinatesbyascalingfactor(that'stypicallyapowerof10dependingonthedesiredprecision).Thenwiththesolutionpaths,dividethereturnedcoordinatesbythissamescalingfactor.Clipperacceptsintegercoordinatesaslargeas±4.6e18,soitcanaccommodateverylargescaling.

DoesClipperhandlepolygonswithholes?'Holes'aredefinedbythespecifiedpolygonfillingrule.(SeealsoClipper.Execute)

Somepolygonsinthesolutionshareacommonedge.Isthisabug?No,thoughthisshouldhappenrarelyasofversion6.(SeeClipper.Executeformoreaboutthis.)

IhavelotsofpolygonsthatIwantto'union'.CanIdothisinoneoperation?Yes.JustaddallthepolygonsassubjectpolygonstotheClipperobject.(Youdon'thavetoassignbothsubjectandclippolygons.)

ThepolygonsproducedbyClipperOffsethavetinyartefacts?Couldthisbeabug?Makesuretheinputpolygonsdon'tself-intersect.Tinyself-intersectionscansometimesbeproducedbypreviousclippingoperations.ThesecanbecleanedupusingtheCleanPolygonandCleanPolygonsfunctions.Also,makesurethesuppliedpolygonsdon'toverlap.Iftheydo,offset

http://www.mpi-inf.mpg.de/~kettner/pub/nonrobust_cgta_06.pdf

theseseparately.Finally,theprecisionoftheinputcoordinatesmaybeaproblem.BecausetheClipperLibraryonlyoperatesonintegercoordinates,youmayneedtoscaleyourcoordinates(egbyafactorof10)toimproveprecision.

Isthereaneasywaytoreversepolygonorientations?Yes,seeReversePaths.

Mydrawingscontainlotsofbeziers,ellipsesandarcs.HowcanIperformclippingoperationsonthese?You'llhavetoconvertthemto'flattened'paths.Foranexampleofhowthiscanbedone(andevenreconstructedbackintobeziers,arcsetc),seetheCurvesDemoapplicationincludedinthislibrary.

SeeAlsoClipper.Execute,ClipperOffset,CleanPolygon,CleanPolygons,ReversePaths,PolyFillType


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License

TheClipperLibrary(includingDelphi,C++&C#sourcecode,otheraccompanyingcode,examplesanddocumentation),hereaftercalled"theSoftware",hasbeenreleasedunderthefollowinglicense,termsandconditions:BoostSoftwareLicense-Version1.0-August17th,2003http://www.boost.org/LICENSE_1_0.txtPermissionisherebygranted,freeofcharge,toanypersonororganizationobtainingacopyoftheSoftwarecoveredbythislicensetouse,reproduce,display,distribute,execute,andtransmittheSoftware,andtopreparederivativeworksoftheSoftware,andtopermitthird-partiestowhomtheSoftwareisfurnishedtodoso,allsubjecttothefollowing:ThecopyrightnoticesintheSoftwareandthisentirestatement,includingtheabovelicensegrant,thisrestrictionandthefollowingdisclaimer,mustbeincludedinallcopiesoftheSoftware,inwholeorinpart,andallderivativeworksoftheSoftware,unlesssuchcopiesorderivativeworksaresolelyintheformofmachine-executableobjectcodegeneratedbyasourcelanguageprocessor.THESOFTWAREISPROVIDED"ASIS",WITHOUTWARRANTYOFANYKIND,EXPRESSORIMPLIED,INCLUDINGBUTNOTLIMITEDTOTHEWARRANTIESOFMERCHANTABILITY,FITNESSFORAPARTICULARPURPOSE,TITLEANDNON-INFRINGEMENT.INNOEVENTSHALLTHECOPYRIGHTHOLDERSORANYONEDISTRIBUTINGTHESOFTWAREBELIABLEFORANYDAMAGESOROTHERLIABILITY,WHETHERINCONTRACT,TORTOROTHERWISE,ARISINGFROM,OUTOFORINCONNECTIONWITHTHESOFTWAREORTHEUSEOROTHERDEALINGSINTHESOFTWARE.


http://www.boost.org/LICENSE_1_0.txt

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Rounding

Byusinganintegertypeforpolygoncoordinates,theClipperLibraryhasbeenabletoavoidproblemsofnumericalrobustnessthatcancausehavocwithgeometriccomputations.Problemsassociatedwithintegerroundingandtheirpossiblesolutionsarediscussedbelow.

It'simportanttostressattheoutsetthatroundingcausesverticestomovefractionsofaunitawayfromtheir'true'positions.

Nevertheless,theresultingimprecisioncanbeveryeffectivelymanagedbyappropriatescaling.

TheClipperLibrarysupportsscalingtoveryhighdegreesofprecisionbyacceptingintegercoordinatevaluesintherange±0x3FFFFFFFFFFFFFFF(±4.6e+18).

Anothercomplicationofusingadiscretenumbers(asopposedtorealnumbers)isthatveryoccasionallytinyself-intersectionartefactsarise.Intheunscaledimageontheleft(whereoneunitequalsonepixel),theareaofintersectionoftwopolygonshasbeenhighlightedinbrightgreen.

A30X'closeup'ofthelowerpointsofintersectionofthesesametwo

http://www.mpi-inf.mpg.de/~kettner/pub/nonrobust_cgta_06.pdfhttp://en.wikipedia.org/wiki/Real_number

polygonsshowsthepresenceofatinyself-intersectingartefact.Thethree'blackdots'highlighttheactualpointsofintersection(withtheirfractionalcoordinatesdisplayed).The'reddots'showwherethesepointsofintersectionarelocatedonceroundingisapplied.Withalittlecareyoucanseethatroundingreversestheorientationoftheseverticesandcausesatinyself-intersectingartefact.

Althoughthesetinyself-intersectionsareuncommon,ifit'sdeemednecessary,theyarebestremovedwithCleanPolygons.(SettingClipper'sStrictlySimplepropertytotruewouldalsoaddressthisself-intersectionbutthetiny(sub-unit)polygon'artefact'withincorrectorientationwouldstillappearinthesolution.)

Inthisfinalexample,thesinglepolygonontheleftalsohasatinyself-intersection.However,theclippingalgorithmseesthisvertex(88,50)assimply'touching'ratherthanintersectingtherightedgeofthepolygon(thoughonlybyafractionofaunit).Sincethisintersectionwon't

normallybedetected,theclippingsolution(egfollowingaunionoperation)willstillcontainthistinyself-intersection.SettingClipper'sStrictlySimplepropertytotrueavoidsthisuncommonproblem.

SeeAlsoClipper.StrictlySimple,CleanPolygons


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CInt

Del.»{$IFDEFuse_int32}cInt=Int32;{$ELSE}cInt=Int64;{$ENDIF}C++»#ifdefuse_int32typedefintcInt;#elsetypedefsignedlonglongcInt;#endifC#»#ifuse_int32usingcInt=Int32;#elseusingcInt=Int64;#endif

cIntistheintegertypeusedbytheClipperLibrarytorepresentvertexcoordinatevalues.(SeealsoIntPoint.)

Thelibraryusesintegersinsteadoffloatingpointvaluestopreservenumericalrobustness.(Veryearlyversionsofthelibraryusedfloatingpointcoordinates,butitbecameapparentthatfloatingpointimprecisionwasalwaysgoingtocauseoccasionalerrors.)

BydefaultcIntrepresentsasigned64bitintegerandpolygoncoordinatescanhaveanyvalueintherange±9.2e+18.Thisaccommodatesthescalingoffloatingpointcoordinatevaluestoverylargeintegerssothatveryhighdegreesofprecisioncanberetainedduringclipping.However,ifcoordinatevaluescanbekeptwithintherange±3.0e+9,thenbyavoidinglargeintegermath,amodest~10%improvementinclippingperformanceisachieved.

Ifthepreprocessordirectiveuse_int32isdefined,cIntwillrepresenta


signed32bitinteger.Thisimprovesclippingperformanceby20-30%butthetrade-offisthatcoordinatevaluesarerestrictedtothemuchnarrowerrangeof±46340.

SeeAlsoDefines,IntPoint


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ClipType

Del.»typeTClipType=(ctIntersection,ctUnion,ctDifference,ctXor);C++»enumClipType{ctIntersection,ctUnion,ctDifference,ctXor};C#»publicenumClipType{ctIntersection,ctUnion,ctDifference,ctXor};

Therearefourbooleanoperations-AND,OR,NOT&XOR.

Giventhatsubjectandclippolygonbrush'filling'isdefinedbothbytheirverticesandtheirrespectivefillingrules,thefourbooleanoperationscanbeappliedtopolygonstodefinenewfillingregions:

AND(intersection)-createregionswherebothsubjectandclippolygonsarefilledOR(union)-createregionswhereeithersubjectorclippolygons

(orboth)arefilledNOT(difference)-createregionswheresubjectpolygonsarefilled

exceptwhereclippolygonsarefilledXOR(exclusiveor)-createregionswhereeithersubjectorclip

polygonsarefilledbutnotwherebotharefilled

AllpolygonclippingisperformedwithaClipperobjectwiththespecificbooleanoperationindicatedbytheClipTypeparameterpassedinitsExecutemethod.

Withregardtoopenpaths(polylines),clippingrulesgenerallymatchthoseofclosedpaths(polygons).However,whentherearebothpolylineandpolygonsubjects,thefollowingclippingrulesapply:

unionoperations-polylineswillbeclippedbyanyoverlappingpolygonssothatnon-overlappedportionswillbereturnedinthesolutiontogetherwiththeunion-edpolygonsintersection,differenceandxoroperations-polylineswillbeclipped

onlyby'clip'polygonsandtherewillbenotinteractionbetweenpolylinesandsubjectpolygons.

Exampleofclippingbehaviourwhenmixingpolylineandpolygonsubjects:

SeeAlsoOverview,Clipper,Clipper.Execute,PolyFillType


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EndType

Del.»typeTEndType=(etClosedPolygon,etClosedLine,etOpenSquare,etOpenRound,etOpenButt);C++»enumEndType{etClosedPolygon,etClosedLine,etOpenSquare,etOpenRound,etOpenButt};C#»publicenumEndType{etClosedPolygon,etClosedLine,etOpenSquare,etOpenRound,etOpenButt};

TheEndTypeenumeratorhas5values:

etClosedPolygon:EndsarejoinedusingtheJoinTypevalueandthepathfilledasapolygonetClosedLine:EndsarejoinedusingtheJoinTypevalueandthe

pathfilledasapolylineetOpenSquare:EndsaresquaredoffandextendeddeltaunitsetOpenRound:EndsareroundedoffandextendeddeltaunitsetOpenButt:Endsaresquaredoffwithnoextension.etOpenSingle:Offsetsanopenpathinasingledirection.Planned

forafutureupdate.

Note:WithetClosedPolygonandetClosedLinetypes,thepathclosurewillbethesameregardlessofwhetherornotthefirstandlastverticesinthepathmatch.

SeeAlsoClipperOffset.AddPath,ClipperOffset.AddPaths


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InitOptions

Del.»typeTInitOption=(ioReverseSolution,ioStrictlySimple,ioPreserveCollinear);C++»enumInitOptions{ioReverseSolution=1,ioStrictlySimple=2,ioPreserveCollinear=4};C#»publicconstintioReverseSolution=1;publicconstintioStrictlySimple=2;publicconstintioPreserveCollinear=4;

SeeAlsoClipper.Constructor,Clipper.PreserveCollinear,Clipper.ReverseSolution,Clipper.StrictlySimple


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IntPoint

Del.»TIntPoint=recordX,Y:cInt;end;C++»structIntPoint{cIntX;cIntY;...};C#»publicclassIntPoint{publiccIntX;{get;set;}publiccIntY;{get;set;}...};

TheIntPointstructureisusedtorepresentallverticesintheClipperLibrary.Anintegerstoragetypehasbeendeliberatelychosentopreservenumericalrobustness.(Earlyversionsofthelibraryusedfloatingpointcoordinates,butitbecameapparentthatfloatingpointimprecisionwouldalwayscauseoccasionalerrors.)

AsequenceofIntPointsarecontainedwithinaPathstructuretorepresentasinglecontour.

Asofversion6,IntPointnowhasanoptionalthirdmember'Z'.Thiscanbeenabledbyexposing(ieuncommenting)thePreProcessordefine'use_xyz'.WhentheZmemberisused,itsvalueswillbecopiedtocorrespondingverticiesinsolutionstoclippingoperations.However,atpointsofintersectionwherethere'snocorrespondingZvalue,thevaluewillbeassignedzerounlessanewvalueisprovidedbyausersuppliedcallbackfunction.

UserswishingtocliporoffsetpolygonscontainingfloatingpointcoordinatesneedtouseappropriatescalingwhenconvertingthesevaluestoandfromIntPoints.

Seealsothenotesonrounding.


SeeAlsoRounding,Clipper.ZFillFunction,Defines,CInt,Path,Paths


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IntRect

Del.»TIntRect=recordleft,top,right,bottom:cInt;end;C++»structIntRect{cIntleft;cInttop;cIntright;cIntbottom;...};C#»publicclassIntRect{publiccIntleft;{get;set;}publiccInttop;{get;set;}publiccIntright;{get;set;}publiccIntbottom;{get;set;}...};

StructurereturnedbyClipper'sGetBoundsmethod.

SeeAlsoClipperBase.GetBounds,CInt


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JoinType

Del.»typeTJoinType=(jtSquare,jtRound,jtMiter);C++»enumJoinType{jtSquare,jtRound,jtMiter};C#»publicenumJoinType{jtSquare,jtRound,jtMiter};

WhenaddingpathstoaClipperOffsetobjectviatheAddPathsmethod,thejoinTypeparametermaybeoneofthreetypes-jtMiter,jtSquareorjtRound.

jtMiter:There'sanecessarylimittomiteredjoinssinceoffsettingedgesthatjoinatveryacuteangleswillproduceexcessivelylongandnarrow'spikes'.Tocontainthesepotentialspikes,theClippOffsetobject'sMiterLimitpropertyspecifiesamaximumdistancethatverticeswillbeoffset(inmultiplesofdelta).Foranygivenedgejoin,whenmiteroffsettingwouldexceedthatmaximumdistance,'square'joiningisapplied.jtRound:Whileflattenedpathscanneverperfectlytraceanarc,they

areapproximatedbyaseriesofarcchords(seeClipperObject'sArcToleranceproperty).jtSquare:Squaringisapplieduniformallyatallconvexedgejoinsat

1×delta.

SeeAlsoClipperOffset,ClipperOffset.AddPaths,ClipperOffset.ArcTolerance,ClipperOffset.MiterLimit


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Path

Del.»TPath=arrayofTIntPoint;C++»typedefstd::vectorPath;C#»usingPath=List;

ThisstructurecontainsasequenceofIntPointverticesdefiningasinglecontour(seealsoterminology).Pathsmaybeopenandrepresentaseriesoflinesegmentsboundedby2ormorevertices,ortheymaybeclosedandrepresentpolygons.Whetherornotapathisopendependsoncontext.Closedpathsmaybe'outer'contoursor'hole'contours.Whichtheyaredependsonorientation.

MultiplepathscanbegroupedintoaPathsstructure.

SeeAlsoOverview,Example,ClipperBase.AddPath,PolyTree,Orientation,IntPoint,Paths


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Paths

Del.»TPaths=arrayofTPath;C++»typedefstd::vector<Path>Paths;C#»usingPaths=List>;

ThisstructureisfundamentaltotheClipperLibrary.It'salistorarrayofoneormorePathstructures.(ThePathstructurecontainsanorderedlistofverticesthatmakeasinglecontour.)

Pathsmayopen(aseriesoflinesegments),ortheymayclosed(polygons).Whetherornotapathisopendependsoncontext.Closedpathsmaybe'outer'contoursor'hole'contours.Whichtheyaredependsonorientation.

SeeAlsoClipper.Execute,ClipperBase.AddPath,ClipperBase.AddPaths,OffsetPaths,IntPoint,Path


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PolyFillType

Del.»typeTPolyFillType=(pftEvenOdd,pftNonZero,pftPositive,pftNegative);C++»enumPolyFillType{pftEvenOdd,pftNonZero,pftPositive,pftNegative};C#»publicenumPolyFillType{pftEvenOdd,pftNonZero,pftPositive,pftNegative};

Fillingindicatesthoseregionsthatareinsideaclosedpath(ie'filled'withabrushcolororpatterninagraphicaldisplay)andthoseregionsthatareoutside.TheClipperLibrarysupports4fillingrules:Even-Odd,Non-Zero,PositiveandNegative.

ThesimplestfillingruleisEven-Oddfilling(sometimescalledalternatefilling).Givenagroupofclosedpathsstartfromapointoutsidethepathsandprogressalonganimaginarylinethroughthepaths.Whenthefirstpathiscrossedtheencounteredregionisfilled.Whenthenextpathiscrossedtheencounteredregionisnotfilled.Likewise,eachtimeapathiscrossed,fillingstartsifithadstoppedandstopsifithadstarted.

WiththeexceptionofEven-Oddfilling,allotherfillingrulesrelyonedgedirectionandwindingnumberstodeterminefilling.Edgedirectionisdeterminedbytheorderinwhichverticesaredeclaredwhenconstructingapath.Edgedirectionisusedtodeterminethewindingnumberofeachpolygonsubregion.

Thewindingnumberforeachpolygonsub-regioncanbederivedby:

1. startingwithawindingnumberofzeroand2. fromapoint(P1)that'soutsideallpolygons,drawanimaginary

linetoapointthat'sinsideagivensub-region(P2)3. whiletraversingthelinefromP1toP2,foreachpaththatcrosses

theimaginarylinefromrighttoleftincrementthewindingnumber,andforeachpaththatcrossesthelinefromlefttorightdecrementthewindingnumber.

4. Onceyouarriveatthegivensub-regionyouhaveitswindingnumber.

Even-Odd(Alternate):Oddnumberedsub-regionsarefilled,whileevennumberedsub-regionsarenot.Non-Zero(Winding):Allnon-zerosub-regionsarefilled.Positive:Allsub-regionswithwindingcounts>0arefilled.Negative:Allsub-regionswithwindingcounts<0arefilled.

PathsareaddedtoaClipperobjectusingtheAddPathorAddPathsmethodsandthefillingrules(forsubjectandclippolygonsseparately)arespecifiedintheExecutemethod.

Polygonregionsaredefinedbyoneormoreclosedpathswhichmayormaynotintersect.Asinglepolygonregioncanbedefinedbyasinglenon-intersectingpathorbymultiplenon-intersectingpathswherethere'stypicallyan'outer'pathandoneormoreinner'hole'paths.Lookingatthethreeshapesintheimageabove,themiddleshapeconsistsoftwoconcentricrectanglessharingthesameclockwiseorientation.Witheven-oddfilling,whereorientationcanbedisregarded,theinnerrectanglewouldcreateaholeintheouterrectangularpolygon.Therewouldbenoholewithnon-zerofilling.Intheconcentricrectanglesontheright,wheretheinnerrectangleisorientatedoppositetotheouter,aholewillberenderedwitheithereven-oddornon-zerofilling.Asinglepathcanalsodefinemultiplesubregionsifitself-intersectsasintheexampleofthe5pointedstarshapebelow.

ByfarthemostwidelyusedfillrulesareEven-Odd(akaAlternate)andNon-Zero(akaWinding).Mostgraphicsrenderinglibraries(AGG,AndroidGraphics,Cairo,GDI+,OpenGL,Quartz2Detc)andvectorgraphicsstorageformats(SVG,Postscript,Photoshopetc)supportboththeserules.Howeversomelibraries(egJava'sGraphics2D)onlysupportonefillrule.AndroidGraphicsandOpenGLaretheonlylibraries(thatI'mawareof)thatsupportmultiplefillingrules.

It'susefultonotethatedgedirectionhasnoaffectonawindingnumber'sodd-nessoreven-ness.(ThisiswhyorientationisignoredwhentheEven-Oddruleisemployed.)

ThedirectionoftheY-axisdoesaffectpolygonorientationandedgedirection.However,changingY-axisorientationwillonlychangethesignofwindingnumbers,nottheirmagnitudes,andhasnoeffectoneitherEven-OddorNon-Zerofilling.

http://www.antigrain.com/__code/include/agg_basics.h.html#filling_rule_ehttp://developer.android.com/reference/android/graphics/Path.FillType.htmlhttp://cairographics.org/manual/cairo-cairo-t.html#cairo-fill-rule-thttp://msdn.microsoft.com/en-us/library/windows/desktop/ms534120(v=vs.85).aspxhttp://www.glprogramming.com/red/chapter11.htmlhttp://developer.apple.com/library/ios/#documentation/GraphicsImaging/Conceptual/drawingwithquartz2d/dq_paths/dq_paths.html#//apple_ref/doc/uid/TP30001066-CH211-TPXREF101http://www.w3.org/TR/SVG/painting.html#FillRulePropertyhttp://www.adobe.com/devnet-apps/photoshop/fileformatashtml/PhotoshopFileFormats.htm#50577409_17587http://docs.oracle.com/javase/6/docs/api/java/awt/Graphics.html#fillPolygon(int[], int[], int)

SeeAlsoClipper.Execute,ClipperBase.AddPath,ClipperBase.AddPaths,Orientation


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PolyType

Del.»typeTPolyType=(ptSubject,ptClip);C++»enumPolyType{ptSubject,ptClip};C#»publicenumPolyType{ptSubject,ptClip};

Boolean(clipping)operationsaremostlyappliedtotwosetsofPolygons,representedinthislibraryassubjectandclippolygons.WheneverPolygonsareaddedtotheClipperobject,theymustbeassignedtoeithersubjectorclippolygons.

UNIONoperationscanbeperformedononesetorbothsetsofpolygons,butallotherbooleanoperationsrequirebothsetsofpolygonstoderivemeaningfulsolutions.

SeeAlsoClipperBase.AddPath,ClipperBase.AddPaths,ClipType


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ZFillCallback

Del.»typeTZFillCallback=procedure(constE1Bot,E1Top,E2Bot,E2Top:TIntPoint;varPt:TIntPoint);C++»typedefvoid(*ZFillCallback)(constIntPoint&e1bot,IntPoint&e1top,IntPoint&e2bot,IntPoint&e2top,IntPoint&pt);C#»publicdelegatevoidZFillCallback(IntPointbot1,IntPointtop1,IntPointbot2,IntPointtop2,refIntPointpt);

Iftheuse_xyzpre-processordirectiveisenabled,thentheIntPointclasswillhaveanextra'Z'memberandtheClipperclass'sZFillFunctionpropertywillbeexposedsoitcanbeassignedacustomcallbackfunction.

ThiscustomcallbackprocedurerequiresfiveIntPointparameters:thefirst2parametersaretheverticesthatdefineonelinesegmentinvolvedintheintersectionandthenexttwoparameterstheotherlinesegment.(SincetheClipperlibraryhasbeendevelopedinanenvironmentthatusesaninvertedYaxisdisplay,e1botande2botwillalwayshaveYvaluesgreaterthanorequaltotheircorrespondinge1topande2topYvalues.)ThelastIntPointparametercontaintheactualcoordinatesattheintersection.ThislastparameterispassedbyreferencesothatitsZmembercanbeassignedwithacustomvalue.

SeeAlsoClipper.ZFillFunction,Defines


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Area

Del.»functionArea(constpts:TPath):double;C++»doubleArea(constPath&poly);C#»publicstaticdoubleArea(Pathpoly);

Thisfunctionreturnstheareaofthesuppliedpolygon.It'sassumedthatthepathisclosedanddoesnotself-intersect.Dependingonorientation,thisvaluemaybepositiveornegative.IfOrientationistrue,thentheareawillbepositiveandconversely,ifOrientationisfalse,thentheareawillbenegative.

SeeAlsoOrientation,Path


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CleanPolygon

Del.»functionCleanPolygon(constPoly:TPath;Distance:double=1.415):TPath;C++»voidCleanPolygon(constPath&in_poly,Path&out_poly,doubledistance=1.415);C++»voidCleanPolygon(Path&poly,doubledistance=1.415);C#»publicstaticPathCleanPolygon(Pathpoly,doubledistance=1.415);

Removesvertices:

thatjoinco-linearedges,orjoinedgesthatarealmostco-linear(suchthatifthevertexwasmovednomorethanthespecifieddistancetheedgeswouldbeco-linear)thatarewithinthespecifieddistanceofanadjacentvertexthatarewithinthespecifieddistanceofasemi-adjacentvertex

togetherwiththeirout-lyingvertices

Verticesaresemi-adjacentwhentheyareseparatedbyasingle(out-lying)vertex.

Thedistanceparameter'sdefaultvalueisapproximately√2sothatavertexwillberemovedwhenadjacentorsemi-adjacentverticeshavingtheircorrespondingXandYcoordinatesdifferingbynomorethan1unit.(Iftheegdesaresemi-adjacenttheout-lyingvertexwillberemovedtoo.)

C++only:Thisfunctionisoverloaded.Inthefirstdefinition,thein_polyandout_polyparameterscanreferencethesamePathobjectthoughinthatcasethecallingcodemightbecleareriftheseconddefinition(acceptingasinglePathsparameter)isused.

SeeAlsoCleanPolygons,SimplifyPolygon,Path


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CleanPolygons

Del.»functionCleanPolygons(constPolys:TPaths;Distance:double=1.415):TPaths;C++»voidCleanPolygons(constPaths&in_polys,Paths&out_polys,doubledistance=1.415);C++»voidCleanPolygons(Paths&polys,doubledistance=1.415);C#»publicstaticPathsCleanPolygons(Pathspolys,doubledistance=1.415);

Removesvertices:

thatjoinco-linearedges,orjoinedgesthatarealmostco-linear(suchthatifthevertexwasmovednomorethanthespecifieddistancetheedgeswouldbeco-linear)thatarewithinthespecifieddistanceofanadjacentvertexthatarewithinthespecifieddistanceofasemi-adjacentvertex

togetherwiththeirout-lyingvertices

Verticesaresemi-adjacentwhentheyareseparatedbyasingle(out-lying)vertex.

Thedistanceparameter'sdefaultvalueisapproximately√2sothatavertexwillberemovedwhenadjacentorsemi-adjacentverticeshavingtheircorrespondingXandYcoordinatesdifferingbynomorethan1unit.(Iftheegdesaresemi-adjacenttheout-lyingvertexwillberemovedtoo.)

C++only:Thisfunctionisoverloaded.Inthefirstdefinition,thein_polysandout_polysparameterscanreferencethesamePathsobjectthoughinthatcasethecallingcodemightbecleareriftheseconddefinition(acceptingasinglePathsparameter)isused.

SeeAlsoCleanPolygon,SimplifyPolygons


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ClosedPathsFromPolyTree

Del.»functionClosedPathsFromPolyTree(PolyTree:TPolyTree):TPaths;C++»voidClosedPathsFromPolyTree(PolyTree&polytree,Paths&paths);C#»publicstaticvoidClosedPathsFromPolyTree(PolyTreepolytree,Pathspaths);

ThisfunctionfiltersoutopenpathsfromthePolyTreestructureandreturnsonlyclosedpathsinaPathsstructure.

SeeAlsoPolyTree,Paths


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MinkowskiDiff

Del.»functionMinkowskiDiff(constPoly1:TPath;constPoly2:TPath):TPaths;C++»voidMinkowskiDiff(constPath&poly1,constPath&poly2,Paths&solution);C#»publicstaticPathsMinkowskiDiff(Pathpoly1,Pathpoly2);

MinkowskiDifferenceisperformedbysubtractingeachpointinapolygonfromthesetofpointsinanopenorclosedpath.AkeyfeatureofMinkowskiDifferenceisthatwhenit'sappliedtotwopolygons,theresultingpolygonwillcontainthecoordinatespaceoriginwheneverthetwopolygonstouchoroverlap.(Thisfunctionisoftenusedtodeterminewhenpolygonscollide.)

Intheimageontheleftthebluepolygonisthe'minkowskidifference'ofthetworedboxes.Theblackdotrepresentsthecoordinatespaceorigin.

SeeAlsoMinkowskiSum,Path


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MinkowskiSum

Del.»functionMinkowskiSum(constPattern:TPath;constPath:TPath;PathIsClosed:Boolean):TPaths;overload;Del.»functionMinkowskiSum(constPattern:TPath;constPaths:TPaths;PathFillType:TPolyFillType;PathIsClosed:Boolean):TPaths;overload;C++»voidMinkowskiSum(constPath&pattern,constPath&path,Paths&solution,boolpathIsClosed);C++»voidMinkowskiSum(constPath&pattern,constPaths&paths,Paths&solution,PolyFillTypepathFillType,boolpathIsClosed);C#»publicstaticPathsMinkowskiSum(Pathpattern,Pathpath,boolpathIsClosed);C#»publicstaticPathsMinkowskiSum(Pathpattern,Pathspaths,PolyFillTypepathFillType,boolpathIsClosed);

MinkowskiAdditionisperformedbyaddingeachpointinapolygon'pattern'tothesetofpointsinanopenorclosedpath.Theresultingpolygon(orpolygons)definestheregionthatthe'pattern'wouldpassoverinmovingfromthebeginningtotheendofthe'path'.

Pathpath=newPath();Pathpattern=newPath();Pathssolution=newPaths();

//Greekcapitalsigma(sumsign)...Int64[]ints1=newInt64[]{300,400,100,400,200,300,100,200,300,200};path=IntsToPolygon(ints1);

//diagonalbrushpattern...Int64[]ints2=newInt64[]{4,-6,6,-6,-4,6,-6,6};pattern=IntsToPolygon(ints2);

solution=Clipper.MinkowskiSum(pattern,path,false);//move'pattern'totheendof'path'...

pattern=TranslatePath(pattern,300,200);

//Displaysolution±pattern...

SeeAlsoMinkowskiDiff


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OffsetPaths

Del.»functionOffsetPaths(constpolys:Paths;constdelta:double;JoinType:TJoinType=jtSquare;EndType:TEndType=etClosed;Limit:double=0.0):TPaths;C++»voidOffsetPaths(constPaths&in_polys,Paths&out_polys,doubledelta,JoinTypejointype=jtSquare,EndTypeendtype=etClosed,doublelimit=0.0);C#»publicstaticPathsOffsetPaths(Pathspolys,doubledelta,JoinTypejointype=JoinType.jtSquare,EndTypeendtype=EndType.etClosed,doublelimit=0.0);

Deprecated.(SeeClipperOffset.)

SeeAlsoClipperOffset


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OpenPathsFromPolyTree

Del.»functionOpenPathsFromPolyTree(PolyTree:TPolyTree):TPaths;C++»voidOpenPathsFromPolyTree(PolyTree&polytree,Paths&paths);C#»publicstaticvoidOpenPathsFromPolyTree(PolyTreepolytree,Pathspaths);

ThisfunctionfiltersoutclosedpathsfromthePolyTreestructureandreturnsonlyopenpathsinaPathsstructure.

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Orientation

Del.»functionOrientation(constpoly:TPath):boolean;C++»boolOrientation(constPath&poly);//FunctionintheClipperLibnamespace.C#»publicstaticboolOrientation(Pathpoly);//StaticmethodoftheClipperclassintheClipperLibnamespace.

Orientationisonlyimportanttoclosedpaths.Giventhatverticesaredeclaredinaspecificorder,orientationreferstothedirection(clockwiseorcounter-clockwise)thattheseverticesprogressaroundaclosedpath.

Orientationisalsodependentonaxisdirection:

OnY-axispositiveupwarddisplays,Orientationwillreturntrueifthepolygon'sorientationiscounter-clockwise.OnY-axispositivedownwarddisplays,Orientationwillreturntrue

ifthepolygon'sorientationisclockwise.

Notes:

Self-intersectingpolygonshaveindeterminateorientationsinwhichcasethisfunctionwon'treturnameaningfulvalue.Themajorityof2Dgraphicdisplaylibraries(egGDI,GDI+,XLib,

Cairo,AGG,Graphics32)andeventheSVGfileformathavetheircoordinateoriginsatthetop-leftcorneroftheirrespectiveviewportswiththeirYaxesincreasingdownward.However,somedisplay

libraries(egQuartz,OpenGL)havetheircoordinateoriginsundefinedorintheclassicbottom-leftpositionwiththeirYaxesincreasingupward.ForNon-Zerofilledpolygons,theorientationofholesmustbe

oppositethatofouterpolygons.Forclosedpaths(polygons)inthesolutionreturnedbyClipper's

Executemethod,theirorientationswillalwaysbetrueforouterpolygonsandfalseforholepolygons(unlesstheReverseSolutionpropertyhasbeenenabled).

SeeAlsoOverview,Clipper.ReverseSolution,Path


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PointInPolygon

Del.»functionPointInPolygon(constPt:TIntPoint;constpoly:TPath):Integer;C++»intPointInPolygon(constIntPointpt,constPath&poly);//FunctionintheClipperLibnamespace.C#»publicstaticintPointInPolygon(IntPointpt,Pathpoly);//StaticmethodoftheClipperclass.

Returns0whenfalse,-1whenptisonpolyand+1whenptisinpoly.

It'sassumedthat'poly'isclosedanddoesnotself-intersect.

SeeAlsoIntPoint,Path


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PolyTreeToPaths

Del.»functionPolyTreeToPaths(PolyTree:TPolyTree):TPaths;C++»voidPolyTreeToPaths(PolyTree&polytree,Paths&paths);C#»publicstaticPathsPolyTreeToPaths(PolyTreepolytree);

ThisfunctionconvertsaPolyTreestructureintoaPathsstructure.

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ReversePath

Del.»functionReversePath(constpolys:TPath):TPath;C++»voidReversePath(constPath&p);C#»//CallPath.Reverse().

Reversesthevertexorder(andhenceorientation)inthespecifiedpath.

SeeAlsoPath


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ReversePaths

Del.»functionReversePaths(constp:TPaths):TPaths;C++»voidReversePaths(constPaths&p);C#»voidReversePaths(Pathsp);

Reversesthevertexorder(andhenceorientation)ineachcontainedpath.


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SimplifyPolygon

Del.»functionSimplifyPolygon(constPoly:TPath;FillType:TPolyFillType=pftEvenOdd):TPaths;C++»voidSimplifyPolygon(constPath&in_poly,Paths&out_polys,PolyFillTypefillType=pftEvenOdd);C#»publicstaticPathsSimplifyPolygon(Pathpoly,PolyFillTypefillType=PolyFillType.pftEvenOdd);

Removesself-intersectionsfromthesuppliedpolygon(byperformingabooleanunionoperationusingthenominatedPolyFillType).Polygonswithnon-contiguousduplicatevertices(ie'touching')willbesplitintotwopolygons.

Note:There'scurrentlynoguaranteethatpolygonswillbestrictlysimplesince'simplifying'isstillaworkinprogress.

SeeAlsoClipper.StrictlySimple,CleanPolygon,Path,PolyFillType


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SimplifyPolygons

Del.»functionSimplifyPolygons(constpolys:TPaths;FillType:TPolyFillType=pftEvenOdd):TPaths;C++»voidSimplifyPolygons(constPaths&in_polys,Paths&out_polys,PolyFillTypefillType=pftEvenOdd);C++»voidSimplifyPolygons(Paths&polys,PolyFillTypefillType=pftEvenOdd);C#»publicstaticPolygonsSimplifyPolygons(Pathspolys,PolyFillTypefillType=PolyFillType.pftEvenOdd);

Removesself-intersectionsfromthesuppliedpolygons(byperformingabooleanunionoperationusingthenominatedPolyFillType).Polygonswithnon-contiguousduplicatevertices(ie'verticesaretouching')willbesplitintotwopolygons.

C++only:Thisfunctionisoverloaded.Inthefirstdefinition,thein_polysandout_polysparameterscanreferencethesamePathsobjectthoughinthatcasethecallingcodemightbecleareriftheseconddefinition(acceptingasinglePathsparameter)isused.


SeeAlsoClipper.StrictlySimple,CleanPolygons,PolyFillType


Home ClipperLib Clipper

//C++constructorsettingStrictlySimpleandPreserveCollinearproperties...Clipperclipper(ioStrictlySimple|ioPreserveCollinear);

//C#constructorsettingStrictlySimpleandPreserveCollinearproperties...Clipperclipper=newClipper(Clipper.ioStrictlySimple|Clipper.ioPreserveCollinear);

//DelphiconstructorsettingStrictlySimpleandPreserveCollinearproperties...clipper:=TClipper.Create([ioStrictlySimple,ioPreserveCollinear]);

Clipper.Constructor

Del.»constructorTClipper.Create(InitOptions:TInitOptions=[]);C++»Clipper::Clipper(intinitOptions=0):ClipperBase();C#»publicClipper(initOptions=0):base(){};

TheClipperconstructorcreatesaninstanceoftheClipperclass.OneormoreInitOptionsmaybepassedasaparametertosetthecorrespondingproperties.(Thesepropertiescanstillbesetorresetafterconstruction.)

Examples:

SeeAlsoPreserveCollinear,ReverseSolution,StrictlySimple,InitOptions


Clipper.Execute

Del.»functionExecute(clipType:TClipType;outsolution:TPaths;subjFillType:TPolyFillType=pftEvenOdd;clipFillType:TPolyFillType=pftEvenOdd):boolean;overload;

functionExecute(clipType:TClipType;outsolution:TPolyTree;subjFillType:TPolyFillType=pftEvenOdd;clipFillType:TPolyFillType=pftEvenOdd):boolean;overload;C++»boolExecute(ClipTypeclipType,Paths&solution,PolyFillTypesubjFillType=pftEvenOdd,PolyFillTypeclipFillType=pftEvenOdd);

boolExecute(ClipTypeclipType,PolyTree&solution,PolyFillTypesubjFillType=pftEvenOdd,PolyFillTypeclipFillType=pftEvenOdd);C#»publicboolExecute(ClipTypeclipType,Pathssolution,PolyFillTypesubjFillType,PolyFillTypeclipFillType);

publicboolExecute(ClipTypeclipType,PolyTreesolution,PolyFillTypesubjFillType,PolyFillTypeclipFillType);

Oncesubjectandclippathshavebeenassigned(viaAddPathand/orAddPaths),Executecanthenperformtheclippingoperation(intersection,union,differenceorXOR)specifiedbytheclipType

parameter.

ThesolutionparametercanbeeitheraPathsorPolyTreestructure.ThePathsstructureissimplerthanthePolyTreestucture.Becauseofthisitisquickertopopulateandhenceclippingperformanceisalittlebetter(it'sroughly10%faster).However,thePolyTreedatastructureprovidesmoreinformationaboutthereturnedpathswhichmaybeimportanttousers.Firstly,thePolyTreestructurepreservesnestedparent-childpolygonrelationships(ieouterpolygonsowning/containingholesandholesowning/containingotherouterpolygonsetc).Also,onlythePolyTreestructurecandifferentiatebetweenopenandclosedpathssinceeachPolyNodehasanIsOpenproperty.(ThePathstructurehasnomemberindicatingwhetherit'sopenorclosed.)Forthisreason,whenopenpathsarepassedtoaClipperobject,theusermustuseaPolyTreeobjectasthesolutionparameter,otherwiseanexceptionwillberaised.

WhenaPolyTreeobjectisusedinaclippingoperationonopenpaths,twoancilliaryfunctionshavebeenprovidedtoquicklyseparateoutopenandclosedpathsfromthesolution-OpenPathsFromPolyTreeandClosedPathsFromPolyTree.PolyTreeToPathsisalsoavailabletoconvertpathdatatoaPathsstructure(irrespectiveofwhetherthey'reopenorclosed).

Thereareseveralthingstonoteaboutthesolutionpathsreturned:

theyaren'tinany

specificordertheyshouldneveroverlaporbeself-intersecting(butseenoteson

rounding)holeswillbeorientedoppositeouterpolygonsthesolutionfilltypecanbeconsideredeitherEvenOddorNonZero

sinceitwillcomplywitheitherfillingrulepolygonsmayrarelyshareacommonedge(thoughthisisnowvery

rareasofversion6)

ThesubjFillTypeandclipFillTypeparametersdefinethepolygonfillruletobeappliedtothepolygons(ieclosedpaths)inthesubjectandclippathsrespectively.(It'susualthoughobviouslynotessentialthatbothsetsofpolygonsusethesamefillrule.)

Executecanbecalledmultipletimeswithoutreassigningsubjectandclippolygons(iewhendifferentclippingoperationsarerequiredonthesamepolygonsets).

SeeAlsoExample,Rounding,ClipperBase.AddPath,ClipperBase.AddPaths,PolyNode.IsOpen,PolyTree,ClosedPathsFromPolyTree,OpenPathsFromPolyTree,PolyTreeToPaths,ClipType,Path,Paths,PolyFillType


Clipper.PreserveCollinear

Del.»propertyPreserveCollinear:boolean;override;C++»voidPreserveCollinear(boolvalue);C#»publicboolPreserveCollinear{get{}set{}};

Bydefault,whenthreeormoreverticesarecollinearininputpolygons(subjectorclip),theClipperobjectremovesthe'inner'verticesbeforeclipping.WhenenabledthePreserveCollinearpropertypreventsthisdefaultbehaviortoallowtheseinnerverticestoappearinthesolution.

SeeAlsoConstructor


Clipper.ReverseSolution

Del.»propertyReverseSolution:boolean;override;C++»voidReverseSolution(boolvalue);C#»publicboolReverseSolution{get{}set{}};

Whenthispropertyissettotrue,polygonsreturnedinthesolutionparameteroftheExecute()methodwillhaveorientationsoppositetotheirnormalorientations.

SeeAlsoExecute,Orientation


Clipper.StrictlySimple

Del.»propertyStrictlySimple:boolean;override;C++»voidStrictlySimple(boolvalue);C#»publicboolStrictlySimple{get{}set{}};

Terminology:

Asimplepolygonisonethatdoesnotself-intersect.Aweaklysimplepolygonisasimplepolygonthatcontains'touching'

vertices,or'touching'edges.Astrictlysimplepolygonisasimplepolygonthatdoesnotcontain

'touching'vertices,or'touching'edges.

Vertices'touch'iftheysharethesamecoordinates(andarenotadjacent).Anedgetouchesanotherifoneofitsendverticestouchesanotheredgeexcludingitsadjacentedges,oriftheyareco-linearandoverlapping(includingadjacentedges).

Polygonsreturnedbyclippingoperations(seeClipper.Execute())shouldalwaysbesimplepolygons.WhentheStrictlySimplypropertyisenabled,polygonsreturnedwillbestrictlysimple,otherwisetheymaybeweaklysimple.It'scomputationallyexpensiveensuringpolygonsarestrictlysimpleandsothispropertyisdisabledbydefault.


Intheimageabove,thetwoexamplesshowweaklysimplepolygonsbeingbrokenintotwostrictlysimplepolygons.(Theoutlineswitharrowsareintendedtoaidvisualizingvertexorder.)

SeealsothearticleonSimplePolygonsonWikipedia.

http://en.wikipedia.org/wiki/Simple_polygon

SeeAlsoExecute,SimplifyPolygons


Clipper.ZFillFunction

Del.»propertyZFillFunction:TZFillCallbackreadFZFillCallbackwriteFZFillCallback;C++»voidZFillFunction(ZFillCallbackzFillFunc);C#»publicZFillCallbackZFillFunction{get;set;};

Thispropertyisonlyexposedwhenthepre-processordirectiveuse_xyzhasbeendefined.Ifthisisthecase,a'Z'memberwillbeincludedintheIntPointstructurewhereuserscanstorecustomdata.Whilemostverticesinaclippingsolutionwillcorrespondtoinput(subjectandclip)vertices,therewillalsobenewverticeswhereveredgesintersect.ThispropertyassignsacustomcallbackfunctiontotheClipperobjectsothatcustom'Z'valuescanbeassignedtotheseintersectionvertices.(Notethat'Z'valuesinthesolutionatnon-intersectingverticeswillsimplybecopiedfrommatchinginputverticesalongwiththeXandYvalues.)

Itisuptothelibraryusertoassign'Z'valuesfornewintersectionvertices(otherwisethesevalueswillremain0).Thefourverticesthatdefinetheintersectinglinesegmentswillbepassedtothecallbackfunction(togetherwiththenewintersectionvertex)toaidtheuserindeterminingappropriateZvalues.

SeeAlsoDefines,IntPoint,ZFillCallback


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ClipperBase.AddPath

Del.»functionAddPath(constpath:TPath;polyType:TPolyType;Closed:Boolean):Boolean;C++»boolAddPath(constPath&pg,PolyTypepolyType,boolclosed);C#»publicvirtualboolAddPath(Pathpg,PolyTypepolyType,boolclosed);

Anynumberofsubjectandclippathscanbeaddedtoaclippingtask,eitherindividuallyviatheAddPath()method,orasgroupsviatheAddPaths()method,orevenusingbothmethods.

'Subject'pathsmaybeeitheropen(lines)orclosed(polygons)orevenamixtureofboth,but'clipping'pathsmustalwaysbeclosed.Clipperallowspolygonstoclipbothlinesandotherpolygons,butdoesn'tallowlinestoclipeitherlinesorpolygons.

Withclosedpaths,orientationshouldconformwiththefillingrulethatwillbepassedviaClippper'sExecutemethod.

PathCoordinaterange:Pathcoordinatesmustbebetween±0x3FFFFFFFFFFFFFFF(±4.6e+18),otherwisearangeerrorwillbethrownwhenattemptingtoaddthepathtotheClipperobject.Ifcoordinatescanbekeptbetween±0x3FFFFFFF(±1.0e+9),amodestincreaseinperformance(approx.15-20%)overthelargerrangecanbeachievedbyavoidinglargeintegermath.Ifthepreprocessordirectiveuse_int32isdefined(allowingafurtherincreaseinperformanceof20-30%),thenthemaximumrangeisrestrictedto±32,767.

ReturnValue:Thefunctionwillreturnfalseifthepathisinvalidforclipping.Apathis

invalidforclippingwhen:

ithaslessthan2verticesithas2verticesbutisnotanopenpaththeverticesareallco-linearanditisnotanopenpath

SeeAlsoExample,Clipper.Execute,AddPaths,Orientation,Defines,Path,PolyFillType,PolyType


ClipperBase.AddPaths

Del.»functionAddPaths(constpaths:TPaths;polyType:TPolyType;Closed:Boolean):boolean;C++»boolAddPaths(constPaths&ppg,PolyTypepolyType,boolclosed);C#»publicvirtualboolAddPaths(Pathsppg,PolyTypepolyType,boolclosed);

Anynumberofsubjectandclippathscanbeaddedtoaclippingtask,eitherindividuallyviatheAddPath()method,orasgroupsviatheAddPaths()method,orevenusingbothmethods.

'Subject'pathsmaybeeitheropen(lines)orclosed(polygons)orevenamixtureofboth,but'clipping'pathsmustalwaysbeclosed.Clipperallowspolygonstoclipbothlinesandotherpolygons,butdoesn'tallowlinestoclipeitherlinesorpolygons.

Withclosedpaths,orientationshouldconformwiththefillingrulethatwillbepassedviaClippper'sExecutemethod.

PathCoordinaterange:Pathcoordinatesmustbebetween±0x3FFFFFFFFFFFFFFF(±4.6e+18),otherwisearangeerrorwillbethrownwhenattemptingtoaddthepathtotheClipperobject.Ifcoordinatescanbekeptbetween±0x3FFFFFFF(±1.0e+9),amodestincreaseinperformance(approx.15-20%)overthelargerrangecanbeachievedbyavoidinglargeintegermath.Ifthepreprocessordirectiveuse_int32isdefined(allowingafurtherincreaseinperformanceof20-30%),thenthemaximumrangeisrestrictedto±32,767.

ReturnValue:Thefunctionwillreturnfalseifthepathisinvalidforclipping.Apathis

invalidforclippingwhen:

ithaslessthan2verticesithas2verticesbutisnotanopenpaththeverticesareallco-linearanditisnotanopenpath

SeeAlsoExample,Clipper.Execute,AddPaths,Orientation,Defines,Paths,PolyFillType,PolyType


ClipperBase.Clear

Del.»procedureClear;C++»virtualvoidClear();C#»publicvoidClear(){};

TheClearmethodremovesanyexistingsubjectandclippolygonsallowingtheClipperobjecttobereusedforclippingoperationsondifferentpolygonsets.


ClipperBase.GetBounds

Del.»functionGetBounds:TIntRect;C++»IntRectGetBounds();C#»publicIntRectGetBounds(){...};

Thismethodreturnstheaxis-alignedboundingrectangleofallpolygonsthathavebeenaddedtotheClipperobject.

SeeAlsoExample,IntRect


Home ClipperLib ClipperOffset

ClipperOffset.AddPath

Del.»procedureAddPath(constPath:TPath;JoinType:TJoinType;EndType:TEndType);C++»voidAddPath(constPath&path,JoinTypejointype,EndTypeendtype);C#»publicvoidAddPath(Pathpath,JoinTypejointype,EndTypeendtype);

AddsaPathtoaClipperOffsetobjectinpreparationforoffsetting.

Anynumberofpathscanbeadded,andeachhasitsownJoinTypeandEndType.All'outer'Pathsmusthavethesameorientation,andany'hole'pathsmusthavereverseorientation.Closedpathsmusthaveatleast3vertices.Openpathsmayhaveasfewasonevertex.Openpathscanonlybeoffsetwithpositivedeltas.

SeeAlsoEndType,JoinType,Path


ClipperOffset.AddPaths

Del.»procedureAddPaths(constPaths:TPaths;JoinType:TJoinType;EndType:TEndType);C++»voidAddPaths(constPaths&paths,JoinTypejointype,EndTypeendtype);C#»publicvoidAddPaths(Pathspaths,JoinTypejointype,EndTypeendtype);

AddsPathstoaClipperOffsetobjectinpreparationforoffsetting.

Anynumberofpathscanbeadded,andeachpathhasitsownJoinTypeandEndType.All'outer'Pathsmusthavethesameorientation,andany'hole'pathsmusthavereverseorientation.Closedpathsmusthaveatleast3vertices.Openpathsmayhaveasfewasonevertex.Openpathscanonlybeoffsetwithpositivedeltas.

SeeAlsoEndType,JoinType,Paths


ClipperOffset.Clear

Del.»procedureClear;C++»voidClear();C#»publicvoidClear();

ThismethodclearsallpathsfromtheClipperOffsetobject,allowingnewpathstobeassigned.


ClipperOffset.Constructor

Del.»constructorCreate(MiterLimit:Double=2;RoundPrecision:Double=0.25);C++»ClipperOffset(doublemiterLimit=2.0,doubleroundPrecision=0.25);C#»publicClipperOffset(doublemiterLimit=2.0,doubleroundPrecision=0.25);

TheClipperOffsetconstructortakes2optionalparameters:MiterLimitandArcTolerance.Thestwoparameterscorrespondstopropertiesofthesamename.MiterLimitisonlyrelevantwhenJoinTypeisjtMiter,andArcToleranceisonlyrelevantwhenJoinTypeisjtRoundorwhenEndTypeisetOpenRound.

SeeAlsoArcTolerance,MiterLimit


ClipperOffset.Execute

Del.»procedureExecute(outsolution:TPaths;Delta:Double);overload;C++»voidExecute(Paths&solution,doubledelta);C#»publicvoidExecute(refPathssolution,doubledelta);Del.»procedureExecute(outPolyTree:TPolyTree;Delta:Double);overload;C++»voidExecute(PolyTree&polytree,doubledelta);C#»publicvoidExecute(refPolyTreepolytree,doubledelta);

Thismethodtakestwoparameters.Thefirstisthestructurethatreceivestheresultoftheoffsetoperation(eitheraPolyTreeoraPathsstructure).Thesecondparameteristheamounttowhichthesuppliedpathswillbeoffset.Negativedeltavaluesshrinkpolygonsandpositivedeltaexpandthem.

Thismethodcanbecalledmultipletimes,offsettingthesamepathsbydifferentamounts(ieusingdifferentdeltas).

#include"clipper.hpp"...usingnamespaceClipperLib;

intmain(){Pathsubj;Pathssolution;subj

ClipperOffset.ArcTolerance

Del.»propertyArcTolerance:double;//readandwriteC++»doubleArcTolerance;C#»publicdoubleArcTolerance{get;set;}

Firstly,thisfield/propertyisonlyrelevantwhenJoinType=jtRoundand/orEndType=etRound.

Sinceflattenedpathscanneverperfectlyrepresentarcs,thisfield/propertyspecifiesamaximumacceptableimprecision('tolerance')whenarcsareapproximatedinanoffsettingoperation.Smallervalueswillincrease'smoothness'uptoapointthoughatacostofperformanceandincreatingmoreverticestoconstructthearc.

ThedefaultArcToleranceis0.25units.Thismeansthatthemaximumdistancetheflattenedpathwilldeviatefromthe'true'arcwillbenomorethan0.25units(beforerounding).

Reducingtolerancesbelow0.25willnotimprovesmoothnesssincevertexcoordinateswillstillberoundedtointegervalues.Theonlywaytoachievesub-integerprecisionisthroughcoordinatescalingbeforeandafteroffsetting(seeexamplebelow).

It'simportanttomakeArcToleranceasensiblefractionoftheoffsetdelta(arcradius).Largetolerancesrelativetotheoffsetdeltawillproducepoorarcapproximationsbut,justasimportantly,verysmalltoleranceswillsubstantiallyslowoffsettingperformancewhileprovidingunnecessarydegreesofprecision.Thisismostlikelytobeanissuewhenoffsettingpolygonswhosecoordinateshavebeenscaledtopreservefloatingpointprecision.

Example:Imagineasetofpolygons(definedinfloatingpointcoordinates)thatistobeoffsetby10unitsusingroundjoins,andthesolutionistoretainfloatingpointprecisionuptoatleast6decimalplaces.Topreservethisdegreeoffloatingpointprecision,andgiventhatClipper

andClipperOffsetbothoperateonintegercoordinates,thepolygoncoordinateswillbescaledupby108(androundedtointegers)priortooffsetting.BothoffsetdeltaandArcTolerancewillalsoneedtobescaledbythissamefactor.IfArcTolerancewasleftunscaledatthedefault0.25units,everyarcinthesolutionwouldcontainafractionof44THOUSANDverticeswhilethefinalarcimprecisionwouldbe0.25×10-8units(ieoncescalingwasreversed).However,if0.1unitswasanacceptableimprecisioninthefinalunscaledsolution,thenArcToleranceshouldbesetto0.1×scaling_factor(0.1×108).NowifscalingisappliedequallytobothArcToleranceandtoDeltaOffset,theninthisexamplethenumberofvertices(steps)definingeacharcwouldbeafractionof23.

Theformulaforthenumberofstepsinafullcirculararcis...Pi/acos(1-arc_tolerance/abs(delta))

SeeAlsooffset_triginometry2


ClipperOffset.MiterLimit

Del.»propertyMiterLimit:double;//readandwriteC++»doubleMiterLimit;C#»publicdoubleMiterLimit{get;set;}

Thispropertysetsthemaximumdistanceinmultiplesofdeltathatverticescanbeoffsetfromtheiroriginalpositionsbeforesquaringisapplied.(Squaringtruncatesamiterby'cuttingitoff'at1×deltadistancefromtheoriginalvertex.)

ThedefaultvalueforMiterLimitis2(ietwicedelta).ThisisalsothesmallestMiterLimitthat'sallowed.Ifmiteringwasunrestricted(iewithoutanysquaring),thenoffsetsatveryacuteangleswouldgenerateunacceptablylong'spikes'.

Anexampleofanoffsetting'spike'atanarrowanglethat'saconsequenceofusingalargeMiterLimit(25)...

SeeAlsoJoinType


Home ClipperLib PolyNode

PolyTreepolytree;//calltoClipper.Executemethodherewhichfills'polytree'PolyNode*polynode=polytree.GetFirst();while(polynode){//dostuffwithpolynodeherepolynode=polynode->GetNext();}

PolyNode.GetNext

Del.»functionGetNext:TPolyNode;C++»PolyNode*GetNext();C#»publicPolyNodeGetNext();

ThereturnedPolynodewillbethefirstchildifany,otherwisethenextsibling,otherwisethenextsiblingoftheParentetc.

APolyTreecanbetraversedveryeasilybycallingGetFirst()followedbyGetNext()inaloopuntilthereturnedobjectisanullpointer...

SeeAlsoPolyTree.GetFirst


PolyNode.ChildCount

Del.»propertyChildCount:Integer;//readonlyC++»ChildCount();//readonlyC#»publicintChildCount;//readonly

ReturnsthenumberofPolyNodeChildsdirectlyownedbythePolyNodeobject.

SeeAlsoChilds


PolyNode.Childs

Del.»propertyChilds[index:Integer]:TPolyNode;//readonlyC++»std::vector<PolyNode*>Childs;//publicfieldC#»publicList<PolyNode>Childs;//readonlyproperty

Aread-onlylistofPolyNode.OuterPolyNodechildscontainholePolyNodes,andholePolyNodechildscontainnestedouterPolyNodes.

SeeAlsoChildCount


PolyNode.Contour

Del.»propertyContour:TPath;//readonlyC++»PathContour;//publicfieldC#»publicPathContour;//readonlyproperty

Returnsapathlistwhichcontainsanynumberofvertices.


PolyNode.IsHole

Del.»IsHole:Boolean;//readonlyC++»boolIsHole;//fieldC#»publicboolIsHole;//readonlyproperty

ReturnstruewhenthePolyNode'spolygon(Contour)isahole.

Childrenofouterpolygonsarealwaysholes,andchildrenofholesarealways(nested)outerpolygons.TheIsHolepropertyofaPolyTreeobjectisundefinedbutitschildrenarealwaystop-levelouterpolygons.

SeeAlsoOverview,Contour,PolyTree


PolyNode.IsOpen

Del.»IsOpen:Boolean;//readonlyC++»boolIsOpen;//fieldC#»publicboolIsOpen;//readonlyproperty

ReturnstruewhenthePolyNode'sContourresultsfromaclippingoperationonanopencontour(path).Onlytop-levelPolyNodescancontainopencontours.

SeeAlsoContour


PolyNode.Parent

Del.»Parent:TPolyNode;//readonlyC++»PolyNode*Parent;//fieldC#»publicPolyNodeParent;//readonlyproperty

ReturnstheparentPolyNode.

ThePolyTreeobject(whichisalsoaPolyNode)doesnothaveaparentandwillreturnanullpointer.


Home ClipperLib PolyTree

PolyTree.Clear

Del.»procedureClear;C++»voidClear();C#»publicvoidClear();

ThismethodclearsanyPolyNodechildrencontainedbyPolyTreetheobject.

Cleardoesnotneedtobecalledexplicitly.TheClipper.ExecutemethodthatacceptsaPolyTreeparameterwillautomaticallyclearthePolyTreeobjectbeforepropagatingitwithnewPolyNodes.Likewise,PolyTree'sdestructorwillalsoautomaticallyclearanycontainedPolyNodes.

SeeAlsoClipper.Execute


PolyTree.GetFirst

Del.»functionGetFirst:TPolyNode;C++»PolyNode*GetFirst();C#»publicPolyNodeGetFirst();

Thismethodreturnsthefirstouterpolygoncontourifany,otherwiseanullpointer.

ThisfunctionisalmostequivalenttocallingChilds[0]exceptthatwhenaPolyTreeobjectisempty(hasnochildren),callingChilds[0]wouldraiseanoutofrangeexception.

SeeAlsoPolyNode.GetNext,PolyNode.ChildCount,PolyNode.Childs


PolyTree.Total

Del.»propertyTotal:Integer;//readonlyC++»Total();//readonlyC#»publicintTotal;//readonly

ReturnsthetotalnumberofPolyNodes(polygons)containedwithinthePolyTree.ThisvalueisnottobeconfusedwithChildCountwhichreturnsthenumberofimmediatechildrenonly(Childs)containedbyPolyTree.

SeeAlsoPolyNode.ChildCount,PolyNode.Childs


Overview

TheClipperLibraryperformsclipping,andoffsettingofbothlinesandpolygons.

AnumberoffeaturessetClipperapartfromotherclippinglibraries:

itacceptsalltypesofpolygonsincludingself-intersectingonesitsupportsmultiplepolygonfillingrules(EvenOdd,NonZero,

Positive,Negative)it'sveryfastrelativetootherlibrariesit'snumericallyrobustitalsoperformslineandpolygonoffsettingit'sfreetouseinbothfreewareandcommercialapplications

CurrentVersion:6.2.0

Author&copyright:AngusJohnson.Copyright©2010-2014License,termsandconditions:BoostSoftwareLicense

Terminology:

Clipping:commonlyreferstotheprocessofcuttingawayfromasetof2-dimensionalgeometricshapesthosepartsthatareoutsidearectangular'clipping'window.Thiscanbeachievedbyintersecting

http://www.angusj.com/delphi/clipper.php#featureshttp://www.mpi-inf.mpg.de/~kettner/pub/nonrobust_cgta_06.pdf

subjectpaths(linesandpolygons)withaclippingrectangle.Inamoregeneralsense,theclippingwindowneednotberectangularbutcanbeanytypeofpolygon,evenmultiplepolygons.Also,whileclippingtypicallyreferstoanintersectionoperation,inthisdocumentationitwillrefertoanyoneofthefourbooleanoperations(intersection,union,differenceandexclusive-or).Path:isanorderedsequenceofverticesdefiningasinglegeometric

contourthat'seitheraline(anopenpath)orapolygon(aclosedpath).Line:orpolylineisanopenpathcontaining2ormorevertices.Polygon:commonlyreferstoatwo-dimensionalregionboundedby

anouternon-intersectingclosedcontour.Thatregionmayalsocontainanumberof'holes'.Inthisdocumentationhowever,polygonwillsimplyrefertoaclosedpath.Contour:synonymouswithpath.Hole:isaclosedregionwithinapolygonthat'snotpartofthe

polygon.A'holepolygon'isaclosedpaththatformstheouterboundariesofahole.PolygonFillingRule:thefillingrule,togetherwithalistofclosed

paths,definesthoseregions(boundedbypaths)thatareinside(ieregions'brushfilled'inagraphicaldisplay)andthosewhichareoutside(ie'holes').

Distributionpackagecontents:

TheZIPpackagecontainstheClipperlibrary'ssourcecode,aWindowsCHMhelpfile,HTMLhelp,andanumberofcompileddemoapplications(withfullsourcecode).ThelibrarywasinitiallywritteninDelphiPascal(andcompileswithDelphiversion7orabove)butnowcontainsC++,C#andPythontranslationstoo.Thelibrary'ssourcecodeineachlanguageisabout5000lines.TheDelphicodecontainsreasonablyextensivecomments,butcommentsarefewerintheC++andC#code.TheincludedsampleapplicationsshowhowClippercanbeusedwiththedifferentlanguagesusinganumberofgraphicsdisplaylibrariesincluding-AGG,Cairo,OpenGL,Graphics32,GDI+andSVG.

DownloadLink:

SourceForge

References:

TheLibraryisbasedonbutsignificantlyextendsBalaVatti'spolygonclippingalgorithmasdescribedin"Agenericsolutiontopolygonclipping",CommunicationsoftheACM,Vol35,Issue7(July1992)pp56-63.

Asectionin"Computergraphicsandgeometricmodeling:implementationandalgorithms"byByMaxK.Agoston(Springer,2005)discussingVattiPolygonClippingwasalsohelpfulincreatingtheinitialClipperimplementation.

Thepapertitled"PolygonOffsettingbyComputingWindingNumbers"byChen&McMains(Paperno.DETC2005-85513,ASME2005.Pages565-575)containshelpfuldiscussiononthecomplexitiesofpolygonoffsettingtogetherwithsomesolutions.

http://sourceforge.net/projects/polyclippinghttp://portal.acm.org/citation.cfm?id=129906http://books.google.com/books?q=vatti+clipping+agostonhttp://www.me.berkeley.edu/~mcmains/pubs/DAC05OffsetPolygon.pdf

SeeAlsoSource,License,Clipper,ClipperOffset,ClipType,PolyFillType


Home ClipperLib

ClipperBase

ClipperBaseisanabstractbaseclassforClipper.AClipperBaseobjectshouldnotbeinstantiateddirectly.

ReferenceMethods

InClipperBase:AddPathAddPathsClearGetBounds

SeeAlsoClipper


Home ClipperLib

Clipper

Hierarchy|ClipperBase

TheClipperclassencapsulatesbooleanoperationsonpolygons(intersection,union,differenceandXOR),whichisalsocalledpolygonclipping.

Inputpolygons,bothsubjectandclipsets,arepassedtoaClipperobjectbyitsAddPathandAddPathsmethods,andtheclippingoperationisperformedbycallingitsExecutemethod.MultiplebooleanoperationscanbeperformedonthesameinputpolygonsetsbyrepeatcallstoExecute.

ReferenceMethods PropertiesInClipper:Constructor PreserveCollinearExecute ReverseSolution

StrictlySimpleZFillFunction

InClipperBase:AddPathAddPathsClearGetBounds

SeeAlsoOverview,ClipType


Home ClipperLib

#include"clipper.hpp"...usingnamespaceClipperLib;

intmain(){

ClipperOffset

TheClipperOffsetclassencapsulatestheprocessofoffsetting(inflating/deflating)bothopenandclosedpathsusinganumberofdifferentjointypesandendtypes.

(ThisclassreplacesthenowdeprecatedOffsetPathsfunctionwhichwaslessflexible.)

Preconditionsforoffsetting:1.Theorientationsofclosedpathsmustbeconsistentsuchthatouterpolygonssharethesameorientation,andanyholeshavetheoppositeorientation(ienon-zerofilling).Openpathsmustbeorientedwithclosedouterpolygons.2.Polygonsmustnotself-intersect.

Limitations:Whenoffsetting,smallartefactsmayappearwherepolygonsoverlap.Toavoidtheseartefacts,offsetoverlappingpolygonsseparately.

Pathsubj;Pathssolution;subj

ReferenceMethods PropertiesInClipperOffset:AddPath ArcToleranceAddPaths MiterLimitClearConstructorExecute


Home ClipperLib

PolyNode

PolyNodesareencapsulatedwithinaPolyTreecontainer,andtogetherprovideadatastructurerepresentingtheparent-childrelationshipsofpolygoncontoursreturnedbyClipper'sExecutemethod.

APolyNodeobjectrepresentsasinglepolygon.ItsIsHolepropertyindicateswhetherit'sanouterorahole.PolyNodesmayownanynumberofPolyNodechildren(Childs),wherechildrenofouterpolygonsareholes,andchildrenofholesare(nested)outerpolygons.

ReferenceMethods PropertiesInPolyNode:GetNext ChildCount

ChildsContourIsHoleIsOpenParent

SeeAlsoOverview,Clipper.Execute,PolyTree


Home ClipperLib

PolyTree

Hierarchy|PolyNode

PolyTreeisintendedasaread-onlydatastructurethatshouldonlybeusedtoreceivesolutionsfromclippingandoffsettingoperations.It'sanalternativetothePathsdatastructurewhichalsoreceivesthesesolutions.PolyTree'stwomajoradvantagesoverthePathsstructureare:itproperlyrepresentstheparent-childrelationshipsofthereturnedpolygons;itdifferentiatesbetweenopenandclosedpaths.However,sincePolyTreeisamorecomplexstructurethanthePathsstructure,andsinceit'smorecomputationallyexpensivetoprocess(theExecutemethodbeingroughly5-10%slower),itshouldusedonlybewhenparent-childpolygonrelationshipsareneeded,orwhenopenpathsarebeing'clipped'.

AnemptyPolyTreeobjectcanbepassedasthesolutionparameterinClipper.ExecuteandinClipperOffset.Execute.Oncetheclippingoroffsetingoperationiscompleted,themethodreturnswiththePolyTreestructurefilledwithdatarepresentingthesolution.

APolyTreeobjectisacontainerforanynumberofPolyNodechildren,witheachcontainedPolyNoderepresentingasinglepolygoncontour(eitheranouterorholepolygon).PolyTreeitselfisaspecializedPolyNodewhoseimmediatechildrenrepresentthetop-levelouterpolygonsofthesolution.(ItsownContourpropertyisalwaysempty.)Thecontainedtop-levelPolyNodesmaycontaintheirownPolyNodechildrenrepresentingholepolygonsthatmayalsocontainchildrenrepresentingnestedouterpolygonsetc.Childrenofouterswillalwaysbeholes,andchildrenofholeswillalwaysbeouters.

PolyTreescanalsocontainopenpaths.OpenpathswillalwaysberepresentedbytoplevelPolyNodes.Twofunctionsareprovidedtoquicklyseparateoutopenandclosedpathsfromapolytree-OpenPathsFromPolyTreeandClosedPathsFromPolyTree.

polytree:Contour=()ChildCount=1Childs[0]:Contour=((10,10),(100,10),(100,100),(10,100))IsHole=FalseChildCount=1Childs[0]:Contour=((20,20),(20,90),(90,90),(90,20))IsHole=TrueChildCount=2Childs[0]:Contour=((30,30),(50,30),(50,50),(30,50))IsHole=FalseChildCount=0Childs[1]:Contour=((60,60),(80,60),(80,80),(60,80))IsHole=FalseChildCount=0

ReferenceMethods PropertiesInPolyTree:Clear TotalGetFirstInPolyNode:GetNext ChildCount

ChildsContourIsHoleIsOpenParent

SeeAlsoOverview,Clipper.Execute,ClipperOffset.Execute,PolyNode,ClosedPathsFromPolyTree,OpenPathsFromPolyTree,Paths


ClipperLib

Filenames:clipper.pas;clipper.hppandclipper.cpp;clipper.cs

Namespace:ClipperLib

ContentsTypes Classes Functions

CInt Clipper AreaClipType ClipperBase CleanPolygonEndType ClipperOffset CleanPolygonsInitOptions PolyNode ClosedPathsFromPolyTreeIntPoint PolyTree MinkowskiDiffIntRect MinkowskiSumJoinType OffsetPathsPath OpenPathsFromPolyTreePaths OrientationPolyFillType PointInPolygonPolyType PolyTreeToPathsZFillCallback ReversePath

ReversePathsSimplifyPolygonSimplifyPolygons


Graphics32 HelpOverviewChangesDeprecatedExampleFAQLicenseRoundingClipperLibCIntClipTypeEndTypeInitOptionsIntPointIntRectJoinTypePathPathsPolyFillTypePolyTypeZFillCallbackAreaCleanPolygonCleanPolygonsClosedPathsFromPolyTreeMinkowskiDiffMinkowskiSumOffsetPathsOpenPathsFromPolyTreeOrientationPointInPolygonPolyTreeToPathsReversePathReversePathsSimplifyPolygonSimplifyPolygonsClipperConstructorExecutePreserveCollinearReverseSolutionStrictlySimpleZFillFunctionClipperBaseAddPathAddPathsClearGetBoundsClipperOffsetAddPathAddPathsClearConstructorExecuteArcToleranceMiterLimitPolyNodeGetNextChildCountChildsContourIsHoleIsOpenParentPolyTreeClearGetFirstTotal

the clipper library - version 6 · ver 6 is a major update that adds support for open path...

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