Logicoperationisalogicaldeductionmethodofnumbersymbolization,includingunion,intersection,andsubtraction.Thiskindoflogicoperationmethodisusedingraphicsprocessingoperationstomakesimplebasicgraphicscombinationsproducenewshapes,anddevelopfromtwo-dimensionallogicoperationstothree-dimensionalgraphicslogicoperations.
BecauseofthespecialcontributionofBooleaninsymboliclogicoperations,manycomputerlanguagescalllogicaloperationsBooleanoperations,andtheresultsarecalledBooleanvalues.
Booleanusesmathematicalmethodstostudylogicproblemsandsuccessfullyestablisheslogiccalculations.Heusesequationstoexpressjudgments,andseesreasoningasatransformationofequations.Theeffectivenessofthistransformationdoesnotdependonpeople'sinterpretationofsymbols,butonlyonthecombinationofsymbols.ThislogicaltheoryisoftencalledBooleanalgebra.Inthe1930s,logicalgebrawasappliedtocircuitsystems.Later,duetothedevelopmentofelectronictechnologyandcomputers,variouscomplexlarge-scalesystemsappeared,andtheirtransformationlawsalsoobeyedthelawsrevealedbyBoolean.
"∧"means"and".
"┐"means"Not".
"="means"equivalent".
1.Logicalconstantsandvariables:Thereareonlytwologicalconstants,namely0and1,Usedtorepresenttwoopposinglogicstates.Likeordinaryalgebra,logicalvariablescanalsoberepresentedbyletters,symbols,numbersandtheircombinations,butthereareessentialdifferencesbetweenthem,becauselogicalconstantshaveonlytwovalues,namely0and1,andthereisnointermediatevalue.
2.Logicoperations:Inlogicalgebra,therearethreebasiclogicoperations:AND,OR,andNOT.Therearemanywaystoexpresslogicaloperations,suchasstatementdescriptions,logicalalgebraicexpressions,truthtables,Karnaughmaps,etc.
3.Logicalfunction:Logicalfunctionisanalgebraicformulaconnectedbylogicalvariablesandconstantsthroughoperators.Similarly,logicfunctionscanalsobeexpressedintheformoftablesandgraphs.
4.Logicalalgebra:Logicalalgebraisamathematicalsystemthatstudiestheoperationandsimplificationoflogicalfunctions.Thecalculationandsimplificationoflogicfunctionsarethefoundationofdigitalcircuitcoursesandthekeytodigitalcircuitanalysisanddesign.
Logicoperationsareusuallyusedtotesttrueandfalsevalues.Themostcommonlogicoperationistheprocessingoftheloop,whichisusedtodeterminewhethertoleavethelooporcontinuetoexecutetheinstructionsintheloop.
Function | C | Pascal |
Equalto | == | = |
Notequalto | != | |
Lessthan | | |
Greaterthan | > | > |
Lessthanorequalto | | |
Greaterthanorequalto | >= | >= |
and | && | and |
or | || | or |
Non | ! | not |
ExclusiveOR | ^ | xor |
table>RuleofOperation
Combination\Result\Operator.....And.......Or.........Xor
0......0.......................0..........0............0
1......0.......................0..........1............1
0......1.......................0..........1............1
1......1.......................1..........1............0
Simplyspeaking
And:Truewhenthesameistrue
Or:Falsewhenthesameisfalse
Xor:Sameisfalse
p>Three-dimensionalgraphicsBooleanoperation
Function
Boolean(Booleanoperation)performsunion,difference,andintersectionoperationsontwoormoreobjectstoobtainnewTheshapeoftheobject.Thesystemprovides4Booleanoperations:Union(Union),Intersection(Intersection)andSubtraction(Subtraction,includingA-BandB-A).
Effect
TheobjectcanmodifythetwooperandsatanytimeafterBooleanoperation.ThemethodandeffectofBooleanoperationcanalsobeeditedandmodified,andtheprocessofBooleanoperationmodificationcanberecorded.Itisananimation,showingamagicalcuttingeffect.
Components
TheparameterpanelofBoolean(Booleanoperation)canbedividedintothreeparts.
Booleanoperationpracticemodel:dice
PickBoolean(PickBooleanoperand)rollout
ThisrolloutisusedtopickoperandB.
InBooleanoperations,twoprimitiveobjectsarecalledoperands,oneiscalledoperandAandtheotheriscalledoperandB.BeforecreatingaBooleanoperation,youmustfirstselectanoriginalobjectintheview,thentheBooleanbuttoncanbeused.AfterenteringtheBooleanoperationcommandpanel,clickthePickOperandBcommandbuttontoselectthesecondoperand.
·PickOperandB:ClickthisbuttontoselectanotherobjectinthescenetocompleteBooleansynthesis.ThefouroptionsbelowareusedtocontroltheattributesofoperandB,andtheymustbedeterminedbeforepickingoperandB.
·Reference:UsethereferencecopyoftheoriginalobjectasoperandB.ChangingtheoriginalobjectinthefuturewillalsochangeoperandBintheBooleanobject,butchangingoperandBwillnotChangetheoriginalobject.
·Copy:CopytheoriginalobjectasoperandBwithoutchangingtheoriginalobject.Usethismethodwhentheoriginalobjectneedstobeusedforotherpurposes.
·Move:TheoriginalobjectisdirectlyusedasoperandB,anditwillnolongerexist.Choosethismethodwhentheoriginalobjecthasnootherpurpose.Thismodeisthedefaultmode.
·Instance(association):TheassociatedcopyoftheoriginalobjectisusedastheoperandB,andsubsequentmodificationstooneofthetwowillaffecttheotheratthesametime.
Parametersrollout
Theparametersoftherolloutcanbedividedintothreeareas.
Operands(operatingobject)optiongroup
Thisgroupofparametersisusedtodisplaythenamesofalloperandsandcanperformrelatedoperationsonthem.
OperandsList:Alloperandsarelistedinthislistboxforselectionduringeditingoperations.
Name:Displaythenameoftheoperationobjectselectedinthelistbox.Itcanbeedited.
ExtractOperand(ExtractOperand):Itre-extractsthecurrentlyspecifiedoperandintothesceneasanewusableobject,includingInstance(association)andCopy(copy)twoattributes.Inthisway,objectsthathaveenteredtheBooleanoperationcanstillbereleasedintothescene.Thisbuttoncanonlybeactivatedafterselectinganoperationobjectfromthelistboxaboveit.
Note:Thisbuttonisonlyavailableintheeditpanel.Whenthecreationpanelisactive,theoperationobjectcannotbeextractedfromtheBooleanobject.
Ithinkofthedeformedobjectmentionedabove,afterenteringthepreparedobjectfordeformation,itcannotreturntothescene.However,thereisanotherfeasiblemethodforthis,whichistousetheSnapshottooltocloneanewshapefromthedeformedkeyframesnapshot.
Operation(operationmode)optiongroup
Thisgroupofparametersprovides4operationmodestochoosefrom.
·Union(Union):Usedtomergetwoshapes,theintersectingpartwillbedeleted,andthetwoobjectswillbecomeoneobjectafterthecalculationiscompleted.
·Intersection(intersection):usedtokeeptheintersectingpartoftwoshapesanddeletethedisjointpart.
·Subtraction(A-B)(A-Bpart):SubtractthepartthatcoincideswiththeBobjectfromtheAobject.
·Subtraction(B-A)(B-Apart):SubtractthepartthatcoincideswiththeAobjectfromtheBobject.
Comparisonoftheabove4Booleanoperations.Fromlefttorightare:union,intersection,partA-B,partB-A.
·Cut(cut):CutoffobjectAwithobjectB,butdon'taddanypartofobjectBtoobjectA.WhentheCutradiobuttonisselected,itwillactivatethe4radiobuttonsbelowittoallowuserstoselectdifferenttypesofcuts.
·Refine:AddthenumberofverticesandedgesontheAobjectalongthesurfacewheretheBobjectandtheAobjectintersecttorefinethesurfaceoftheAobject.Inotherwords,thesurfaceoftheAobjectissubdividedaccordingtotheshapeoftheBobject.
·Split:ItsworkingmethodissimilartoRefine.It'sjustthatanextrarowofverticesisaddedtotheedgeofthepartwheretheobjectBcutstheobjectA.Usingthismethod,anobjectcanbedividedintotwopartsaccordingtotheshapeofotherobjects.
Comparedthesetworesectionmethods.ObjectAisacone,objectBisacuboid,fromlefttoright:Refine(refinement),Split(split).
·RemoveInside(removetheinside):deleteallthefragmentsoftheAobjectinsidetheBobject.ItsworkingmethodissimilartoSubtraction(A-B)(PartA-B),exceptthatthesurfaceofObjectBisalsoremovedatthesametime.
·RemoveOutside(removetheoutside):deleteallthefragmentsoftheAobjectoutsidetheBobject.ItsworkingmethodissimilartoIntersection,exceptthatthesurfaceofobjectBisalsocutoffatthesametime.
Display/Updaterollout
Thisrolloutparameterisusedtocontrolwhethertodisplaythecalculationresultintheviewandwhentorenewitaftereachmodification.Calculateandupdatetheview.
Displayoptiongroup
ThisgroupofparametersisusedtodeterminewhethertodisplaytheresultoftheBooleanoperationintheview.Itcontainsthreeoptions.
·Result:DisplaythecalculationresultofeachBooleanoperation.
·Operands(operatingobjects):OnlydisplayBooleancompositeobjectswithouttheresultsofoperations.Thiscanspeedupthedisplay.
·Result+HiddenOps(Result+HiddenOps):Displayhiddenoperandsinawireframewithinthecoloredentity,mainlyusedforeditingoperationsofdynamicBooleanoperations.
Updateoptiongroup
ThisgroupofparametersisusedtodeterminewhentorecalculateanddisplaytheBooleaneffect.
·Always:Booleanresultsaredisplayedimmediatelyaftereachoperation.
·WhenRendering:Recalculatetheupdateeffectonlyinthelastrendering.
·Manually(manual):selectthisoption,thefollowingUpdatebuttonisavailable,itprovidesmanualupdatecontrol.
·Update:Whenyouneedtowatchtheupdateeffect,pressthisbutton,andthesystemwillrecalculate.
