简介:Afamilyofpiecewiserationalquinticinterpolationispresented.Eachinterpolationofthefamily,whichisidentifieduniquelybythevalueofaparameterαi,isofC2continuitywithoutsolvingasystemofconsistencyequationsforthederivativevaluesattheknots,andcanbeexpressedbythebasisfunctions.InterpolantisofO(hr)accuracywhenf(x)?Cr[a,b],andtheerrorshaveonlyasmallfloatingforabigchangeoftheparameterαi,itmeanstheinterpolationisstablefortheparameter.Theinterpolationcanpreservetheshapepropertiesofthegivendata,suchasmonotonicityandconvexity,andaproperchoiceofparameterαiisgiven.
简介:Resortingtocubicsplinefunctioninsteadofparametricsplinerepresentation,anexplicitfairnessindicatorandanefficientfairingalgorithmfor2Dcurvesarepresented.Theinputpointsequenceisfirstlypartitionedintoseveraloverlappedfunctionsegments.Foreachsegment,acubicsplinefunctionisusedastherepresentationtoolwhichentailsapolylineapproximationofcurvatureplot.Basedontheextrinsicrelationshipbetweenthepolylineandthepositionsofdatapoints,acoarse-to-finefaringmethodisproposedwhichefficientlyidentifiesandeliminatestheunnecessaryinflectionpoints.Ouralgorithmgeneratesthebestresultstodate,whichisvalidatedbynumerouspracticalexamples.