简介:Resortingtocubicsplinefunctioninsteadofparametricsplinerepresentation,anexplicitfairnessindicatorandanefficientfairingalgorithmfor2Dcurvesarepresented.Theinputpointsequenceisfirstlypartitionedintoseveraloverlappedfunctionsegments.Foreachsegment,acubicsplinefunctionisusedastherepresentationtoolwhichentailsapolylineapproximationofcurvatureplot.Basedontheextrinsicrelationshipbetweenthepolylineandthepositionsofdatapoints,acoarse-to-finefaringmethodisproposedwhichefficientlyidentifiesandeliminatestheunnecessaryinflectionpoints.Ouralgorithmgeneratesthebestresultstodate,whichisvalidatedbynumerouspracticalexamples.
简介:Triangulationiswidelyusedinscientificresearch,suchasfiniteelementmeshgeneration,surfacereconstructionandthereconstructionofthedensityfielddata.Thispaperproposesanewmethodcombiningimageprocessinganddensity-controlledCentroidalVoronoitessellationstoquicklygenerateadensity-controlledconstrainedDelaunaytriangulationfor2Dseaarea.Firstly,preprocessdigitalimagesoftheseaareaandextracttheboundaryofseawaterregionbyeight-neighborsearchingalgorithm.Then,Iuse"Odd-EvenTesting"methodtocheckifonerandomvertexisinsidetheboundaryandinsertrandomverticesintotheboundary.Finally,wegettheCDTofrandomverticesbydensity-controlledCVT-Lloydmethod.Wealsogivesomecomparisonswithexistingmethods,andourmethodperformsbetterinfinalresultoftriangulation.
简介:TheexplicitexpressionoftheG~3basisfunctionispresentedinthispaper.ItisderivedbyconstructingtheconversionmatrixbetweenG~3basisfunctionandBézierrepresentation.Afterthematrixdecomposition,equationsforconstructingG~3splinescanbepresentedindependentlyofgeometricshapeparameters’values.Itmakestheequation’ssolvingeasier.ItisalsoknownthatthegeneralformoftheG~3splinebasisfunctionisgiveninthefirsttime.Itsgeometricconstructionmethodispresented.