Energy and B-Spline Interproximation .pdf

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1、Computer-AidedDesign,Vol.29,No.7,pp.465-496,1997c1997ElsevierScienceLtd.AllriahtsreservedPrintedinGreatBritain.PII:SOOlO-4485(96)00087-5OOlo-4465/97/$17oo+o.ooEnergyandB-splineinterproximationXuefuWang,Fuhua(Frank)ChengandBrianABarsky*understandingoftheperformanceofthestrainenergy

2、Inthispaper,westudyB-splinecurveinterproximationwithapproximationmethodsisimportantsincesomeofdifferentenergyformsandparametrizationtechniques,andthedesignprocessesusetheenergyasameanstopresentaninterproximationschemeforB-splinesurfaces.Itoptimizetheshape(geometricsmoothness)ofacu

3、rveshowsthattheenergyformhasamuchbiggerimpactontheorsurfaceO,2-6J4-?7.Oneexampleistheprocessofgeneratedcurvethantheparametrizationtechnique.Withtheconstructingasmoothsurfacetointerpolateanetworksameenergyform,differentparametrizationtechniquesofcurves14,whereanenergyfunctionismini

4、mizedtogeneraterelativelysmalldifferenceonthecorrespondingfindtheoptimaltwistvectorsfortheinterpolatingcurves.Withthesameparametrizationtechnique,however,surface.Anotherexampleisthecurveinterproximationdifferentenergyformsmakesignificantdifferenceontheshapeprocess45whereacurvewith

5、thesmoothestshapeisandsmoothnessoftheresultingcurves.Furthermore,inter-soughttointerpolategivendate.ThedatacouldbeproximatingB-splinecurvesgeneratedbyminimizingapproxi-pointsorregions.Thecurveinterpolatesthepointsandmatedenergyformsarefarfrombeinggoodapproximationstopassesthrought

6、heregions.Thecurveinterproximationtheoptimalcurves.Theytendtogenerateflatterregionsandprocessiscarriedoutbyminimizingtheenergyofthesharperturnsthancurvesgeneratedbyminimizingtheexactcurvetoachievegeometricsmoothness.Asurfaceenergyform.Theinterproximationschemeforsurfacesisinterpro

7、ximationtechniqueisnotavailableintheaimedatgeneratingasmoothsurfacetointerpolateagridofliteratureyet.datawhichcouldeitherbeapointoraregion.ThisisachievedActually,thegeometricsmoothnessofaninterpolat-byminimizingastrainenergybasedonsquaredprincipalingcurveorsurfacedependsonknotpara

8、metrizationcurvaturesforbicubicB-