空间插值算法-反距离加权法

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1、Show InverseDistanceWeightedInterpolationOneofthemostcommonlyusedtechniquesforinterpolationofscatterpointsisinversedistanceweighted(IDW)interpolation.Inversedistanceweightedmethodsarebasedontheassumptionthattheinterpolatingsurfaceshouldbeinfluencedmostbythenearbypointsandlessbythemoredista

2、ntpoints.Theinterpolatingsurfaceisaweightedaverageofthescatterpointsandtheweightassignedtoeachscatterpointdiminishesasthedistancefromtheinterpolationpointtothescatterpointincreases.Severaloptionsareavailableforinversedistanceweightedinterpolation.TheoptionsareselectedusingtheInverseDistanc

3、eWeightedInterpolationOptionsdialog.ThisdialogisaccessedthroughtheOptionsbuttonnexttotheInversedistanceweightediteminthe2DInterpolationOptionsdialog.SMSusesShepard'sMethodforIDW:Shepard'sMethodThesimplestformofinversedistanceweightedinterpolationissometimescalled"Shepard'smethod"(Shepard19

4、68).Theequationusedisasfollows: wherenisthenumberofscatterpointsintheset,fiaretheprescribedfunctionvaluesatthescatterpoints(e.g.thedatasetvalues),andwiaretheweightfunctionsassignedtoeachscatterpoint.Theclassicalformoftheweightfunctionis: wherepisanarbitrarypositiverealnumbercalledthepowerp

5、arameter(typically,p=2)andhiisthedistancefromthescatterpointtotheinterpolationpointorwhere(x,y)arethecoordinatesoftheinterpolationpointand(xi,yi)arethecoordinatesofeachscatterpoint.Theweightfunctionvariesfromavalueofunityatthescatterpointtoavalueapproachingzeroasthedistancefromthescatterpo

6、intincreases.Theweightfunctionsarenormalizedsothattheweightssumtounity.Theeffectoftheweightfunctionisthatthesurfaceinterpolateseachscatterpointandisinfluencedmoststronglybetweenscatterpointsbythepointsclosesttothepointbeinginterpolated.Althoughtheweightfunctionshownaboveistheclassicalformo

7、ftheweightfunctionininversedistanceweightedinterpolation,thefollowingequationisusedinSMS:wherehiisthedistancefromtheinterpolationpointtoscatterpointi,Risthedistancefromtheinterpolationpointtothemostdistantscatterpoint,andnisthetotalnumberofscatterpoints.Thiseq