Integrating Dynamic Deformations into Interactive Volume(2)

Acommonapproachforhardwarerenderingofvolumesplacesthevolumeina3Dtexture,see[EHK 04]forde-tails.Brie y,theintegraloflightattenuationovereachraythroughthevolumeisapproximatedbysampling.Thesam-plesaregeneratedbyrenderingproxygeometry,andaccu-mulatedintheframebufferwithcompositingoperations.Toprovideforcorrectsamplingthroughtheobjectspace,asetofparallelgeometricelementsareusedfortheproxygeometry.Mostoften,theseareviewalignedplanes.Un-derperspectiveprojection,thespacingofthesamplesisnon-uniform(Figure2).Whiletheseerrorsareoftensmallenoughtobeignored,theycanbeaddressedthroughtheuseofnon-planarproxygeometryorapplyingaper-pixel(e.g.ray)correctionfactor.Ourimplementationdoesthelatter.Volumerenderingisimplementedbyrenderingpolygonsintheviewalignedplanesinbacktofrontorder.Eachpoly-gonisassignedtexturecoordinatessuchthatitsfragmentssampletheappropriatelocationinobjectspace.3.2.DeformedVolumeRendering

ThedeformedvolumerenderingprocessisschematizedinFigure2.First,theundeformedvolumedataisplacedina3Dtexture.Therenderingprocessdrawsaseriesofpolygonsthatarealignedwiththeimageplane.Eachpolygonisas-signedtexturecoordinatesthatareitsdeformedobject-spacecoordinates.Whenthepolygonisrasterized,eachfragment’sexecutionisprovideditsdeformedobject-spacecoordinatesandthevolumetrictextureasinputparameters.Tosamplethedeformation,itmustthereforeconvertthedeformedob-jectspacecoordinatesintoundeformedobjectspace,ortex-turespace,coordinatesbyapplyingtheinversedeformationfunctionbeforeperformingthetexturelookup.

cTheEurographicsAssociation2006.

Renderingadeformedvolumerequiresreplacingalleval-uationsoftheundeformedvolume,v,withthedeformedvol-ume,v′,meaningthatreferencestovarereplacedbyv u.

Fromanimplementationpointofview,foreachfragment,weapplytheinversedeformationfunctiontothedeformedobjectspacecoordinatesandusetheresultingundeformedobjectspacecoordinatestosamplethetexture.Thatis,thefragmentprogramforanundeformedtexturehasthefollow-ingstructure:

Vec3uvw=textCoord;

floatd=texture3D(texD,uvw);Vec4color=transfer(d);

thedeformedrenderingcanbeachievedsimplybyinsertingtheinversedeformationintotheevaluation:

Vec3uvwo=textCoord;

Vec3uvw=invDeform(uvwo);

floatd=texture3D(texD,uvw);Vec4color=transfer(d);

Thelookupintothevolumetextureperformsapointsam-plingwhichmayleadtoaliasing.Thisproblemshouldbeaddressedwhetherornotdeformationisused.Anyvolumetexturesamplingsolution,suchasa3Danalogtoamipmap,appliestothedeformedcaseaswell.Tocorrectly lterthewarp,thekernelradiusmustbedeterminedforthespacingofthesamplingintexturespace,notobjectspace.Ourpresentimplementationimplementspointsampling.

Withthedeformationfunction“encapsulated”insideofthefragmentprogram,otheraspectsofthevolumerender-ingprocessareunchanged.Theundeformedvolumedataisstillstoreddirectlyinthe3Dtexture.Anyproxygeometrycanbeused,althoughitismostsensibletouseview-alignedplanestoavoidartifacts.Proxygeometryisprovidedwithobjectspacelocationsastexturecoordinates,justasbeforedeformationsbecamepartoftherenderingprocess.Thefactthatthisobjectspaceisdeformedobjectspaceishiddenas

Non-linear geometric deformation (or warping) is a useful tool for working with volumes. Unfortunately, the computational expense of performing the resampling needed to implement volume deformation has precluded its use in interactive applications. In this

thetransformationbetweendeformedandundeformedob-jectspaceinthefragmentprogram.

Unfortunately,thereareseveralhurdlesthatwemustad-dressinordertorealizesuchanapproach:

1.Fragmentprogramshavelimitedresourcesmakingsomedeformationfunctionsimpracticaltoimplement.2.Shadingneedsthegradientofthedeformedvolume.3.Giventhelargenumberoffragmentsthatmustberen-dered,theamountofcomputationmightleadtoperfor-manceissues.Thefollowingtwosectionsconsiderhowweaddressthese rsttwohurdles.TheperformanceconsiderationisdeferreduntilSection6.2.

3.3.DeformationFunctions

Onedif cultyinourmethodisthatthedeformationfunc-tionmustbeencodedintothefragmentprogram.While,inprinciple,thefragmentprogramsmaybegeneralpurposecomputations,inpracticetheresourcesavailabletofragmentprogramsaremorelimitedthanthosetotheCPU.Afurtherpracticallimitationisthatsincetheseprogramsareexecutedforeveryfragmentrendered,theymustbeef cient.Thecontinuedevolutionofhardwareandshadinglan-guagesexpandsthesetoffunctionsthatcanbeimplementedeffectivelyasfragmentprograms.However,theremayal-waysbesomefunctionsthataretoocomplexorcomputa-tionallyexpensivetoapplyinthefragmentprograms.Weevaluatesuchfunctionsusingadatacentricrepresentationofstoringatableofsamplesandinterpolating.

Theideaofstoringasampledrepresentationofthefunc-tionuina3Dtexturewassuggestedin[RSSSG01].Priortorendering,theinversedeformationfunctionisevaluatedontheCPUforallpointsonaregular3Dgrid.Thesesam-plesarestoredina3Dtexturethatisaccessedbythefrag-mentprograms.Becausetextureaccessprovidestrilinearin-terpolation,thisapproacheffectivelyconstructsanef cienttoevaluate,piecewise-linearapproximationtothedeforma-tionfunction.Evaluationoftheinversedeformationfunctioninthefragmentprogramsrequiresonlyasingle3Dtexturesamplingoperation,independentofthecomplexityofthefunctionitself.Thisdeformationtextureneednothavethesameresolutionasthevolumedata.

Theuseofasampleddeformationfunctionhasdraw-backs.Forone,itcomputesapiecewiselinearapproximationthatmayfailtocapturedesiredsmoothnessorhighfrequen-ciesunlesslargenumbersofsamplesareused(Figure3).Second,theentiretablemustbeevaluateddensely,whichmaybeexpensive.However,formanycategoriesoffunc-tions(suchaspolynomialsplines),methodsforcomputingregularsamplescanbemoreef cientthancomputinginde-pendentsamples.Third,fragmentprogramsoftenbecometexture-lookup

bound.

(a)163control

texture(b)323control

texture

(c)643control

texture

(d)Fragmentdeformation

Figure3:Imagesofasolidbrickinsideofa2563volumeun-derasinedeformation.Thedeformationisperformedwithcontroltexureso …… 此处隐藏：6204字，全部文档内容请下载后查看。喜欢就下载吧 ……