Subsurface Texture Mapping

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Guillaume François, Sumanta Pattanaik, Kadi Bouatouch, Gaspard Breton

To cite this version:

Guillaume François, Sumanta Pattanaik, Kadi Bouatouch, Gaspard Breton. Subsurface Texture Map- ping. [Research Report] 2006. �inria-00084106�

a p p o r t

d e r e c h e r c h e

9-6399ISRNINRIA/RR--????--FR+ENG

Thème COG

Subsurface Texture Mapping

Guillaume Francois & Sumanta Pattanaik & Kadi Bouatouch & Gaspard Breton

N° ????

juillet 2006

GuillaumeFranois

∗

&SumantaPattanaik

†

& Kadi Bouatouh

‡

&

GaspardBreton

§

ThèmeCOGSystèmesognitifs

ProjetSiames

Rapportdereherhe n° ???? juillet200628pages

Abstrat: Subsurfae sattering within transluent objets is a omplex phenomenon.

Designingandrenderingthiskindofmaterialrequiresafaithfuldesriptionoftheiraspets

as well as a realisti simulation of their interation with light. This paper presents an

eientrenderingtehniqueofmultilayeredtransluentobjets. Wepresentanewmethod

for modeling and renderingsuh omplexorgani materialsmade up of multiple layersof

variable thikness. Based on the relief texturemapping algorithm, our method alulates

the single sattering ontribution for this kind of material in real-time using ommodity

graphishardware. Ourapproahneedsthealulationofdistanestraversedbyalightray

throughatransluentobjet. This alulationisrequiredforevaluatingtheattenuationof

light within the material. We use a surfae approximation algorithm to quikly evaluate

thesedistanes. Ourwholealgorithmisimplementedusingpixelshaders.

Key-words: Realtimegraphis,GPU, Subsurfaesattering

EnollaborationaveFraneTéléomR&DRennesetavel'UniversitédeFlorideCentrale(UCF)

∗

gfranoiirisa.fr

†

sumants.uf.edu

‡

kadiirisa.fr

§

gaspard.bretonfraneteleom.om

omplexe. Pourmodéliseretrendredetelsmatériaux,ilestnéessaired'avoirunedesription

adaptée de eux-i ainsi qu'une simulation réaliste de leurs interations ave la lumière.

Ce papier présente une tehnique de rendu adaptée aux matériaux multiouhes. Cette

nouvelle méthode permet de modéliser des matériaux organiques omplexes omposés de

ouhes multiples à épaisseur variable. Basée sur l'algorithme du relief mapping , notre

méthode permet le alul temps réel de la diusion simple pour e type de matériau, et

een exploitantlesperformanesdesartesgraphiques. Notreméthode néessitelealul

desdistanesparouruesparlalumièreàl'intérieurdesdiérentesouhesdumatériau. Ce

alulestnéessairepourl'évaluationdel'atténuationdelalumièreàl'intérieurdumatériau.

Nousproposonsd'utiliserunalgorithmed'approximationdesurfaepourréalisere alul

rapidement. Notrealgorithmeestimplementéàl'aidedepixel shader.

Mots-lés : Rendutempsreel,GPU,Diusionsous-surfaique

newpage

Contents

1 Introdution 4

1.1 RelatedWorkandMotivations . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 OurMethod 8

2.1 SubsurfaeTextureMapping . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 ReduedIntensityEstimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3 Results 19

4 Conlusion and FutureWork 23

1 Introdution

Rendering realistimaterials is essential for reatingonvining images. The interations

betweenlightand materialsareoften modeled by aBRDF(BidiretionalReetane Dis-

tributionFuntion)whihassumesthatlightentersandexitsthesurfaeatthesamepoint.

This assumption does nothold for many materials suh as marble, wax, milk, leavesand

humanskin. Forthese transluentmaterials,lightdoesnotonlyreetothesurfae,but

sattersinsidethemediumbeforeleavingthesurfae. Thisphenomenonisalledsubsurfae

sattering. Sine suh materialsareoftenseenin ourday-to-daylife,itisessentialtooer

solutionsto therenderingoftransluentmaterials. Theeets ofsubsurfaesatteringare

multiple: theobjetsappearsmoothand softsinelight isdiused beneath their surfae.

For some omplex materials, this phenomenon an also exhibit their inner omposition.

Veinsarevisibleunderhumanskin,forinstane.

Figure1: Subsurfae texturemapping.

This paper presents a rendering tehnique for materials made up of multiple layers, the

thikness of whih is not neessarily onsidered as onstant unlike existing methods. In

suh a ase, the inner omposition of the material an be pereived as shown in Figure

1, exhibiting blurry details inside the transluent objet where the sattering parameters

vary. Weused theoneptofrelieftexturemapping[1℄tomodeltheinteriorofamaterial.

However, insteadof representing the surfaedetails, we use this method to representthe

innerstrutureoftheobjet. Therefore,thelayersofthematerialaredesribedbyasimple

2D texture, where eah hannel enodes a thikness. Sine our method is not limited to

loally at surfaes, auseful surfae approximationis used to quikly estimate thesingle

satteringterm.

Weproposeasimplebutrealistimethodthatoersareal-timeestimationofthesinglesat-

teringtermforsuhomplexmaterials. Ourmethodouldbeonsideredbetweensubsurfae

renderingmethods based on surfaes and 3D texture-basedalgorithms. Furthermore,our

solutionalsoprovidesaompatwaytodesigntransluentobjetsusingasmallamountof

data,whereas3Dtexturing requiresalargeamountofmemorystorage.

Thispaperisstrutured asfollows. Setion 1.1summarizestherelatedworksandpresents

ourmotivationswhileSetion1.2outlinesourmethod thatisdesribedindetailin Setion

2. Setion3showssomeresultsandSetion4onludes thispaper.

1.1 Related Work and Motivations

Theradiativetransport Equation[2℄, desribingthe subsurfaesattering phenomenon, is

tooomplexto befully omputedatinterativeframerates. Furthermore,theparameters

ofthisequationsuhasthesatteringoeientorthephasefuntion,anvaryinthease

ofnonuniformmediaortransluentobjet. Therefore,formaterialssuhasmarble,smoke,

orlayeredmaterialssuh asskinorplantleaves,weannotusetheapproximationsusually

proposedforsimplifying theequations.

Lightsattering within partiipatingmedia or transluent objets an beomputed using

multiplemethodssuhaspathtraing[3℄,volumetriphotonmapping[4℄anddiusionap-

proximation[5℄. Mostofthesemethodsoeranaurateestimationofsubsurfaesattering

foroinerenderingbutdoesnotallowafastrenderingoftransluentmaterials. However,

in most ases, the omputational ost of those methods prevents their use for real-time

renderingoftransluentobjets.

ThedipolebasedmethodduetoJensenetal[6℄andproposedinreal-timeby[7,8℄,dealswith

uniform materials, usinga BSSRDF model (bidiretional subsurfaesattering reetane

distribution funtion). Donner et al. [9℄ reently proposed amultipole based method to

estimatesubsurfaesatteringwithinlayeredmaterials. Thisnewmethod, extensionofthe

previousdipole approximation,providesrealistiresultslose to Monte Carloestimations.

Nevertheless,ifthealgorithmproposesrealistiandlosetophysiallyorretresults,itdoes

notoerinterativeframeratesusefulinmanyappliations. Anotherreal-timemethod[10℄

addresses sattering for general partiipating media but does not deal with multilayered

materials.

3Dtextures[11℄istheommonlyusedmethodtodesribeomplexandtransluentobjets.

Theyallowto desribetheinner omposition of anobjet,suh as theorgansof ahuman

body andthereby, as wellas therenderingof theinteriorofthe objets. Pathtraingan

be used for a orret estimation of subsurfae sattering. Implementation relying on 3D

texturesandusingtheGPUhavebeenproposedin[12℄. However,3Dtexturesrequirelarge

amounts ofdata whih an be amajor onstraintfor real-timerendering. Note that some

objets do notrequire aomplex desriptiondeep beneath thesurfae. For example, the

humanskinpresentspartiularities,suhasveins,withinasmalldepthbeneaththesurfae.

In this ase, 3D textures appear unneessary and limiting. For that partiular ase, we

needbothasurfaedesriptionandavolumedesription,givingfurtherdetailslosetothe

objet'ssurfaeonly.

In this paper, we propose a novel desription of omplex materials. Rather than using

the well-known 3D textures, we propose the use of simple 2D textures well handled by

graphishardware. Ourmethodanbeonsideredas analternativemethodforomputing

singlesatteringwithin multilayeredmaterialsinreal-time. Ourapproahallowsarealisti

desriptionofthelayersofvariablethiknessusingsubsurfaetexturemapping. Ourmethod

followsasimilaroneptthanrelieftexturemappingintroduedbyPoliarpoetal. [1℄and

reentlyproposedtodesribenon-height-eldsurfaedetailswithmultiplelayers[13℄. Relief

texturemappingoershighlyrealistiappearanetosynthetiobjetswhileusingasimple

geometry: ne details upon the surfae are represented with a 2D texture. However, in

our ase, the details are not above but beneath the surfae, whih reates, for instane,

partiularveinseet.

1.2 Overview

(a) (b)

Figure2: Figure2(a)presentsasimplelayeredmaterialandgure2(b)amaterialomposed

oflayerswithvariablethikness.

Inthispaperweproposeanewapproahtomodelingandreal-timerenderingoftransluent

organimaterials. Thematerialsonsideredinouraseareomposedofmultiplelayers,eah

one having partiular properties. In ontrast to methods using planarlayers,our method

omputes single sattering into layers of variable thikness (f. Figure 2). With these

material properties one an rendernew eets notvisible for layersof onstant thikness.

Inorder to provide areal-time but realisti rendering,welimitour omputation tosingle

sattering. Ourmethod,implementedongraphishardware,usesaraymarhingalgorithm

illustratedin Figure3.

Modeling of layered material requires information about the thikness of the layerssine

this thikness varies beneath the surfae. We propose in Subsetion 2.1 the use of a 2D

texturetostorethethiknessofeahlayer. Weusethistexturetodeterminethesattering

parameters. Theomputationofsubsurfaesatteringwithinthiskindofnonhomogeneous

material requires aknowledge of thelayers' parameters. To this end, wepropose apoint

andpathloalizationmethod.

Asshown inFigure 3,thereetedluminane at pointP ^{isdueto singlesatteringevents}

ourringalongtheviewingrayunderneaththeobjet'ssurfae. Weomputetheontribu-

tionsofaertainnumberofsamplepointsM ^{ontheviewingrayuntilaertainpoint}Mmax

afterwhihsatteringisonsideredasnegligible.

Figure3: Raymarhingalgorithmin amultilayeredmaterial.

The singlesattering ontribution, LM(P, ωout)^{, at a visible point} P ^{and due to an inner}

samplepointM ^{ontheviewing ray,isexpressedas:}

LM(P, ωout) = Q(M, ωout)e RP

M−σt(s)ds

(1)

Q(M, ωout) = σs(M)p(M, ωout, ωin)Lri(M, ωin), ⁽²⁾

whereLri(M, ωin)^{isthereduedintensity atpoint} M ^{omingfromdiretion} ωin ^andrep-

resentsthe amount ofinidentlightarriving at the inner pointM ^after attenuation. The terme

RP

M−σt(s)ds

representstheattenuationofthesatteredradianeduetoabsorptionand

satteringalongthepathfromM ^toP^. p(M, ωout, ωin)^{isthephasefuntionanddesribes}

howthelightomingfrom theinidentdiretionωin^{is satteredin theoutgoingdiretion}

ωout ^{at point}M^.

Thetotalsattered radianedue tosingle satteringarriving atthe pointP ^{is thesumof}

theontributionsofallpointsMontheviewing ray:

L(P, ωout) =

Z M_max

P

LM(P, ωout)dM ⁽³⁾

Weevaluatethislastequationusingaraymarhingalgorithm,whihdisretizestheequation

as:

L(P, ωout) =

M_max

X

P

LM(P, ωout)δM ⁽⁴⁾

=

M_max

X

P

Q(M, ωout)e RP

M−σt(s)ds

δM ⁽⁵⁾

whereδM ^{isthesamplingstepalong}P Mmax^.

Theterme RP

M−σt(s)ds

isestimatedbyaraymarhingalgorithm. Thislatterperformsdepth

omparisons to determine the extintion oeient σt ^{for eah layer. The estimation of}

the term Q(M, ωout) ^{of Equation 1 requires the alulationof the redued intensity. We}

showinSubsetion2.2thattheestimationofthereduedintensityneedsanestimateofthe

distane kKMk ^{traversed by the light in thematerial. Weproposeamethod to ompute}

anapproximate valueof thisdistane. Thisis one oftheontributionsofthis paper. The

singlesattering resultQ(M, ωout)^{at an inner point} M ^{alsodepends onthe properties of}

thematerial. Thereby, weneedto determinethelayerin whihis loatedthepointM^{, to}

knowforinstane theorrespondingsatteringoeientσs(M)^{. Tothis end,wepropose}

asimplematerial desriptionthat allowsfastpointloalization guided by textures. With

theseontributions,detailedinthenextsetion,real-timerenderingofsubsurfaesattering

in suh materialsan be ahieved using graphishardware. InSubsetion 2.3 we propose

implementationsolutionsforgraphishardware.

2 Our Method

We propose a simple but realisti solution to the rendering of multilayered materials. In

ourase,wedonotassumethelayerswithaonstantthikness. Welimitouromputation

ofsubsurfaesatteringtosinglesatteringtomeetthereal-timeonstraint. Thenexttwo

subsetions presentthe subsurfae texture mapping idea and a novel method to estimate

the redued intensity on arbitrary, non planar, polygonal surfae desribed by a mesh.

Thesolutions provided bythese two subsetions areombinedin our renderingalgorithm

presentedinSubsetion2.3.

2.1 Subsurfae Texture Mapping

In this setion, we present the notion of subsurfae texture used to desribe the internal

struture of a transluent objet. Our method, built on the same idea as relief texture

mappingproposed by [1℄, usesatextureas adepthmap whih allowstodesribeomplex

objets when mappedonto aat polygon as shown in Figure 4. We propose to use a2D

(a) (b) ()

Figure4: Subsurfae Mapping: TheFigure 4(a)presentsthesubsurfaetexture. Thered

hannel enodesalayerwith aonstantthikness,thegreen andblue ones desribelayers

omposed of veins with dierentwidth. The alphalayer,not visiblehere, enodes alayer

with a uniform thikness. Figure 4(b) shows the representation (ross-setion) of suh a

material. Figure4()showstheresultingimageobtainedwhenapplyingsuhamaterialon

anarbitrarysurfae.

texture to desribeour multilayeredmaterial. Indeed, thedepth ofeah non planarlayer

an beenoded usinga reliefmap. Thepresene ofthe four RGBα^{hannels of atexture}

allowstodenethethiknessoffourlayers. Theredhannelisrelatedtotherstlayerand

theotherhannelstothefollowinglayers.

Asshownin Figure5,thedepthstoredineahhannelrepresentsthedistaneofthelayers

tothesurfaeinthediretionofthenormal. Thethiknessofalayeranbeobtainedusing

thedepthinformationstoredinto twoonseutivehannels. N ^{texturesandesribeupto} 4N ^{layers,whihallowsaomplexdenitionofa}multilayeredmaterial. Analgorithmusing raytrainganbeusedtoomputethesubsurfaetexturewheneah layerisdesribedby

amesh.

Estimatingthesinglesattering atapoint M ^{beneaththe surfaerequires} informationon thelayerin whihis loated M^{. Byomparingthe depth ofthe point}M ^{and therelated}

depthofeahlayersstoredinto thetexture,weandeterminethelayerofinterestanduse

itsspei parameters.

Theproessofmappingourtextureoflayerthiknessontoapolygonalsurfaeispresented

inFigure6andexplainedasfollows:

ˆ determineP M^{,withthepoint}M ^{insidethemediumandlyingontheviewingray.}

ˆ ProjetthevetorP M ^{inthetangentspae(denedbythetangent}T^,normalN ^and

bi-normalB ^vetors).

(ds, dt) = (P M·T, P M·B)

Figure5: Denitionofthesubsurfaemap

ˆ usetheprojetedP M^,(ds, dt)^{, andthetextureoordinatesofthepoint}P^,(uP, vP)^,

toomputethetextureoordinatesofM^′: (uM′, vM′) = (uP, vP) + (ds, dt)

ˆ determine the layer of the point M ^{by omparing its depth with the depths of the}

layersstoredin thesubsurfaetextureat(uM^′, vM^′)^.

(a)Proleofthematerial (b)Projetedvetorintothetexture

Figure6: Projetionin thetangentspae.

ThisproessisillustratedinFigure6. PointPhasadepthequaltozero. 6(b) presentsthe

projetionof thevetorP M ^{into thetexture spae. Note that thetangentand bi-normal}

arerelatedto thetextureoordinates. Thetangentgivesthediretionofvariationoftheu

textureoordinateand thebi-normalgivesthediretion of thevariationofthe oordinate

v^{. Formoredetailssee[14℄and[1℄.}

Thismappingallowsaomplexdesriptionoflayeredmaterialswith simpleloalizationof

points within it using a singletexture lookup. Wean desribe upto 4N ^layersusing N

RGBα^{textures. This isoneof our}ontributions. Wewill seein theSubsetion2.3 howto omputethesinglesatteringusingsuh amaterialdesription.

2.2 Redued Intensity Estimation

Thissetiongivesdetails onthealulationofthereduedintensityLri(M, ωin)^(seeEqua-

tion 2) whih aounts for the attenuation of light within a multilayered material before

beingsattered. RefertoFigure7(a)fortheexplanationsgivenhereafter.

Forthesakeoflarity,werstonsidertheaseofasinglelayermaterialhavingaonstant

extintion oeientσt^{. The alulationof the reduedintensity depends onthe amount}

oflightLi(K, ωin)^{impingingonto thesurfaeofthemediumatapoint}K^{and dependson}

thedistane||KM||^{traversedbythelightraywithinthemedium. Thereduedintensityis}

givenby:

Lri(M, ωin) =Li(K, ωin)e^{−σt||KM|| (6)}

TheproblemanbereduedtotheomputationofthedistanekKMk^,thetermLi(K, ωin)

is given by thelight soureintensity. This distane an be aurately obtainedusing ray

traing. Nevertheless,using thegraphis hardware,weannot omputeeasily theinterse-

tionbetweenthelightraySM^{andthesurfae. Forafastestimationofthedistane}||KM||^,

withoutthe need of detailed information about thesurfae, we propose to use planarap-

proximationsofthesurfaewhih,whenintersetedbythelightraySM^{,givesareasonable}

estimateofthepositionofthepointK ^{(seeFigure7).}

Note that in [15℄ the authors present a method addressing a similar problem and imple-

mentedontheGPU.Theyuseaplanarapproximationmethodtoomputethepointhitby

areeted or a refratedray. Their method providesmore aurateresults and performs

planar approximations at runtime based on the model's geometry and rays (reeted or

refrated). Our method is faster sine all the planar approximations are performed in a

simplepreproessingstep,onlybasedonthemodel'sgeometryandthematerialproperties

(extintionoeient).

First,letusonsiderthepointsM ^{ontheraypathlosetopoint}P^{. Inthisase,weobserve}

thatreplaingthesurfaebyitstangentplaneatP ^{oersareliableestimateofthedistane.}

This isdue to theproximityof theintersetion betweenthe realsurfaeand thelightray

andtheintersetion ofthelightraywiththetangentplane. Mostof thelightsattered at

pointslosetoP ^{strikesthesurfaeatpointsalsolosetothepoint}P^{. Figure7(b)presents}

thesurfaeapproximation(inred)thatanbeusedforthesepointsM^{. NoteinFigure7(b)}

thatthisapproahisnotreliablewhenthelightentersatpointsfarfromP^{sinethetangent}

planegivesaninorretestimateofthelightentrypoint. Nevertheless,intheselatterases,

theattenuationoflightissigniantomparedtotheattenuationoflightimpingingontoa

loseneighborhood of P^{. This isdue to thedistane of lighttraversal. Weonsider then}

that the tangent plane oersa reliableapproahof the surfaeto estimatethe sattering