高级计算机图形学ACG04

AdvancedLightingandShading

Outline

•RadiometryandPhotometry,colorimetry

•BRDFtheory,implementingBRDFs

•Vertexshaders,pixelshadingandshadingLanguage

•MotionBlur,depthoffield,reflections,refractions,

shadows

RadiometryandPhotometry

•Radiometry

-Themeasurementofopticalradiation,whichis

electromagneticradiationwithinthefrequencyrangebetween

3xlOnand3xl016Hz

-includestheentireopticalradiationspectrum

•Photometry

-Themeasurementoflight,whichisdefinedas

electromagneticradiationwhichisdetectablebythehuman

eye

-Itisthusrestrictedtothewavelengthrangefromabout380to

780nm

-limitedtothevisiblespectrumasdefinedbytheresponseof

theeye

Photometry

•TheCIEphotometriccurve

Photopic

luminous

efficiency

Wavelength(nm)

Radiometry

•RadiantEnergy

-Q(measuredinjoules)

•RadiantFluxdi

FigurelaIrradiance

-Energyperunittimeisradiantflux(watt)

-①=dQ/dt

•RadiantFluxDensity

-Irradiance

•E=d①/dA

-Radiantexitance(alsocalledradiosity)

M=d(b/dA

dA

FigurelbRadiantexitance

Radiance

ds

projected

、aiea

•ProjectedareaXXX」

-rectilinearprojectionofasurfaceof

anyshapeontoaplane工

-Solidangle

•InCG,lightsandviewersare

oftentreatedaspoints.

•Measurementsintermofareasdof

notapply.

3

•4兀steradiansofsolidangleina卜二Z

sphere.\〃

duj

Radiance

中

Photometry

QUANTITYRADIOMETRICPHOTOMETRIC

powerwatt(W)lumen(Im)

powerperunitareaW/m2Im/in2=lux(lx)

powerperunitsolidangleW/srIm/sr=candela(cd)

powerperunitareaperunitsolidangleW/m2-srlm/jn2-sr=cd/m2=nit

Colorimetry

Colormatchingexperiment

•r=645nm

•g=526nm

•b=444nm

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RGBColorMatchingFunctions

•Showthethreecolorrequiredtomatchapurecolorat

thewavelength

-0,10

wavelength,nm

RGBColorMatchingFunctions

•Negativeweightsforvariouswavelengths.

•TheCIEproposedthreedifferenthypotheticallightsourcesthat

didnotusemonochromaticlight

1.40••

1.20--

1,00--

0.80

0.60--

0.40

0.20••

0.00L

350

wavelength,nm

Colorimetry

•TristimulusvaluesareweightsthatdefineacolorinCIEXYZ

space

•WhereC（X）isthespectralenergydistributionforwhateverlight

sourceischosen.

780

-X=j

380

780

-Y=jC（2）y（2）J2

_380

—780

Z=jC（2）z（2）M

380

CIEchromaticitydiagram

520

Y-x5401931CIEChromaticity

UniqueDiagram

X+Y+Zgreen

aboutUniqueyellow

here

Y

y-

X+Y+Z

z=l-x-y600

...0.2

UniqueUniqueredplots

blueabouthere

aboutThecomersofthistriangleis

hereapproximatelywherethephosphors

ofatypicalcolormonitorplot

00.20.40.60.8

X

BRDFTheory

•BRDF

-howlightinteractswithmatter

•Complicatedlight-matterdynamicsoccurs

•Dependsoncharacteristicsofboththelightandthematter

-E.g.,aroughopaquesurfacew川reflectlight

differentlythanasmoothreflectivesurface

BRDFTheory

•BRDF

-Viewer/lightpositiondependency(incoming/outgoingraysof

light)

-Differentwavelengths(colors)oflightmaybeabsorbed,

reflected,transmitteddifferently

-Positionalvariance-lightinteractsdifferentlywithdifferent

regionsofasurface,e.g.wood

•BRDFmustcapturethisviewandlightdependentnatureof

reflectedlight

BRDFTheory

•GeneralBRDFinfunctionalnotation

-3HD玛电血&爆

-Xisusedtoindicatethelightswavelength

-0i,A:incominglightdirectioninsphericalcoordinates

-九0。outgoingreflecteddirectioninsphericalcoordinates

-uandvrepresentthesurfacepositionparameterizedin

texturespace.

BRDF泡曲

•Position-invariantBRDF

BRDF

L（九”））=于在。。,a:公L叫，勿）cos（q）

L3）=/3，M）乙3）（〃四）

Blinn5sformofPhonghighlighting

L（%）=①"（①）（皿）4=((〃3”

、/、h）%

p"。例）

•ThePhongspeculartermisabitodd

-itsBRDFcancelsoutthereflectanceequation'scosinetermfrom

theangleofincidence.

-Phonghighlightingmodelisadhocandignorestheeffectofthe

projectedarea

BRDFTheory

•2importantproperties

-Reciprocity

BRDF<R，a，，，4）=BRDF入（9。0。,乱曲）

-Conservationofenergy

Q

SomeBRDFModelingConcept

•Micro-facets(Cook-Torranceetal.)

-heightcorrelation(HTSGBRDFmodel)

•Fresnelreflectance

•Anisotropyandisotropic

Micro-facets

•Micro-facets

-Thesurfaceconsistsofalargenumberofsmallflat“micro

mirrors”(facets)

-Facetsreflectlightonlyinthespeculardirection

-Diffusereflectionasinterreflectionofseveralfacets.

Micro-facets

-Ontheleft,themicro-facetcan“see”indirectionskland

k2,soitcontributestotheBRDF.

-Ontheright,directionk2isblockedandthemicro-facet

doesnotcontribute.

Fresnelreflectance

•Whenadielectricislookedatalongagrazingangle,ifis

morereflective.

•Incomparison,metalsvaryrelativelylittle.

1

o8

•

o6

•

o4

•

o2

•

0

0102030405060708090

angleofincidence

Fresnelreflectance

1(g*j+[c(g+C)­l]2>

2

5(g-C)2[[c(g-C)+l]?

c=vh____

g=+C2-1

Anisotropy

ImprovementonBRDF

•BRDFassumeslightentersandleavesasurfaceatthe

samepoint,whichisn5ttrueinreallife

•Bi-directionScatteringSurfaceReflectionDistribution

Functions(BSSRDF)

妥添

\

\

\4

XAJ/

<1

ution-function

BRDFandBSSRDF

ImplementingBRDFs

•Factorization

-BRDFisa4Dfunction

•usea4Dlookuptable(i.e.a4Dtexture)tostorethe

BRDF

•atrun-timedoaper-pixeltexturelookuptocomputethe

lightingequationabove.

-ConvertaBRDFintoasetoftwo-dimensionaltextures

Factorization

•Factorization

-Firstphase-preprocess

•SeparatetheBRDFintotwo2Dfunctionsrepresentedas

apairoftexturemaps

-Secondphase

•ReconstructingtheBRDFandcomputationoftheBRDF

lightingequation

Factorization-Decomposition

•Factorization几

-Findp,q/(co,,%卜Zp/g)%.(q)

•SVDj=i

-Singularvaluedecomposition

-Optimal

-expensiveintimeandspace

•ND

-Normalizeddecomposition

-simple

Example

•FactorizationofaBRDFforgold

-Thetwotexturesareaccessedwiththeincominglightand

outgoingviewdirections

-Multiplytexturestogetherateachpixeltogeneratetheteapofs

illumination

Drawbackoffactorization

•Drawbacks

-Foreachlightsourceinthescene,atleasttwotextureaccess

areneeded.

-Theradiancecoiningfromarealight,thesky,orother

surroundingobjectscannotbecaptured.

anansotropicsurface

aphotomicrographshowingasimilar

(brushedmetal).

surface

directionalityofthedetail

Outline

•RadiometryandPhotometry,colorimetry

•BRDFtheory,implementingBRDFs

•Vertexshaders,pixelshadingandshadingLanguage

•MotionBlur,depthoffield,reflections,refractions,

shadows,global川umination

VertexDataTessellationData

Geometry

Stage

Rasterizer

Stage

Shader

•Vertexshaderwastoreplacehardwaretransformand

lighting(T&L)unit

-Developersgainmorecontroloverthelightingmodel

ofvertices.

•Specialeffectsandobjectdeformations

•PixelShaderwastoreplaceTexturingStages

-Developerscanmanipulateeachpixelsdirectly

•makinghandcraftedphongshadingandotherper-

pixeleffectspossible.

-Canmodifythez-depthvalue

-Maketextureaccessingandmanipulationeveneasier:

•Accesstoupto16textures.

•Manipulationoftexturecoordinates,likescaling

andoffsetting.

•ShadingLanguages

-Assembly-likelanguages.

VertexShader

•HardwareT&LversusVertexShader:

-HardwareT&L

•ThetaskofT&Lofverticeswasoffloadedtographic

hardware

-freeCPUforothertasks.

•Thedrawback

-itforcedtheuseofbasichard-wiredGouraud/Phong

lightingmodel.

-VertexShader

•Hardware-assistedandprogrammableversionof

HardwareT&Lstage.

•V.ScanemulateallofthefunctionalityoftheHardware

T&L,andwithoptimizationsitcanevenbefasterthanthe

hard-wiredpath.

VertexShader

•Thefirstversion(DX8)ofvertexshaderspecification:

-Upto128steps.

-17differentinstructions.

-Noexplicitflowcontrolinstructions.

-4Typesofmemory

•Per-vertexinput.

•Per-vertexoutput.

•Temp.registers.

•Constantmemory.

VertexShader

•Memory

-Dataarestoredas“Vectors"，whichconsistofonetofour

elements(aelementisasigned32-bitfloatingpoint).

-Constantmemoryisread-onlytotheshader,andholdsthe

samedataforallverticesprocessed.(Ex.Lightattributes).

-Thevertex5shomogeneousclippositionmustalwaysbe

output,otherthingslikediffuseandspecularcolors,texture

coordinates,fogandpointsizecanalsobeoutput.

VertexShader

-Objectdeformation.

•Deformorevendefine

theobjecfsverticesby

V.S.

-Pagecurls,heathaze,

waterripples.

•Byusingtheentire

framebuffer'scontents

asatextureonamesh.

PixelShader

•PixelShader

-storedas"vector"

-Threesetsofinputs:

•Theinterpolated/lampeddiffuseandspecularcolorsand

alphas.

•8constantsregisters

•4ormoretexturecoordinates.

-These“texturecoordinates"actuallycanrepresent

anything.

»E.g.lightvector(x,y,z),halfangle(x,y,z)orplanar

coordinates(x,y).

Pixelshader

>rgbaoutput

——Az-depthoutput

PixelShader

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Texture1

Texture2

PixelShader

•Textureaddressinginstructions

-Performdependenttextureread

•"texldrxtx”：

-rxisregisterx,txistexturecoordinatesx.

-Accessspecifictextureusingtxastexturecoordinates,

andstorethefetchedvalueinrx.

-Theselectionoftexturebeingaccessedisdetermined

bythenumberofregister.

-Specialusesofdependenttextureread:

•Normalization:accessanormalizingcubemap,the

normalizedvalueoftxisstoredinrx.

•Powerfunction:accessapowerfunction

PixelShader

Implementsuccessiverenderingpasses

-Thebestway

•useP.S's"phase”command.

-"Rendertoatexture55

•storeintermediateresultsintextures,andaccessthemas

texturesinsuccessivepasses.

•Mainproblem:limitedprecisionoftexture.

-Usebackbuffersor“pixelbuffers"

•whenthegraphichardwaredonotsupportthe"renderto

atexture"feature,wecanonlystoreintermediateresults

inbuffersinhost/CPU.

PixelShader

•ImplementphongshadingbyP.S.

-Formula:c=(nJ+a)*d+(n.h)Ashi*g

•c:finalcolor.-ShallbeoutputtedinrO.

•n:pixelnormal.-Storedinbumpednormalmap.

•I:lightdirection.-Storedintex.coordinatet1.

•a:ambientconstant.-Storedconstantc7.

•d:diffusecolor-Storedindiffusemap.

•h:half-anglevector.-Storedint2.

•shi:shininessconstant.-Storedinshininessmap.

•g:glossconstant.-Storedinglossmap.

PixelShader

•ImplementphongshadingbyP.S.

-Texturespreparation:

•Diffusemap/glossmapissettobeassociatedwithrO.

•Bumpednormalmap/shininessmapistobeassociated

withr1.

•Normalizingmapistobeassociatedwithr2.

•Powerfunctionmapistobeassociatedwithr3.

-Registerpreparation:

•to：surfacelocation.

•t1:lightvector.

•t2:half-anglevector.

•c7:ambientconstant.

PixelShader

•ImplementphongshadingbyP.S.

-texIdrl,tO//Accessnormal/shininessmapNbysurfacelocation

andstorefetchedvalueinrl

texIdr2,tl//StorenormalizedvalueoflightvectorLinr2

texcrdr3.rgb,t2//Carryhalf^anglevaluedirectlyintor3.

dp3_satr5.xyz,rl_bx2,r2_bx2//Calculate(n.l)andstoretheresult

inr5;

dp3_satr2.xyz,rl_bx2,r3//Calculaten.handstoretheresultinr2

movr2.y,rl.a//Carryshininess(alphaofrl)intor2,nowr2hasn.h

inxandshininessiny

PixelShader

一phase//Becausewewanttoperformtextureinstructionsagain,

startsecondphase.

texIdrO,tO//Accessdiffuse/glossmapbysurfacelocationand

storefetchedvalueinrO

texIdr3,r2//Byaccessingthepowerfunctionmap,store

(n.h)Ashininessvalueinr3

addr4.rgb,r5,c7//Calculate(n.l+a)andstoretheresultinr4

mulrO.rgb,rO,r4//Calculate(n.l+a)*dandstoretheresultinr4

+mul_x2rO.a,rO.a,r3.a//Calculateg*(n.h)Ashininessandstorethe

resultinrO.a

addrO.rgb,rO,rO.a//Calculate(n.h+a)*d+g*n.h)Ashininess

andstoreitinrO

nVIDIA'sRegisterCombiner

•nVIDIA5sRegisterCombiner

-Customableper-pixelshadingand

multitexturing.

-Per-pixelphongshading.

-Bumpmapping

-Modulatespecularlightingwithtexturemap.

ShadingLanguage

•Thebenefitsofusinghigherlevelshadinglanguage

-Easeofuse.

•Easytowrite.

•Easytomaintain

-Portability.

-Optimization.

•Theshadinglanguagecompilercanperformoptimization

onthegeneratedcodes.

-Infact,thesebenefitscanapplytoanyhighlevel

programminglanguages,likeCoverassemblycodes.

ShadingLanguage

•ExamplesofShadingLanguages:

-Cooks"ShadeTree"

•Expressiontreeofshadingoperations.

-"QuakeIIIArena"scriptinglanguage.

-The“RenderMan“specificationofashadinglanguage.

-Stanfordreal-timeshadinglanguage(RTSL)

-DX95sHighLevelShadingLanguage(HLSL):

ShadeTree

finalcolorfloatka=0.5,ks=0.5;

floatroughness=0.1;

.卜floatintensity;

colorcopper=(0.8,0.3,0.1);

intensity=ka*ambient()+

、ks*specular(normal,viewer,roughness);

final_color=intensity*copper;

copper/丁

color

*

•/,\

specular

weightofambientweightof.function

specular仅黑

ambient

component/\

component

normalviewersurfaceroughness

ShaderlanguageusedinTM

Outline

•RadiometryandPhotometry,colorimetry

•BRDFtheory,implementingBRDFs

•Vertexshaders,pixelshadingandshadingLanguage

•MotionBlur,depthoffield,reflections,refractions,

shadows,global川umination

MotionBlur

•Modelandrenderthebluritself

-Usetheaccumulationbuffer

•Addinfollowingnframe

•Lowerstheframerate

•Cleverway:subtractoutthefirst

sceneandaddinthelast

MotionBlur

•Twopassesvertexshaders

-Firstpass:normallyrender

-Secondpass:usevectorshader

•N:normalvector

•M:motionvector

•N-M:<0outputpreviousposition,elsecurrentposition

•Misusedtomodulatethealphacomponent

MotionBlur

Visualizationofthe

velocitybuffer

Blurringeffect

DepthofField

•Useaccumulationbuffer

-Varytheviewpointandkeepfocuspointfixed

•Layer-basedsystems:blurparticularlayer

-Usefilteringtechniquestoblur

-Usepixelshadertointerpolateforeachpixel

viewer

focalpoint

Reflections

•Environmentmapping

-Assumethatreflectedobjectsarefar

•PlanarReflections

•GlossyEffects

•ReflectionsfromCurvedReflectors

Reflections—PlanarReflections

•Lawofreflection:

-angleofincidence=angleofreflection

1.Createacopyoftheobject

2.Transformitintothereflectedposition

3.Lightsourceshavetobetransformedaswell

4.Rendertheobject

5.Renderrestofthescene

Reflections—PlanarReflections

•R:reflectingplane

•n:reflectingplanenormal

•Scalingmatrix=S(1,-1,1)whenn=(0,1,0)andRgoes

throughtheorigin

F=R(n,(0,1,0))T(-p),p:somepointonR

M=F1S(1,-1,1)7F

ReflectionsPlanarReflections

X

withstencilbuffer

PlanarReflectionsProblems

1.Reflectedgeometryappearatplaceswherethereisnoreflector

geometry

-Solvedbyusingstencilbuffer

2.Backfacecullingisturnedon,thereflectedobjectswillappear

tohavefrontfacecullingturnedon

-Solvedbyturningofffacecullingorswitchtofrontface

culling

3.Objectsbehindthereflectorplaneshouldnotbereflected

一Puteachverticesintoplaneequation

-Ifvaluev0,itisbehindtheplane

一Trianglesintersectingtheplaneneedtobeclipped

-Useauser-definedclippingplane

Reflections—GlossyEffects

•Fogthereflectedobjects

-Fadetheobjectstoblackasthedistancefromthemirror

increases

•Fuzzyreflectionandfrostedglass

一Useaccumulationandstencilbuffers

Fogthereflectedobjects

Fuzzyreflectionandfrostedglass

FuzzyreflectionFuzzyrefraction

a

Refraction

•SnelPsLaw

Refractions

Anotherway

1.Generateacubicenvironmentmapfromeye5spositionand

includeonlyrefractedobjects

2.Rendertherefractionobject,accesstheEMbythe

refractiondirection

Shadows

PlanarShadows

•ProjectionShadows

yvx—lxvy

=Px=

4匕一〃匕,

P=

zly~vy

仕-I00、

0000

M=

0-IzIy0

J-I0fyy

PlanarShadows

/lx1[d+n.1/

/\P=1(””-1)

//\\n.(v-1)

n；(nA+d-l/i-In,一1四一3

\\//\AAxAy

\\M=加”』+"一也-4%一/)”

n・l+d-5-lzd

飞n・l.

兀:irx+d=0

PlanarShadows

•Render

1.Applythematrixtotheobjects

2.Rendertheprojectedobjectwithadarkcolor

-Toavoidrenderingbeneaththereceiver,weshouldadd

somebiastotheprojectedplane

-Ordrawtheplanefirst,anddrawtheshadowwithZ-buffer

off

-Usestencilbuffertoavoiddrawingshadowsoutsidethe

plane

SoftShadows

•Wheneveralightsourcehasanarea,softshadows

appear

•Sampleseveralpointsinthelightarea,rendertothe

accumulationbuffer.