EECS487:Interactive

ComputerGraphics

Lecture15:•  Scenegraph•  LightingandReflection

HierarchicalModelingHierarchicalmodelingisessentialfortransforming

objectswithattachedparts,e.g.,inanimation:•  eyesmovewithhead

•  handsmovewitharms

•  feetmovewithlegs

• …

Withoutsuchstructurethemodel

fallsapart,e.g.,eyesdon’tfollow

whenheadmoves

Thisideacanbeextendedtothe

entirescene→scenegraph•  collecteveryobjectsintoasinglehierarchy

Howtorepresentascene?•  listofobjects•  transformofeachobject•  canuseminimalprimitives:anellipseisatransformedcircle

•  transformappliestopointsonobject

Scenerepresentation:datastructures+transforms

SceneRepresentation

Marschner

Canrepresentsceneasaflatlistofobjects•  butediting(e.g.,delete)requiresupdatingmanynodes

SceneasaFlatListofObjects

Marschner

house roof door window window

Introduceanewabstractdatatype:group•  treatsasetofobjectsasoneobject(group)•  containslistofreferencestomemberobjects

•  letsthedatastructurereflecttherenderingstructure•  enableshigh-leveleditingbychangingjustonenode

HierarchicalRepresentation

Marschner

Allpartsofthescenearerepresentedinonegraph

•  eachnodeinthegraphisonesceneelement,including

•  objects,cameras,lights,materials,transformations,…

•  switch/select:specifywhichchildrentoenable,etc…

•  simulationprocedures,shaders

•  otherscenegraphs

•  simplestform:tree

•  everynodehasoneparent

•  interiornodes=groups

•  leafnodes=objectsinthescene

•  edges=membershipofobjectingroup

•  transformsareassociatedwithnodesoredges

•  eachtransformappliestoallgeometrybelowit

SceneGraphs

Marschner,TP3,Schulze

Marschner,Schulze

SceneGraphExample

TheGraphicsSoftwareStack

graphicsAPI•  interfacetographicshardware,e.g.,OpenGL,

Direct3D

GPU

scenegraph/renderingengine•  as“scenegraphAPI”:middlewareforgraphicsAPI

•  as“3Dtoolkit”:implementgraphicsfunctionalities

commonlyrequiredinapplications

applications• modelingprogramsusescenegraphtomanage

complexity,e.g.,Maya,3dsmax,etc.

•  games,visualization,virtualreality,webapps

Schulze

SceneGraphs

Todrawthescene,thegraphiswalked

•  eachtimeanodeistraversed,eithertherendering

stateischangedorsomethingisrenderedwiththe

currentstate

•  anoperationperformedonanode,suchasrendering,

culling,andtransform,affectsallofitschildren

•  e.g.,traversingalightnodeturnsonthelightforallitschildren•  transformsaccumulatealongpathfromroottoleaves

Makesmodelingandanimationofcomplex

sceneseasierbybreakingthemdownintoa

hierarchyofsimpleroneswiththeirownlocal

behavior

Chenney

SceneGraphAdvantages

Hierarchicalprocessing•  eachsub-hierarchynaturallydefinesaboundingvolume,

e.g.,forculling,collisiondetection,orray-tracing

computation

Object-orientedparadigm•  eachobjectisdefinedinitsownlocalcoordinatesystems

• objectscanhaveotherpropertiesbesidesshape•  color,shadingparameters

•  approximationparameters(e.g.,degreeoftessellation)

•  userinteraction,etc…

•  propertynodescanbeappliedtosub-hierarchy,e.g.,paintentirewindowgreen

• objectsareself-containedandre-usable•  instancing:anobjectcanbeamemberofmultiplegroups

TP3,Marschner

Allowmultiplereferencestonodes

•  reflectsmoreofdrawingstructure

•  allowseditingofrepeatedpartsinoneoperation

InstancingExample

Marschner

MultipleInstantiations

Objectdefinedonce,usedmanytimes,

inmanyplacesinthescene

•  anobjectwithmultipleinstantiationshasmultipleparents•  notthe“makeacopy”instantiationofC++

•  transformsstillaccumulate

alongpathfromroottoleaf

•  objectsmayhavemultiplepaths

fromroottoleaves

•  transformmaybedifferent

foreachinstance

• graphisnolongeratree,butadirectedacyclicgraph

(DAG,nocycle)

Schulze,Marschner,James

SceneGraphToolkitsandAPIsNobroadlyacceptedstandard

APIsfocusondifferentapplications•  OpenSceneGraph(openscenegraph.org)•  scientificvisualization,virtualreality,GIS•  optimizedformemoryrequirements

•  opensourceversionofhistoricalscenegraphAPIsforSGIIRISGL•  OpenInventor(oss.sgi.com/projects/inventor/)•  OpenGLPerformer(oss.sgi.com/projects/performer/)

•  Ogre3D(www.ogre3d.org)andahostofothers•  games,optimizedforhigh-performancerendering(speed)

•  Javascriptscenegraphs,WebGLcompatible:•  three.js(threejs.org)•  “alightweight3Dlibrarywithaverylowlevelofcomplexity”

•  sceneJS(scenejs.org)•  CAD,medical,andengineeringvisualization

•  Modelingsystems’proprietarylibraries•  optimizedforeditingflexibility

BasicSceneGraphOperations

High-levelscenemanagement

•  edittransformation•  needgoodUI

•  transformobjectinworldcoordinateframe•  traversepathfromroottoleaf

•  groupingandungrouping

•  re-parenting•  movingnodefromoneparenttoanother

Marschner

CommonFunctionalities

Resourcemanagement•  assetmanagement(geometry,textures,materials,

animationsequences,audio)

•  shadermanagement

• memorymanagement

• multi-threading

•  (serverclustering)

Renderinglibraries:•  bumpmapping

•  shadows

•  particlesystem

Schulze

PerformanceOptimizationsCulling•  earlydiscardofinvisiblepartsofscene

Level-of-detail•  uselowerpolycountversionfordistant(small)object

Computingboundingvolumehierarchyfor•  culling•  collisiondetection•  rendering,e.g.,ray-tracing,qsplat

Scenegraphcompilation/optimization•  renderobjectswithsimilarattributes(textures,materials,

shaders,geometry)inbatches•  efficientuseoflow-levelAPI

•  avoidstatechangesinrenderingpipeline

Seriousscenegraphsshouldhave

implementationofthesetechniquesSchulze

SceneGraphEncoding

Collada•  assetexchangeusinganXMLschema•  e.g.,passingmodelstoaphysicsengine

•  assettransformationfromhigh-levelmodeling

descriptiontoplatform-specificoptimizeddescription

•  candescribeeverythingtodowithascene:

geometrywithfullskinning,advanced

materialandvisualeffects,animation,

physicalpropertiesandcollisions

customtools

Maya

SceneGraphEncodingX3D (web3d.org)• VRMLwithXMLsyntax,replacedVRMLinJuly2004•  primarygoalisforinteractivevisualizationof3Dassets

•  specifiesbehaviorsandinteractionsandincludes•  arun-timemodelthatenablesviewing,navigation,picking,andscripting

•  anAPItomanipulatethescene-graphatruntime

X3DOM• HTML5/X3Dintegration

•  declarative3D(vs.

proceduralWebGL)

• x3dom.orgview3D (PA2,4)

EECS487:Interactive

ComputerGraphics

Lecture15:•  Scenegraph•  LightingandReflection

ObjectAppearanceinCGI

ObjectappearanceinCGIdependsonits

•  shape:thegeometryofitssurfacesandpositionwrtcamera

•  shade:itsilluminationenvironmentandopticalproperties

Renderingprogramseparates:

•  geometricprocessing:transformation,hiddensurfaceremoval,etc.from

•  opticalprocessing:propagationandfilteringoflight

IlluminationModelsArenderingprocesscanbemodeledasanintegralequationrepresentingthetransportoflightthroughtheenvironment�therenderingequation

Localillumination:anapprox.oftherenderingeqn.•  assumeslightisscatteredonlyonce:lightfromlightsourceisreflectedbyasurfaceandmodulatedonitswaytowardstheeye

Globalillumination:•  lightraystravelingfromlighttosurfacemaybe•  blockedbyinterveningsurfaces(shadows)or

•  bentorscatteredbyinterveningmaterial(refractionandatmosphericeffects)or

•  lightarrivingatasurfacemaycomeindirectlyviaanothersurface(reflectionandcolorbleed)

GlobalIlluminationEffects

Properlydeterminingtherightcolorisreallyhard•  translucency•  refraction• particlescattering•  colorbleed

LocalIllumination

Aphotographofalitsphereshowsnotauniformlycoloredcirclebutacircularshapewithmanygradationorshadesofcolor,givingtheimpressionof3D

Localilluminationconsistsoftwomajoraspects:

1.  lightsourcedistributionfunction2. surfacereflectancedistributionfunction

LightSources

LightisapproximatedbytheRGBcomponents

emittedfromthelightsource

Forlight,theRGBcoefficientsrepresent

percentagesoffullintensityofeachcolor

•  c = (1.0, 1.0, 1.0)iswhite

•  c = (0.5, 0.5, 0.5)iswhiteathalfintensity,

whichappearsgray

LightSources

Grassman’sLaws:

•  iftwolightsemitatc1 = (R1, G1, B1)andc2 = (R2, G2, B2),thelightthatarrivesattheeyeis

c = c1⊕ c2 = (R1 + R2, G1 + G2, B1 + B2)•  scalinglightintensity:c(s a) = s c(a)

a b

LightSources

Typesoflightsources

• pointlight,e.g.,lightbulb:lightdirectionchangesoversurface

• directionallight,e.g.,sunlight:“distant”light,directionisconstant

• spotlight:pointsourcewithdirectionalfall-off

• areasource:luminous2Dsurface:radiateslight

fromallpointsonsurface,generatessoftshadowsspotlightdirectionalpointlight

PointandDirectionalSources

Pointlight:

•  lightarrivingatapoint(x)onthesurface•  lalwayspointstowardsthelight

•  mustbenormalized

•  tospecifyanOpenGLlightatlightposition(1, 1, 1):Glfloat light_position[] = { 1.0, 1.0, 1.0, 1.0 }; glLightfv(GL_LIGHT0, GL_POSITION, light_position);

Directionallight:l(x) = llight

•  thelvectordoesnotvaryacrossthesurface• OpenGLlightshiningfromdirection(1, 1, 1):Glfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 }; glLightfv(GL_LIGHT0, GL_POSITION, light_position);

l(x) =plight -xp

light-x

x

plight

Spotlight

Pointsource,withintensityafunctionof–l,specifiedwith:

•  position:thelocationofthesourceglLightfv(GL_LIGHT0,GL_POSITION,light_posn);

•  direction(sdir):thecenteraxisofthelight

glLightfv(GL_LIGHT0,GL_SPOT_DIRECTION,light_dir);•  intensitymaximalalongdirectionsdir

•  whenlightmoved,directionmustbeupdatedalongwithposition

•  cut-off(α):howbroad(indegree)thebeamisglLightfv(GL_LIGHT0,GL_SPOT_CUTOFF,45.0);•  intensityfallsoffanglingawayfromsdir

•  exponent(sexp):howthelighttapersoffattheedgesoftheconeglLightfv(GL_LIGHT0,GL_SPOT_EXPONENT,1.0);•  intensityscaledbyexponent:sspot = max(−l • sdir, 0)sexp

Spotlight

�

−l

(cosα)sexp

sdir

α

OpenGLLightSources

glLightfv(lightname,param,value) •  parameters

• GL_AMBIENT • GL_DIFFUSE • GL_SPECULAR

• GL_POSITION• GL_SPOT_DIRECTION • GL_SPOT_CUTOFF • GL_SPOT_EXPONENT

• GL_CONSTANT_ATTENUATION • GL_LINEAR_ATTENUATION • GL_QUADRATIC_ATTENUATION

HowLightsArePositioned

Allcomputationsarecarriedoutineyecoordinates

•  storelightsineyecoordinates

•  lightsconvertedtoeyecoordinatesusingcurrentModelViewtransform

•  lightsmovewitheye•  defaultGL_LIGHT0–directionalfromtheback,

withspecularcomponent

•  glEnable(GL_LIGHTING); •  glEnable(GL_LIGHT0); •  don’tforgettosetthenormalsproperly

WhyisWinterLightWeaker

thanSummerLight?

Theamountoflightreceivedandreflectedbyasurface

dependsonangleofincidence(θ)•  biggeratnormalincidence

•  smallerslanted,byhowmuch?

•  Lambert’sCosineLaw:

proportionaltocosθ

Durand,FvD94

n

surface

θ

n

Surface2 Surface1

n

dA

dA cos θθ

π/2 − θ

Recall:

sin(π/2–θ) = cosθ

SurfaceNormalTheintensityofasurfacecolordependsonthe

orientationofthesurfacewrtthelightandviewer

Thesurfacenormalvectordescribes

thisorientationatapoint

•  isperpendiculartothetangentplaneofthesurface(recall

howtotransformnormals)

•  isoftencalledjust“thenormal

vector”or“thenormal”

• willusenorNtodenote

Normalsareeithersupplied

bytheuserorautomaticallycomputed

surface

normal

light

direction

SpecifyingNormals

NormalscanbespecifiedusingglNormal3*()

Normalsareassociatedwithvertices

Specifyinganormalsetsthecurrentnormal•  remainsunchangeduntiluseraltersit

•  usualsequence:glNormal3, glVertex, glNormal3, glVertex, glNormal3, glVertex,…

Normalsarenotnormalizedbydefault•  canbeautomaticallynormalizedbycallingglEnable(GL_NORMALIZE)orglEnable(GL_RESCALE_NORMAL) •  butthisisslow,insteadnormalizeasneeded

MaterialAppearance

Factorseffectingmaterialsappearance•  color•  texture•  intensityandshapeofhighlights•  glossiness

Forsurfacecolor,theRGBcoefficients

representpercentagesofreflected

proportionsofeachcolor

Ngan,Hanrahan

OpenGL’sSimpleReflectanceModel

Ifthelightisemittingcl = (Rl, Gl, Bl)andthematerialreflectscm = (Rm, Gm, Bm),thelightthatarrivesattheeyeisc = cl ⊗ cm = (Rl Rm, Gl Gm, Bl Bm)

Aredballinwhitelightreflectsred

andabsorbsgreenandblue

Aredballingreenlightappearsblack

(nolightisreflected)

OpenGLLightingandReflectance/* Initialize material property, light source, lighting model, and depth buffer. */ void init(void) { GLfloat mat_specular[] = { 1.0, 1.0, 1.0, 1.0 }; GLfloat mat_shininess[] = { 50.0 }; GLfloat light_position[] = { 1.0, 1.0, 1.0, 0.0 }; glClearColor(0.0, 0.0, 0.0, 0.0); glShadeModel(GL_SMOOTH); glMaterialfv(GL_FRONT, GL_SPECULAR, mat_specular); glMaterialfv(GL_FRONT, GL_SHININESS, mat_shininess); glLightfv(GL_LIGHT0, GL_POSITION, light_position); glEnable(GL_LIGHTING); glEnable(GL_LIGHT0); glEnable(GL_DEPTH_TEST); }

Clampingvs.Scaling

RGBcoefficientsmustbein[0.0, 1.0]range

Reflectedcolorc = (c1⊕ c2) ⊗ cm=�[(R1 + R)Rm2, (G1 + G2)Gm, (B1 + B2)Bm] mayhave

component> 1.0,e.g.,brightorangeis(2.5, 1.5, 0.5)•  ifclampedto1.0,(1.0, 1.0, 0.5)isyellow

•  ifscaledby1/2.5instead,weget(1.0, 0.6, 0.2),whichretainstheoriginalorangehueandsaturation

MicrofacetTheory:modelsurfaceasacollection

oftinymirrors[Torrance&Sparrow1967]

Exampleofmicrofacetdistribution:

•  surfaceoftheocean•  viewersees“bright”pixels

•  whenmicrofacetsarepointing

halfwaybetweenthesunandtheeye

•  othermicrofacetsareobstructed,

eitherinshadoworhidden

Torrance-SparrowReflectanceModel

Durand

MicrofacetModel[Cook&Torrance82]Reflectanceat(l,v)isaproductofthe•  numberofmirrorsorientedhalfwaybetweenlandv,•  percentageofunblockedmirrors,and

•  Fresnelcoefficient:fractionoflightreflected(notabsorbed),

functionofangleofincidenceandindexofrefraction

Durand

l

v

h

Lozano-Perez

MeasureofReflectance:BRDF

ωo

ωi

ρ (θi, φi, θo, φo)

Differentmaterialemits,absorbs,

orreflectslightdifferently

BidirectionalReflectanceDistributionFunction(BRDF)

ρ (ωi, ωo):•  ratioofradianceincomingfromone

directionthatgetsreflectedin

anotherdirection•  relatesincominglightenergytooutgoing

•  functionbasedondirectionsofincidenceandview

•  unifyingframeworkformanymaterials

•  (assumeisotropicmaterial,reflectance

isinvarianttorotationaboutthenormal,

unlikevelvetorsatin,e.g.)

Hanrahan

TypesofReflection

Wegenerallyrecognize3typesofreflection:

IdealSpecular• ReflectionLaw

• Mirror

IdealDiffuse•  Lambert’sLaw

• Matte

RoughSpecular• Directionaldiffuse• Glossy

HowtoObtainBRDF?

Gonioreflectometer

Ward,Hanrahan