高级计算机图形学ACG

Spheremapping

alightprobe

http：〃/HDRShop/tutorial/tutorial5.html

Frameofreference

•Accessthespheremap&hyhz0、

U

"xy"z°

fXfyfy0

(0001,

•Transformthesurfacenormalnandvectorefromthe

currenteyepositionusingthismatrix

•nand/inthespheremap5space

r-ey-2(〃

Spheremapping

n/

（QA1）t

rhy/h\toeye加="+-；+（「+1）2

G「+1）

n——,—,---

、mmm

^rigin_________________________y

Spheremapping

•Ifthesphereisatoriginanditsradiusis1

-theunitnormal'scoordinates=the

locationh

-Noneedforhz

•也，4)describeapointonasphere

image,intherange[-1,1].

•Mapthecoordinateto[0,1]

u=-^-+0.5;v=—^-+0.5

2m2m

Spheremapping

•SpheremappingisanimprovementoverBlinnand

NewelPsmethodinanumberofways

-Notextureseamtointerpolateacross

-canbeimplementedonanygraphicshardwarethatsupports

texturemapping

•DisadvantagestotheSpheremapping

-movingbetweentwopointsonthespheremapisnotlinear

-Sphereisvalidforonlyasingleviewdirection.

Paraboloidmapping

•Paraboloidmapping

-ByHeidrichandSeidel

-usingtwoenvironmenttextures

-Eachparaboloidcreatesacirculartexture

similartoaspheremap

•coveranenvironmenthemisphere

Dualparaboloidapproach

Parabolicbasis

Requirestwotextureimages

DualParaboloidMap

Whichofthetwotexturetoaccess?

Signoftherz

Paraboloidmapping

•Paraboloidmapping

-Hardwareshouldsupport

•properprojectivetexturecoordinatetransformation

yA

•interpolation011fX

0111ry

u=——-----F0.5;v=-----------b0.500001

2(1+h2(1+c)

<0022八'z/

•Themaindrawbackofparaboloidmapping

-makingthemapsthemselvesisdifficult

•bywarpingimages

•byusingraytracing

LightingUsingEnvironmentMapping

•Animportantuseofenvironmentmappingtechniquesis

generatingspecularreflectionsandrefractions.

•Environmentsmappingcansolvethehighlightingbyrepresenting

thelightsinthetexture.

Per-pixelspecularLightingusingEnvironmentmappingof

highlightenvironmentmappingentiresurroundingscene

Recursivereflections

•Recursivereflectionsdonewithenvironmentmapping

StumblingblockofEM

•Flatsurfaceusuallydonotworkwell

-raysreflectedoffofitusuallydonotvarybymorethanafew

degrees

-SmallpartofEMtexture'sbeingmappedontoarelativelylarge

surface

-Asmallpartoftextureismagnified

Diffuse,GlossandReflectionMapping

•TousereflectionmappingwithGlossandDiffuse

colortexturing

•TheLightingmodel

o=t1

diff®diff+gloss「spec

RGBtextureMonochrome

glosstexture

Pearexample

Multi-textureexample

RGBdiffuseRGBreflection

texturemaptexture

•Thelightingmodelcanbe

computedusingtwotexture

「specstages

-2RGBcolorinputs

-upto2alphainputs

RGBRGB

StageI"Stage2v•Stage1

diffuselightARGB-Theinterpolateddiffusecolor

'diff------reflectionmap

Xtextureresult

RGBRGBXglossandthepearskin'sRGB

+diffuseRGBtexturearethetwocolorinputs

retrievegloss

alphataffXidiff

alpha-Glossmaptexurevalueinthe

alphachannel

•Stage2：

lglossspecXtgios.

singlechannelo=diff区'diff+'gloss丫spec

glossmap

Bumpmapping

•Bumpmapping

-byBlinnin1978

-Inexpensivewayofsimulatingwrinklesandbumpsongeometry

•Tooexpensivetomodelgeometrically

-letatexturemodifythenormalateachpixel

•usethisnormaltocomputelighting

7/7/

Bumpmappedgeometr

Height-fieldbumpimageanditsuseonasphere

OffsetmapHeight-fieldmap

•Normalvectorn

-modifiedintheuandvdirections

-bythebufbvvaluestakenfromthebumptexture

Offsetvectorbumpmap

•Offsetmap

-Storesinatexturetwosigned

values,bandb,ateach

uv

point

-Correspondtotheamountto

varythenormalalongtheu

andvimageaxes

-Usedtoscaletwovectors

thatareperpendiculartothe

normal

Height-fieldbumpmap

•Height-fieldbumpmap

Eachmonochrometexture

valuerepresentasurface

height

•whitetoahigharea

•blacktoalowone

Theheightfieldisusedto

deriveuandvsignedvalues

•Thedifferencesbetween

neighboringcolumnstogetthe

slopesforuandbetween

neighboringrowsforv

ArtifactofusingBumpmap

•Bumpmapping

-Per-pixelbumpmappingisextremelyconvincing

-offersaninexpensivewaytoaddtheeffectofgeometricdetail

•Artifact

-Atthesilhouettesaroundtheobjects,norealbump,justsmooth

outlines

-Thebumpsdonotcastshadowsontotheownsurface

EmbossBumpMapping

•Embossing

-Oneofthefirstmethodsusedforrealtimebumpmapping

-employsatechniqueborrowedfromtwodimensionalimage

processing

EmbossBumpMapping

Steps

•Renderthesurfacewiththeheightfield

-adiffusemonochrometexture

•Shiftallthevertex(u,v)coordinatesinthedirectionofthe

light

•Renderthissurfacewiththeheightfieldagainappliedasa

diffusestexture,subtractionfromthefirstpassresult

•Renderthesurfaceagainwithnoheightfield,diffusedly

illuminatedandGouraudshaded.Addthisshadedimage

totheresult

DiffuseLightingCalculation

C=(£•?/)XDzXDm

-Lislightvector

-Nisnormalvector

-Dzislightdiffusecolor

-Dmismaterialdiffusecolor

-BumpmappingchangesNperpixel

-Embossbumpmappingapproximates(L,N)

ApproximatediffusefactorL・N

•Texturemaprepresentheightfield

-(Fd+m)approximates(L・N)perpixel

-Firstderivativerepresentsslopem

-mincreases/decreasesbasediffusefactorFd

Approximatederivative

•Embossingapproximatesderivative

-LookupheightHoatpoint(u,v)

-LookupheightH1atpointslightlyperturbedtowardlight

source(u+Au,v+Av)

-subtractoriginalheightHofromperturbedheightH1

-differencerepresentsinstantaneousslopem-HrHg

ComputetheBump

OriginalbumpOriginalbump(Ho)overlaid

(HQwithsecondbump("Jperturbed

towardlightsource

brightensimage

darkensimage

Subtractoriginalbump

fromsecond(H/-H。)

Coordinatesystematavertex

•n

-Retrievetheshadingnormalnatthevertex

•t

-Findsurfacevectortthatfollowsoneofthetwotexture

coordinateaxesuorv

-tisperpendiculartonandtangenttothesurface

•b

-thebinormal

-ismutuallyperpendiculartonandtandrunsinthedirection

oftheothertexturecoordinateaxis

Ztytz0、

久久b二0

&a生0

10001/

(%v)£soffset

ThelightdirectionIistransformed

Thelightdirectioniscastuponthetriangle'splanebysetting/.ztozero

Theresultingvectorisscaledandaddedtothevertex5stexturecoordinates

EmbossBumpMapping

•TransformthelightdirectionI

-Lightvectorsistheninthevertex5stangentspace

n

LimitationstoEmbossBumpMapping

•Appliesonlytodiffusesurface

-Specularhighlightsarenotpossible.

•Whenthelightisdirectlyoverasurface,nooffsetoccurs

-thebumpsdisappearentirely

•Thebasicembossingalgorithmdoesnothandlebumps

thatfaceawayfromthelightonsurfacesthatare

illuminated

DotProductBumpMapping

•Dot3bumpmapping

一Primarymethodofperformingbumpmappingonmodern

graphicshardware

-Theactualnormalsforthesurfacearestoredas(x,y,z)

vectorsinthenormalmaps

-The8-bitsvaluesaremappedto[-1,1]

-Tocomputetheeffectofalightsource,thepositionallight

source'slocationistransformedtothesurface'stangent

spacebasisateachvertex

Normalmap

Diffuseandspecularbumpmapping

EnvironmentMapBumpMapping(EMBM)

•EMBM

-Perturb(u,v)environmentmappingcoordinatesbyuandv

differentialsfoundinthebumptexture

-IntroducedwithDirectX6

-Allowonlyasingleplanarenvironmentmaptobedefined

•somethinglikedefiningacubemapwithonlyoneface.

-auserdefined2X2matrixisappliedinordertorotateandscale

thedifferentialsbeforetheyareadded.

-Thismatrixcontrolstheperceivedbumpinessofthemap

EnvironmentMapBumpMapping(EMBM)

bumpmapaccesswhichisandthenaddedtothe

Bumpmappingofenvironmentmap

Bumpmappingofenvironmentmap

CombineNormalmappingandcubicenvironment

mapping

w

d

d

cEc

d

E

n

m

/support/vpwebsamples2.shtml

Displacementmap

•Displacementmap

-Modifygeometry

BumpmapDisplacementmap

Displacementmap

Theheightfieldontheleftisusedtodisplacetheverticesofamesh

VisualAppearance

Lightmakesright.

AndrewGlassner

Introduction

•Imagerenderingofthreedimensionalmodels

-Lookcorrectgeometrically

-Havearealisticvisualappearance

-Withcombinationoftechniques

•Associatingamaterialwitheachsurface

•Applyingvariouskindsofliahtsources

•Addingtextures

•Usingfog

•Transparency

•Antialiasingtechniques

Outline

Light

Material

Antialiasing

Fog

Gammacorrection

Transparency

LightSources

-photonsbounceoffthesurfaceofobjectandreachtheeyesof

theviewer

•Lightsources

-Directionallights

-Pointlights

-Spotlights

•Directionallights:positionedessentiallyinfinitelyfarawayfrom

theobjectsthatarebeinglit

-Sun

n

•Positionallight(Pointlightandspotlight)

一Singlepointthatemitsphotons

•Lightparameters

Intensityandcolor

-

Squaresubdividedinto100X100X2triangleislitby

AdirectionallightsourceApointlightsourceAspotlight

•Lightintensityandcolor

-ambient,diffuse,specularintensity

•Lightsourceparameters

NotationDescription

SambAmbientintensitycolor

$diffDiffuseintensitycolor

Q

2specSpecularintensitycolor

Q

2PosLightSourceposition

Spotlight.Sdir,Scut>Sexp

SpotLight

Lightattenuation

•Lightdropoffwiththedistance

•Intheareaofrealtimerendering,lightdonotdropoff

withdistance

-Easiertocontrol

•Noneedtoworryabouttheeffectofdistance

•Effectsmaybecomputedmorequickly

Lightattenuation

Lanp=Spot

ReoderTine=15Sec

SpotBi=.150

Light-sourceSpotSi=80

iera

<-helper-lamp

http://www.ru.is/kennarar/hannes/useful/BlenderManual/htmll/ch28sO2.html

Light

MaterialMaterial

Fog

Gammacorrection

Transparency

•Materialconsistsofanumberofparameters

-ambient,diffuse,specular,shininessandemissive

•Thecolorofsurfaceisdeterminedby

-Materialparameters

-Lightsourcesparameters

-Lightmodel

Tableofmaterialparameters

NotationDescription

^ambAmbientmaterialcolor

m防Diffusematerialcolor

m$pecSpecularmaterialcolor

^shiShininessparameter

m

111ermEissmivematerialcolor

LightingandShading

•Lighting

-Designatetheinteractionbetweenmaterialandlightsources

-Interactionwiththegeometryoftheobjecttoberendered

•Shading

-Performinglightingcomputations

-Determinepixelscolors

FlatGouraudPhong

Perpolygonpervertexperpixel

LightingandShading

•FlatShading

-Coloriscomputedforatriangleandthetriangleisfilledwiththe

color

•GouraudShading

一lightateachvertexisdetermined,andlightsamplesare

interpolatedoverthesurface

•PhongShading

一shadingnormalsstoredattheverticesareusedtointerpolate

theshadingnormalateachpixelinthetriangle

LightingandShading

FlatShadingGouraudShadingPhongShading

•FlatShading:

-Fastandsimpletoimplement

-Doesnotgiveasmoothlooktocurvedsurface

•GouraudShading:

-Speedandimprovedquality

-dependentonthelevelofdetailofobjectsthatarerendered

GouraudShading

256102416384triangles

GouraudShading

•GouraudShading

-Missinghighlight

-Failuretocapturespotlighteffects

•Usingtexturetorepresenteffects

Phongshading

GouraudShading

•Gouraudshadingcanachieveessentiallythesameshading

resultasPhongshading

-subdividingasurfaceintotrianglessmallerthanapixel

-Slowinpractice

-Rarelyusedinrealtimesystems

•LightingModel:ambient,diffuse,specular

ambientdiffusespecular

DiffuseComponent

•Lambert'sLaw

-Ideallydiffusereflectlightdeterminedbysurfacenormalnandlight

vectorI

DiffuseComponent

•Viewindependent

•Tomakeuseofdiffusecoloroflightsourceanddiffusecolor

ofmaterial

idiff=Wmdiff®sdifr®

血),-R

idiff=max((®sdiffJ

s的=(1.0,1.0,1.0)m助=(1.0,0.0,0.0)

mdiffsdiff(1.0,0.0,0.0)

SpecularComponent

•Makeobjectlookshinybycreatinghighlights

-Surfacecurvature

-Directionandlocationoflightsource

WithouthighlightWithhighlights

SpecularLighting

i-(rDr)"""二(cosp)”而

Reflectionvectorr

r=2(n•l)n—I

r=2(n-l)n-l

n-l

2(n4)n

LightFormulaofOpenGLandDirectX

以"(〃“产”二(cos8产,

h—'+'(rQ^)m-s，/7/p(〃必)4"无

Z+v

LightFormulaofOpenGLandDirectX

•Withspecularcoloroflightsourceandmaterial

区)

ispec—'(〃»)，"""mspecsspec

•Iftheanglebetweennandhgreaterthan90°,thespecular

contributionis0

〃〃)加

Lsnpe”c=max\((%)""90js5pe"c0spec

o8

•

□

s.o6

gu•

Ic

J

Eo4

W•

O

U

d

so2

•

0

-n/2-K/40K/4兀/2

angle

Asthe/77s/7/increases,thecurveispulledin,makingforatighter

highlightandashinierimpression

ArtifactsinPhongshading

GouraudShadingGouraudShadingPhongshading

LittletessellationHightessellationPer-pixelShading

Otherspecularhighlightfunctions

•Schlick5sapproximation

t-cosp

spec-~~~^spec凶spec

mshi-tmshi+t

Simplefunctions

・)卯比

specmax(nh,0—

•Tisthresholdvalue

-max(c力,0)>T,1;

-Otherwise,0.

•Taffectstheapparentsizeofthelightbeingreflected

AmbientComponent

•Lightemanatingfromsourcemightbounceoffwall

andthenreachobject

•Notaccountedbydiffuseorspecularcomponent

dmb=marnb⑤

LightingEquation

•Locallightingmodel

Kot-1amb+Idiff+'spec

ambientdiffusespecularresult

LightingEquation

•Lightintensityintherealworldisinverselyproportionaltothe

squareofthedistancefromthelightsource

•Diffuseandspecularcomponentsareaffected

+3/SpLP+%Sp°s-p

Lightingattenuation

i.=a,®mh+m.+\ik+dk\ik+ik)I

totglobhambemiN」spott\amb}\drifffspecJI

k=l

=aglob®marnb+merni

«k

5expk

+£max(—〃Dy*,0)(mamb®samb

后二1

।max((疝％),0)加的㊈学疗+max((〃*),0产'加印用㊁

kk

s：+s；spos-p+s：spos-p

AliasingandAntialiasing

Musing

Sampling&filteringprocess

Pixels

Texture

Time

Samplingandreconstruction

•Sampling:

-fromcontinuoussignaltodiscrete

•Reconstructionrecoverstheoriginalsignal

-Caremustbetakentoavoidaliasing

•Nyquisttheorem

一thesamplingfrequencyshouldbeatleast2timesthemax

frequencyinthesignal

Samplingtheorem

•Nyquisttheorem

-thesamplingfrequencyshouldbeatleast2timesthemax

frequencyinthesignal

1cmTP]1sampleperrevolution

0GAlittlemorethan1sample/revolution

2samplesperrevolution

>2samplesperrevolution

OGG。。

Reconstruction

•Assumewehaveabandlimitedsignal(e.g.,atexture)

•Usefiltersforreconstruction

0---1---1---1_b

-101

Reconstructionwithboxfilter

Reconstructionwithtentfilter

32x32

texture

Reconstructionwithsinefilter

•Intheory,theidealfiltersin(zix)

•Notpracticalsinc(x)=

7DC

Resampling

•Enlargingordiminishingsignals

•Assumesamplesareatunit-intervals,i.e.,

•Resamplesothattheyareaapart

-a<1givesmagnification

-a>\givesminification

Magnification

•Halfsampledistance

Minification

•Doublethedistancebetweensamples

Screen-basedAntialiasing

•Supersampling

»usemorethanonesampleperpixel

Formulaandexamplesofdifferentschemes

n

p(x/)=Zw,c(Qxj)

i=l

•wzaretheweightsin[0,1]

•c(zj,y)isthecolorofsampleiinsidepixel

2x2RGSS

1sample4x4checker

1x2sample8rooks