9 camera models

7/21/2019 9 Camera Models

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Introduction to Computer Graphics

Camera ModelsCamera Models


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Rendering with Natural Light


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Fiat Lux


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Light Stage


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Moving the Camera or the World?

Two equivalent operationsTwo equivalent operations

Initial OpenGL camera position is at origin, looking along -ZInitial OpenGL camera position is at origin, looking along -Z

Now create a unit square parallel to camera at z = -10Now create a unit square parallel to camera at z = -10

I we put a z-translation matri! o " on stack, w#at #appens$I we put a z-translation matri! o " on stack, w#at #appens$% &amera mo'es to z = -"&amera mo'es to z = -"

Note OpenGL mo(els 'iewing in let-#an( coor(inatesNote OpenGL mo(els 'iewing in let-#an( coor(inates

%&amera sta)s put, *ut square mo'es to -+&amera sta)s put, *ut square mo'es to -+

Image at camera is t#e same wit# *ot#Image at camera is t#e same wit# *ot#


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!" Scene

Notice the presence ofNotice the presence ofthe camera, thethe camera, the

projection plane, andprojection plane, and

the worldthe world

coordinate axescoordinate axes

Viewing transformations define how to acquire the imageViewing transformations define how to acquire the image

on the projection planeon the projection plane


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#iewing $rans%ormations

Goal: To create a cameracentered viewGoal: To create a cameracentered view

Camera is at originCamera is at origin

Camera is loo!ing along negative "axisCamera is loo!ing along negative "axisCamera#s $up# is aligned with %axisCamera#s $up# is aligned with %axis &what does this mean'(&what does this mean'(


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& 'asic Steps

)tep -: Translate to align world and camera)tep -: Translate to align world and camera

originsorigins


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Constructing #iewing

$rans%ormation( #

Create a vector from e%epoint to loo!atpointCreate a vector from e%epoint to loo!atpoint

Normali"e the vectorNormali"e the vector

3esired rotation matrix should map this vector3esired rotation matrix should map this vector

to 45, 5, *6to 45, 5, *6TT 7h%'7h%'


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$rans%ormation( #

Construct another important vector from theConstruct another important vector from thecross product of the loo!atvector and the vupcross product of the loo!atvector and the vup

vectorvector

This vector, when normali"ed, should align withThis vector, when normali"ed, should align with

4*, 5, 564*, 5, 56TT7h%'7h%'


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$rans%ormation( #

8ne more vector to define98ne more vector to define9

This vector, when normali"ed, should align with 45, *, 56This vector, when normali"ed, should align with 45, *, 56TT

Now let#s compose the resultsNow let#s compose the results


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Composing Matrices to Form #

7e !now the three world axis vectors &x, %, "(7e !now the three world axis vectors &x, %, "(

7e !now the three camera axis vectors &u, v, n(7e !now the three camera axis vectors &u, v, n(

Viewing transformation, V, must convert from world toViewing transformation, V, must convert from world to

camera coordinate s%stemscamera coordinate s%stems


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.ememer.ememer ac# camera a!is 'ector is unit lengt#ac# camera a!is 'ector is unit lengt#

ac# camera a!is 'ector is perpen(icular to ot#ersac# camera a!is 'ector is perpen(icular to ot#ers

Camera matrix is orthogonal and normali"edCamera matrix is orthogonal and normali"ed

Ort#onormalOrt#onormal

Therefore, MTherefore, M**0 M0 MTT


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Therefore, rotation component of viewingTherefore, rotation component of viewingtransformation is just transpose of computedtransformation is just transpose of computed

vectorsvectors


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Translation component tooTranslation component too

Multipl% it throughMultipl% it through


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Final #iewing $rans%ormation( #

To transform vertices, use this matrix:To transform vertices, use this matrix:

+nd %ou get this:+nd %ou get this:


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Canonical #iew #olume

+ standardi"ed viewing volume representation+ standardi"ed viewing volume representation

/arallel &8rthogonal( /erspective/arallel &8rthogonal( /erspective

x or y

-z

x or y

-z

1

-1

-1

Front

Plane

Front

Plane

Back

Plane

Back

Plane

x or y = +/- z


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Wh) do we care?

Canonical View Volume /ermits )tandardi"ationCanonical View Volume /ermits )tandardi"ation &lipping&lipping

% asier to (etermine i an ar*itrar) point is enclose( inasier to (etermine i an ar*itrar) point is enclose( in

'olume'olume% &onsi(er clipping to si! ar*itrar) planes o a 'iewing&onsi(er clipping to si! ar*itrar) planes o a 'iewing

'olume 'ersus canonical 'iew 'olume'olume 'ersus canonical 'iew 'olume

.en(ering.en(ering

% /roection an( rasterization algorit#ms can *e reuse(/roection an( rasterization algorit#ms can *e reuse(


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*ro+ection Normali,ation

8ne additional step of standardi"ation8ne additional step of standardi"ation &on'ert perspecti'e 'iew 'olume to ort#ogonal 'iew 'olume&on'ert perspecti'e 'iew 'olume to ort#ogonal 'iew 'olume

to urt#er stan(ar(ize camera representationto urt#er stan(ar(ize camera representation

% &on'ert all proections into ort#ogonal proections *)&on'ert all proections into ort#ogonal proections *)(istorting points in t#ree space actuall) our space(istorting points in t#ree space actuall) our space

*ecause we inclu(e #omogeneous coor( w2*ecause we inclu(e #omogeneous coor( w2

3istort o*ects using transormation matri!3istort o*ects using transormation matri!


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*ro+ection Normali,ation

uilding a transformationuilding a transformationmatrixmatrix

4ow (o we *uil( a matri! t#at4ow (o we *uil( a matri! t#at

% 5arps an) 'iew 'olume to5arps an) 'iew 'olume to

canonical ort#ograp#ic 'iewcanonical ort#ograp#ic 'iew

'olume'olume

% /ermits ren(ering wit#/ermits ren(ering wit#

ort#ograp#ic cameraort#ograp#ic camera

+ll scenes rendered+ll scenes renderedwith orthographicwith orthographic

cameracamera


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*ro+ection Normali,ation - .rtho

Normali"ing 8rthographic CamerasNormali"ing 8rthographic Cameras Not all ort#ograp#ic cameras (eine 'iewing 'olumes o rig#tNot all ort#ograp#ic cameras (eine 'iewing 'olumes o rig#t

size an( location canonical 'iew 'olume2size an( location canonical 'iew 'olume2

6ransormation must map76ransormation must map7


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*ro+ection Normali,ation - .rtho

Two stepsTwo steps 6ranslate center to 0, 0, 026ranslate center to 0, 0, 02

% 8o'e ! *) %!8o'e ! *) %!ma!ma!9 !9 !minmin2 : ;2 : ;


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*ro+ection Normali,ation - *ersp

/erspective Normali"ation is Tric!ier/erspective Normali"ation is Tric!ier


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*erspective Normali,ation

Consider N0Consider N0

+fter multipl%ing:+fter multipl%ing:

p = Npp = Np

0100

00

00100001


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+fter dividing % w#, p# ; p##+fter dividing % w#, p# ; p##


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7hat aout "'7hat aout "' i z = zi z = zma!ma!

i z = zi z = z

minmin

-1 an( zma! ->1suc# t#at zmin -> -1 an( zma! ->1

.esulting z is nonlinear, *ut preser'es or(ering o points.esulting z is nonlinear, *ut preser'es or(ering o points

% I zI z11? z? z;;@ z@ z11? z? z;;


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7e did it= 1sing matrix, N7e did it= 1sing matrix, N /erspecti'e 'iewing rustum transorme( to cu*e/erspecti'e 'iewing rustum transorme( to cu*e

Ort#ograp#ic ren(ering o cu*e pro(uces same image asOrt#ograp#ic ren(ering o cu*e pro(uces same image as

perspecti'e ren(ering o original rustumperspecti'e ren(ering o original rustum


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Color

Next topic:Next topic: &olor&olor

6o un(erstan( #ow to make realistic images, we nee( a6o un(erstan( #ow to make realistic images, we nee( a

*asic un(erstan(ing o t#e p#)sics an( p#)siolog) o*asic un(erstan(ing o t#e p#)sics an( p#)siolog) o'ision 4ere we step awa) rom t#e co(e an( mat# or a *'ision 4ere we step awa) rom t#e co(e an( mat# or a *

to talk a*out *asic principlesto talk a*out *asic principles


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'asics o% Color

/h%sics:/h%sics: IlluminationIllumination

% lectromagnetic spectralectromagnetic spectra

.election.election

% 8aterial properties8aterial properties%


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*h)siolog) o% #ision

The e%e:The e%e:

The retinaThe retina

.o(s.o(s

&ones&ones

% &olorA&olorA


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*h)siolog) o% #ision

The center of the retina is a densel% pac!edThe center of the retina is a densel% pac!edregion called theregion called the %ovea%ovea==

&ones muc# (enser #ere t#an t#e&ones muc# (enser #ere t#an t#e peripheryperiphery


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*h)siolog) o% #ision/ $he Retina

)trangel%, rods and cones are)trangel%, rods and cones areat theat the 0ac10ac1of the retina,of the retina,ehind a mostl%transparentehind a mostl%transparentneural structure thatneural structure that

collects their response=collects their response=http:??www=trueorigin=org?retina=asphttp:??www=trueorigin=org?retina=asp


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*erception/ Metamers

+ given perceptual sensation of color derives+ given perceptual sensation of color derivesfrom the stimulus of all three cone t%pesfrom the stimulus of all three cone t%pes

2dentical perceptions of color can thus e caused2dentical perceptions of color can thus e caused% ver% different spectra% ver% different spectra


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*erception/ .ther Gotchas

Color perception is also difficult ecause:Color perception is also difficult ecause: It 'aries rom person to personIt 'aries rom person to person

It is aecte( *) a(aptation stare at a lig#t *ul*@ (ont2It is aecte( *) a(aptation stare at a lig#t *ul*@ (ont2

It is aecte( *) surroun(ing color7It is aecte( *) surroun(ing color7


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*erception/ Relative Intensit)

7e are not good at judging asolute intensit%7e are not good at judging asolute intensit%@et#s illuminate pixels with white light on scale of 5 *=5@et#s illuminate pixels with white light on scale of 5 *=5

2ntensit% difference of neighoring colored rectangles2ntensit% difference of neighoring colored rectangleswith intensities:with intensities:

010 -> 011 10E c#ange2010 -> 011 10E c#ange2 0C0 -> 0CC 10E c#ange20C0 -> 0CC 10E c#ange2

will loo! the samewill loo! the same

7e perceive7e perceive relativerelativeintensities, not asoluteintensities, not asolute


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Representing Intensities

.emaining in the world of lac! and white9.emaining in the world of lac! and white91se photometer to otain min and max rightness of1se photometer to otain min and max rightness of

monitormonitor

This is theThis is the d%namic ranged%namic range

2ntensit% ranges from min, 22ntensit% ranges from min, 255, to max, *=5, to max, *=5

Aow do we represent -B shades of gra%'Aow do we represent -B shades of gra%'


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Representing Intensities

>qual distriution etween min and max fails>qual distriution etween min and max fails

relati'e c#ange near ma! is muc# smaller t#an near Irelati'e c#ange near ma! is muc# smaller t#an near I00

!7 F, , H, 1!7 F, , H, 1

/reserve D change/reserve D change

!7 1:, F, , 1!7 1:, F, , 1

IInn= I= I00J rJ rnnII00, n > 0, n > 0

2255020255

22**0 r20 r255

22--0 r20 r2**0 r0 r--2255

99

22-BB-BB0r20r2-BE-BE0r0r-BB-BB2255


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")namic Ranges

3%namic .ange3%namic .ange

Max F ofMax F of

3ispla% 3ispla% &max ? min illum(&max ? min illum(/erceived/erceived2ntensities &r0*=5*(2ntensities &r0*=5*(

C.T:C.T: B5-55B5-55 E55B5E55B5

/hoto &print(/hoto &print( *55*55 EBEB

/hoto &slide(/hoto &slide( *555*555 H55H55

?7 printout?7 printout *55*55 EBEB

Color printoutColor printout B5B5 E55E55

NewspaperNewspaper *5*5 -E-E


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Gamma Correction

ut most displa% devices are inherentl% nonlinear:ut most displa% devices are inherentl% nonlinear:2ntensit% 02ntensit% 0 11&voltage(&voltage(

ie, *rig#tness J 'oltage A= ;J*rig#tness2 J 'oltage:;2ie, *rig#tness J 'oltage A= ;J*rig#tness2 J 'oltage:;2

is *etween ;; an( ;C on most monitorsis *etween ;; an( ;C on most monitors

Common solution:Common solution: gamma correctiongamma correction

/ost-transormation on intensities to map t#em to linear range on/ost-transormation on intensities to map t#em to linear range on

(ispla) (e'ice7(ispla) (e'ice7

&an #a'e separate&an #a'e separate or ., G, Kor ., G, K 1

xy =


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Gamma Correction

)ome monitors perform the gamma correction in)ome monitors perform the gamma correction inhardware &)G2#s(hardware &)G2#s(

8thers do not &most /Cs(8thers do not &most /Cs(

Tough to generate images that loo! good on othTough to generate images that loo! good on othplatforms &i=e= images from we pages(platforms &i=e= images from we pages(

9 camera models

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