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CS-184: Computer Graphics
Lecture 22: Radiometry James OBrien
University of California, Berkeley V2013-F-22-1.0
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Today
Radiometry: measuring light Local Illumination and Raytracing were discussed in an ad hoc fashion Proper discussion requires proper units Not just pretty pictures... but correct pictures
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Matching Reality
Unknown
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Matching Reality
Photo Rendered
Cornell Box Comparison
Cornell Program of Computer Graphics
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Units
Light energy Really power not energy is what we measure Joules / second ( J/s ) = Watts ( W )
Spectral energy density Power per unit spectrum interval Watts / nano-meter ( W/nm ) Properly done as function over spectrum Often just sampled for RGB
Often we assume people know were talking about S.E.D. and just say E...
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IrradianceTotal light striking surface from all directions
Only meaningful w.r.t. a surface Power per square meter ( ) Really S.E.D. per square meter ( ) Not all directions sum the same because of foreshortening
W / m 2W / m 2 / nm
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Total light leaving surface over all directions Only meaningful w.r.t. a surface Power per square meter ( ) Really S.E.D. per square meter ( ) Also called Radiosity
Sum over all directions ! same in all directions
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W / m 2 / nm
Radiant Exitance
W / m 2
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Solid AnglesRegular angles measured in radians
Measured by arc-length on unit circle
Solid angles measured in steradians Measured by area on unit sphere Not necessarily little round pieces...
[0 ..2 ! ]
[0 ..4 ! ]
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Radiance
Light energy passing though a point in space within a givensolid angle
Energy per steradian per square meter ( ) S.E.D. per steradian per square meter ( )
Constant along straight lines in free space Area of surface being sampled is proportional to distance and light inversely proportional to
squared distance
W / m 2 / sr / nmW / m 2 / sr
d
kd
area=D d 2
area=D (kd) 2
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Radiance
Near surfaces, differentiate between Radiance from the surface ( surface radiance ) Radiance from other things ( eld radiance )
L f L s
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Light Fields
Radiance at every point in space , direction, and frequency: 6D function
Collapse frequency to RGB, and assume free space: 4D function
Sample and record it over some volume
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Light Fields
Levoy and Hanrahan, SIGGRAPH 1996
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Light Fields
Levoy and Hanrahan, SIGGRAPH 1996
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Light Fields
MichelangelosStatue of NightFrom the Digital Michelangelo Project
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Computing IrradianceIntegrate incoming radiance (eld radiance) over all direction
Take into account foreshor tening
H = Z ! L f (k ) cos (" )d #
n d
k
!
H = Z 2 !
0 Z ! / 2
0 L f (" , #) cos (" ) sin (" ) d " d #
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Revisiting The BRDFHow much light from direction goes out in direction
Now we can talk about units:
BRDF is ratio of surface radiance to the foreshortened eld radiance
We left out frequency dependance here...
Also note for perfect Lambertian reectorwith constant BRDF ! = 1 "
k i k o
light
detector
k i k o
(k i , k o ) = L s (k o )
L f (k i ) cos(i )
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The Rendering EquationTotal light going out in some direction is given by an integralover all incoming directions:
Note, this is recursive ( my is anothers ) L f L s
L s (k o ) = Z
(k i , k o )L f (k i ) cos(i )d i
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The Rendering Equation
Rewrite explicitly in terms of surface radiances only
L s (k o ) = Z
(k i , k o )L f (k i ) cos(i )d i
L f (k i ) = L s ( k i ) i = A 0 cos( 0 )
|| x x 0 || 2
L s (x , k o ) = Z all x 0
(k i , k o L s (x 0 , x x 0 (x , x 0 cos(i cos(0
|| x x 0 || 2 dA 0
(x , x0 ) = (1 if
x and x 0 are mutually visible0 otherwise
L s (x , k o ) = Z x 0 visible to x
(k i , k o L s (x 0 , x x 0 cos(i cos(0
|| x x 0 || 2 dA 0
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Light Paths
Many paths from light to eye
Characterize by the types of bounces Begin at light
End at eye Specular bounces Diffuse bounces
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Light Paths
Describe paths using strings
LDE, LDSE, LSE,etc.Describe types of paths with regular expressions
L{D|S}*E L{D|S}S*E L{D|S}E LD*E
Visible paths
Standard raytracing
Local illuminationRadiosity method(have not talked about yet)
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