CS 184 Radiometry Lecture UC Berkeley

8/13/2019 CS 184 Radiometry Lecture UC Berkeley

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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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CS 184 Radiometry Lecture UC Berkeley

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