# Quiz 1

Document Sample

```					CPSC 641 Computer Graphics:

Jinxiang Chai

Many slides from Pat Haranhan
Light modeling
Light modeling
Light modeling
Light modeling
Light modeling
Outline

Illumination calculations

The goal of a global illumination algorithm is to compute a
steady-state distribution of light in a scene

To compute this distribution, we need an understanding of
the physical quantities that represent light energy

Radiometry is the basic terminology used to describe light
Photons

The basic quantity in lighting is the photon

The energy (in Joule) of a photon with wavelength λ is:
qλ = hc/λ
- c is the speed of light
In vacuum, c = 299.792.458m/s
- h ≈ 6.63*10-34Js is Planck’s constant

The spectral radiant energy, Qλ, in nλ photons with
wavelength λ is
Q  n q
The radiant energy, Q, is the energy of a collection of
photons, and is given as the integral of Qλ over all
possible wavelengths:


Q   Q d
0

Power: Watts vs. Lumens
- Energy efficiency

- Spectral efficacy

Energy: Joules vs. Talbot
- Exposure
- Film response
- Skin sunburn
Luminance
Y   V ( ) L ( )d 

- Physical measurement of electromagnetic energy
Photometry and Colorimetry [Lumen]
- Sensation as a function of wavelength
- Relative perceptual measurement
1
Brightness [Brils]   B Y       3

- Sensation at different brightness levels
- Absolute perceptual measurement
- Obeys Steven’s Power Law
Fluorescent Bulb
Sunlight

from a point on a light source into a unit solid angle in a
particular direction. And it is measured in watt per

d
I ( ) 
d

 W   lm                 
 sr   sr  cd  candela 
                        
Angles and Solid Angles
l

l                  θ
 Angle   
r

A
 Solid angle     2
R

Differential Solid Angles

r sin

d       r        dA  (r d )(r sin  d )
d
                         r 2 sin  d d


dA
d      2
 sin  d d
r
Differential Solid Angles

dA
d  2  sin  d d
r sin                    r

d       r
d
      d
S2
                           p 2p
   sin  d d
                  0 0
1 2p
     d cos
1 0
d

 4p
Isotropic Point Source

    I d
S2

 4p I


I
4p
Warn’s Spotlight


       ˆ
A                           ˆ )s
I ( )  cos   (  A
s

2p   1
     I ( ) d cos d
0    0
Warn’s Spotlight


       ˆ
A                         ˆ )s
I ( )  cos   (  A
s

2p
2p
1                   1
    I ( ) d cos d  2p  cos  d cos 
s

0 0                     0
s 1
s 1 s
I ( )        cos 
2p
Goniometric Diagrams
Light Source Goniometric Diagrams

Imagine ray of light arriving at or leaving a point on a
surface in a given direction.

contained in this ray.

Definition: The surface radiance (luminance) is
the intensity per unit area leaving a surface.

L ( x,  )       L( x,  ) 
dI ( x,  )
dA
d                   d ( x,  )
2

d dA
 W   cd        lm          
 sr m2   m2  sr m 2  nit 
                           
dA

When the ray is intersecting the surface with an angle θ,
the radiance is computed as follows:

Radiance can be leaving, passing through, or arriving at
a point on a surface

Response of a sensor (camera, human eye) is

Pixel values in image is proportional to radiance
received from that direction (not really true).
Typical Values of Luminance [cd/m2]

Surface of the sun 2,000,000,000 nit
Sunlight clouds                30,000
Clear day                        3,000
Overcast day                       300
Moon                                   0.03
The Invention of Photometry

Bouguer’s classic experiment
 Compare a light source and a
candle
 Intensity is proportional to ratio
of distances squared

Definition of a candela
 Originally a “standard” candle
 Currently 550 nm laser w/ 1/683
W/sr
 1 of 6 fundamental SI units

Definition: The irradiance (illuminance) is the
power per unit area incident on a surface.

d i
E( x) 
dA

 W   lm        
 m2   m2  lux 
               

Sometimes referred to as the radiant (luminous)
incidence.
Lambert’s Cosine Law

A

  EA


E
A
Lambert’s Cosine Law

A    A / cos





    
E          cos
A / cos A


I
4p
        h
r


d       I
4p
        h
r

dA

d  I d


d       I
4p
        h
r

dA

cos
d  2 dA
r


d       I
4p
        h
r

dA
 cos
I d         dA
4p r 2


d       I
4p
        h
r

dA
 cos
I d         dA  E dA
4p r 2

 cos
E
4p r 2


d          I
4p
        h  r cos
r

dA

 cos   cos       3
E        
4p r 2
4p h 2

How to measure the irradiance from the environment?
Directional Power Arriving at a Surface

Li ( x,  )
d
dA


d  i ( x,  )
2
Directional Power Arriving at a Surface

Li ( x,  )
d
dA

d  i ( x,  )  Li ( x,  ) cos  dAd
2

d  i ( x,  )
2

d 2  i ( x,  )  Li ( x,  )cos  dA d  dEdA
Li ( x,  )
dE ( x,  )  Li ( x,  )cos d
d


dA

Light meter                 E( x)     L ( x,)cos d
i
H2
Typical Values of Illuminance [lm/m2]

Sunlight plus skylight                 100,000 lux
Sunlight plus skylight (overcast)    10,000
Interior near window (daylight)     1,000
Artificial light (minimum)           100
Moonlight (full)                              0.02
Starlight                                     0.0003

From Greenler, Rainbows, halos and glories
Gazing Ball  Environment Maps
Miller and Hoffman, 1984

   Photograph of mirror ball
   Maps all spherical directions to a to circle
   Reflection direction indexed by normal
   Resolution function of orientation
Environment Maps

Interface, Chou and Williams (ca. 1985)

L( ,  )   R
E( , )   N

Environment Map      Environment Map

Definition: The radiant (luminous) exitance is the
energy per unit area leaving a surface.

d o
M ( x) 
dA
 W   lm        
m  m
2    2
 lux 
                 
In computer graphics, this quantity is often
referred to as the radiosity (B)
Directional Power Leaving a Surface

Lo ( x ,  )
d
dA

d  o ( x,  )  Lo ( x,  ) cos  dAd
2

d  o ( x,  )
2
Uniform Diffuse Emitter

M   L           o   cos  d
Lo ( x,  )
H2

 Lo     cos d
2
d
H


dA
Projected Solid Angle

   cos d

d


cos d
       cos  d  p
H2
Uniform Diffuse Emitter

M     L        o   cos  d
H2
Lo ( x,  )
 Lo  cos  d
H2                       d
 p Lo                         

M
Lo 
p                        dA

```
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