Graphics
Reflection Model
고려대학교 컴퓨터 그래픽스 연구실
kucg.korea.ac.kr
Graphics Lab @ Korea University
Content
KUCG

Shading
 Light sources


Phong reflection model




Point, distant, and spot lights
Diffuse reflection
Specular reflection
Ambient reflection
Computation of vectors

Normal vectors, angle of reflection, and transmitted
light
kucg.korea.ac.kr
Graphics Lab @ Korea University
Shading
KUCG

Determine a color for each filled pixel
 How to choose a color

the color of the light source and of the surfaces
determines the color of one or more pixels in the
frame buffer
kucg.korea.ac.kr
Graphics Lab @ Korea University
Light and Matter

KUCG
Color is determined by multiple interactions
among light sources and reflective surfaces

recursive reflection of light between surfaces
accounts for subtle shading
Rendering Equation
kucg.korea.ac.kr
Graphics Lab @ Korea University
Light-Material Interactions

Specular surfaces – mirror


scatter reflected light in a narrow range of angle
Diffuse surfaces – chalk, clay


KUCG
scatter reflected light all directions
Translucent surfaces – glass, water

refraction
specular surface
kucg.korea.ac.kr
diffuse surface
translucent surface
Graphics Lab @ Korea University
Light Sources

KUCG
Illumination function I (x, y, z, θ, φ, λ)



each point (x, y, z) on the surface
direction of emission (θ, φ)
wavelength λ
light source
kucg.korea.ac.kr
Graphics Lab @ Korea University
Modeling Light Sources

KUCG
Simple mathematical models:




ambient light
point light
distant light
spot light
kucg.korea.ac.kr
Graphics Lab @ Korea University
Color Sources

KUCG
Three-color theory


human perceive three primary colors – red, green,
and blue
three-component intensity or luminance function
Ir 


I  I g 
 I b 

independent calculations
kucg.korea.ac.kr
Graphics Lab @ Korea University
Ambient Light

KUCG
Uniform lighting

identical at every point in the scene
 I ar 


I a  I ag 
 I a b 
kucg.korea.ac.kr
Graphics Lab @ Korea University
Point Sources (1/2)

KUCG
Emit light equally in all directions

p0: point source location


Ip 0   I r p 0  I g p 0  I b p 0 

T
proportional to the inverse square distance
Ip, p 0  
1
p  p0
2
Ip 0 
point source illuminating a surface
kucg.korea.ac.kr
Graphics Lab @ Korea University
Point Sources (2/2)

Large finite size of most light sources



KUCG
umbra: full shadow
penumbra: partial shadow
Attenuation
Ip, p 0  
1
p  p0
2
Ip 0 
1
Ip, p 0  
Ip 0 
2
kc  kl d  k q d
kucg.korea.ac.kr
shadows created by
finite-size light source
Graphics Lab @ Korea University
Spotlights

KUCG
Characterized by a narrow range of angle
through which light is emitted



ps: apex of a cone
ls: direction of pointing
θ: angle to determine width
spotlight

Distribution of light

concentrate in the center

light intensity drop off
cos  s  l s
cos   s  l s 
e
kucg.korea.ac.kr
e
attenuation
exponent
Graphics Lab @ Korea University
Distant Light Sources

KUCG
far from the surface  vector does not change

location  direction
 x
 y
p0   
z
 
1 
 x
 y
p0   
z
 
0
parallel light source
kucg.korea.ac.kr
Graphics Lab @ Korea University
Phong Reflection Model (1/5)
KUCG

Efficient and close enough approximation to
physical reality to produce good renderings
 Use 4 vectors

n: normal at p
 v: direction from p to the viewer or COP
 l: direction from light source
 r: direction of reflectance

3 types of material-light
interactions

ambient, diffuse, and specular
kucg.korea.ac.kr
vectors used by
the Phong model
Graphics Lab @ Korea University
Phong Reflection Model (2/5)

KUCG
Simple analytic model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
Based on model
proposed by Phong
kucg.korea.ac.kr
Graphics Lab @ Korea University
Phong Reflection Model (2/5)

KUCG
Simple analytic model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
Based on model
proposed by Phong
kucg.korea.ac.kr
Graphics Lab @ Korea University
Diffuse Reflection (1/3)

KUCG
Assume surface reflects equally in all directions

Examples: chalk, clay
kucg.korea.ac.kr
Graphics Lab @ Korea University
Diffuse Reflection (2/3)

KUCG
How much light is reflected?


Depends on angle of incident light
dL  dA cos Q
kucg.korea.ac.kr
Graphics Lab @ Korea University
Diffuse Reflection (3/3)

KUCG
Lambertian model

Cosine law (dot product)
I D  K D N LI L
kucg.korea.ac.kr
Graphics Lab @ Korea University
Phong Reflection Model (2/5)

KUCG
Simple analytic model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
Based on model
proposed by Phong
kucg.korea.ac.kr
Graphics Lab @ Korea University
Specular Reflection (1/3)

KUCG
Reflection is strongest near mirror angle

Examples: mirrors, metals
kucg.korea.ac.kr
Graphics Lab @ Korea University
Specular Reflection (2/3)

KUCG
How much light is seen?

Depends on angle of incident light and angle to
viewer
kucg.korea.ac.kr
Graphics Lab @ Korea University
Specular Reflection (3/3)

KUCG
Phong model

{cos(a)}n
I S  KS V R  I L
n
kucg.korea.ac.kr
Graphics Lab @ Korea University
Phong Reflection Model (2/5)

KUCG
Simple analytic model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
Based on model
proposed by Phong
kucg.korea.ac.kr
Graphics Lab @ Korea University
Emission

KUCG
Represents light emitting directly from polygon
Emission ≠ 0
kucg.korea.ac.kr
Graphics Lab @ Korea University
Phong Reflection Model (2/5)

KUCG
Simple analytic model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
Based on model
proposed by Phong
kucg.korea.ac.kr
Graphics Lab @ Korea University
Ambient Term

KUCG
Represents reflection of all indirect illumination
This is a total hack (avoids complexity of global illumination)!
kucg.korea.ac.kr
Graphics Lab @ Korea University
Phong Reflection Model (3/5)

KUCG
Simple analytic model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
kucg.korea.ac.kr
Graphics Lab @ Korea University
Phong Reflection Model (4/5)

KUCG
Simple analytic model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
kucg.korea.ac.kr
Graphics Lab @ Korea University
Phong Reflection Model (5/5)

KUCG
Sum diffuse, specular, emission, and ambient
kucg.korea.ac.kr
Graphics Lab @ Korea University
Surface Illumination
Calculation (1/2)

KUCG
Single light source:
I  I E  K A I AL  KD N  LI L  KS V R  I L
n
kucg.korea.ac.kr
Graphics Lab @ Korea University
Surface Illumination
Calculation (2/2)

KUCG
Multiple light sources:
I  I E  K A I AL  i ( K D  N  Li I i  K S V  R i  I i )
n
kucg.korea.ac.kr
Graphics Lab @ Korea University
Computation of Reflection


Light source and reflection term
 Rira
 Lira Liga Liba 



L i   Lird Ligd Libd  R i   Rird
 Rirs
 Lirs Ligs Libs 



KUCG
Riba 

Ribd 
Rigs Ribs 
Ex. red intensity I ir  Rira Lira  Rird Lird  Rirs Lirs
Riga
Rigd
 I ira  I ird  I irs
I r   I ira  I ird  I irs   I ar
i

Total Intensity
kucg.korea.ac.kr
I  I a  I d  I s  Ra La  Rd Ld  Rs Ls
Graphics Lab @ Korea University
Ambient Reflection
KUCG

Same at every point on the surface
 Ambient reflection coefficient Ra  k a
0  ka  1

amount reflected



some of light source is absorbed and some is reflected
three ambient coefficients –
k ar , k ag, and k ab
Ambient reflection term
I a  k a La


can be any of the individual light sources
can be a global ambient term
kucg.korea.ac.kr
Graphics Lab @ Korea University
Diffuse Reflection (1/2)

KUCG
Characterized by rough surfaces

perfectly diffuse surface
 so rough that there is no preferred
angle of reflection

Lambert’s law

rough surface
only the vertical component of light source
at noon
kucg.korea.ac.kr
in the afternoon
Lambert’s law
Graphics Lab @ Korea University
Diffuse Reflection (2/2)

KUCG
Lambert’s law (cont’)
Rd  cos
cos  l  n
Lambert’s law

Diffuse reflection term
I d  k d l  nLd

incorporate a distance term
kd
l  n Ld
Id 
2
kc  kl d  k q d
kucg.korea.ac.kr
Graphics Lab @ Korea University
Specular Reflection

KUCG
Specular surface is smooth

highlight in the direction of the viewer
specular surface

specular highlights
Specular reflection term
I s  ks r  v  Ls
a

shininess coefficient



α  infinite : mirror
100 < α < 500 : metal
α < 100 : broad highlight
kucg.korea.ac.kr
effect of shininess coefficient
Graphics Lab @ Korea University
Illumination Equation
KUCG
I  Ia  Id  Is
 Ra La  Rd Ld  Rs Ls
 k a La  k d l  n Ld  k s r  v  Ls
a

Including the distance term
I  k a La  k d l  n Ld  k s r  v  Ls
a

1
a
 k a La 
k d l  n Ld  k s r  v  Ls
2
kc  kl d  k q d
kucg.korea.ac.kr

Graphics Lab @ Korea University
Utah Teapots with Different
Material Properties
kucg.korea.ac.kr
KUCG
Graphics Lab @ Korea University
Computation of Vectors (1/2)

Normal vectors
n  p1  p 0  p 2  p 0 

n
p1
p0
in OpenGL
glNormal3f(nx, ny, nz);
glNormal3fv(pointer_to_normal);

KUCG
p2
Angle of reflection
l  n  r 1
cos i  cos r
l n  nr
coplanar condition
 n  al  n 
 al  n  
①
②
1  r  r  a 2  2a l  n   2
by ① and ②
kucg.korea.ac.kr
r  2l  nn  l
mirror
Graphics Lab @ Korea University
Computation of Vectors (2/2)

Halfway vector

lv
h
lv
half-angle: 2ψ=φ
I s  ks r  v  Ls
I s  ks n  h Ls
a
a

KUCG
halfway vector
Transmitted light

Snell’s law
sin  l  t

sin  t  l


1
2
cos t  1  2 1  cos  l 
 

1/ 2


1
t   l   cos t  cos l n
 


kucg.korea.ac.kr
  t l
1
perfect light transmission
Graphics Lab @ Korea University