School of Computer Science
University of Seoul
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Light and Matter
Light Sources
The Phong Reflection Model
Computation of Vectors
Polygonal Shading
Approximation of a Sphere by Recursive Subdivision
Light Sources in OpenGL
Specification of Materials in OpenGL
Shading of the Sphere Model
Global Illumination

Rendering equation [Kaj86]
Integral eq. resulted by recursive scattering
 Physics-based, slow to compute


Radiosity, raytracing (Ch.12) and photon
mapping
Approximation of rendering equation for particular
surfaces
 Still slow


Phong reflection model

Fast!
Proposed in “The rendering equation” (by
James Kajiya, 1986)
 Based on “conservation of energy”

FEM (Finite Element Method) applied to
solve the rendering equation
 For scenes with diffuse surfaces


Supported by 3D Max, EIAS, etc.
(image courtesy of David Stoddard, EIAS)
(image courtesy of JCM animation, EIAS)
Rendering by tracing rays for each pixel
from the viewer (camera)
 Suitable for reflective surfaces

(image courtesy of Wikipedia)

Supported by POV-Ray, YafaRay, etc.
(“Glasses” by Gilles Tran, POV-Ray)
(“Nikon” by Bert Buchholz, YafaRay)

Rays from the light source & camera are
traced independently
Image courtesy of Wikipedia)
Reflected, absorbed and transmitted
 Depends on

 opaqueness
 wavelength-
“Why does an object look red?”
 roughness - “Why does an object look shiny?”
 Orientation
 etc.
Specular surfaces
 Diffuse surfaces
 Translucent surfaces

Can be modeled by an illumination function
I(x,y,z,,,)
 Each frequency considered
independently
 Total contribution can be
computed by integration
 Directional properties can
vary with frequency
 Too complicated to compute

Four types: ambient lighting, point sources,
spotlights, and distant lights
 Light sources with three components, RGB
- based on “three-color theory”
 Each component calculated independently
 Intensity or luminance:
 Ir 



I  I g 
 I b 
Models uniform illumination
 Simplified as an intensity that is identical at
every point in the scene:

 I ar 
I a   I ag 
 I ab 

Located at p0:
 I r p 0 
Ip 0    I g p 0 
 I b p 0 
Intensity received at p: ip, p 0   p  p 2 Ip 0 
0
 High contrast than surface light
 Can be made soft by
2 1
the distance term: a  bd  cd 

1
Cone-shaped directional range
 Distribution of the light within the cone
usually defined by cos e 

Rays can be assumed parallel
 Direction instead of location:

 x
 y
p0   
z
 
1 
 x
 y
p0   
z
 
0
Introduced by Phong
 Four vectors used
 Three types of material-light interactions –
ambient, diffuse, and specular
 Local model

(image courtesy of Wikipedia)



i-the light source:
L ia   Lira

L i  L id    Lird
 L is   Lirs
Liga
Ligd
Ligb
 R ia   Rira

R i  R id    Rird
 R is   Rirs
Riga
Rigd
Rigb
Liba 

Libd 
Libs 
Reflection terms for a material:
Riba 

Ribd 
Ribs 
Contribution of each light color (e.g., red):
I ir  Rira Lira  Rird Lird  Rirs Lirs  I ira  I ird  I irs

Contribution of all sources (e.g., red):
I r   I ira  I ird  I irs   I ar
i
Intensity same at every point on the surface
 Depends on

 Material

property
Independent of
 Location
of the light source
 Location of the viewer
I a  k a La
Characterized by rough surfaces
 Assumed to be “perfectly diffuse”
 Depends on

 Material
property
 Location of the light source

Independent of
 Location
of the viewer

Lambert’s law (for perfectly diffuse surface):
Rd  cos 
kd
Id 
Ld max l  n,0 
2
a  bd  cd
Characterized by smooth surfaces
 Depends on

 Material
property
 Location of the light source
 Location of the viewer

“shininess coefficient” ()

ks

Is 
Ls max r  v  ,0
2
a  bd  cd




1





I  Ia  Id  Is 
k
L
max
l

n
,
0

k
L
max
r

v
,0  k a La
d d
s s
2
a  bd  cd
Modified by Blinn  a.k.a. “Blinn-Phong
Shading Model”
 Simplified by halfway angle (h) for faster
calculation
lv

 rv

replaced by n h
h
lv
Faster calculation when the light
and the viewer are at infinity (WHY?)
 GL_LIGHT_MODEL_LOCAL_VIEWER

Default model in OpenGL

How to compute the normal vector of
a
triangle?
 a (smooth) surface?

How to compute reflection vector?
r  2l  nn  l

Flat shading
 The

normal of the first vertex used
Gouraud shading
 Lighting
calculation at vertices
 Linearly interpolated at each fragment
 Artifacts for coarse polygon
Lighting computation at each fragment
 Not directly supported by OpenGL
 Can be implemented using GLSL (OpenGL
Shading Language)


Enable/disable:
glEnable(GL_LIGHTING);
 glEnable(GL_LIGHT#);

 At least 8 lights
 Positional or directional light:


glLight*(GL_LIGHT#, GL_POSITION, position);
Ambient, diffuse, specular components:

glLight*(GL_LIGHT#, GL_*, value);
 GL_AMBIENT
 GL_DIFFUSE
 GL_SPECULAR

Global ambient:


Distance-attenuation model:


glLightModel*(GL_LIGHT_MODEL_AMBIENT, value);
glLight*(GL_LIGHT#, GL_*, value);
 GL_CONSTANT_ATTENUATION (a)
 GL_LINEAR_ATTENUATION (b)
 GL_QUADRATIC_ATTENUATION (c)
Spotlight:

glLight*(GL_LIGHT#, GL_*, value);
 GL_SPOT_DIRECTION
 GL_SPOT_EXPONENT
 GL_SPOT_CUTOFF ([0,90] or 180)
1
a  bd  cd 2

Infinite/local viewer:
 glLightModel*(GL_LIGHT_MODEL_LOCAL_VIEW
ER, value);

One/two-sided lighting:
 glLightModel*(GL_LIGHT_MODEL_TWO_SIDED,
value);

Light sources are transformed by
modelview matrices!


Material properties are OpenGL states!
Ambient, diffuse, specular, emissive:
 glMaterial*v(face, GL_*, value);


GL_AMBIENT, GL_DIFFUSE, GL_SPECULAR, GL_EMISSION,
GL_DIFFUSE_AND_SPECULAR
Emissive property
 Does not affect any other surface (it’s not a light!)
 Simply adds color




Shininess:
 glMaterial*(face, GL_SHININESS, value);
Front/back/front&back:
 GL_FRONT, GL_BACK, GL_FRONT_AND_BACK
glColorMaterial
Various materials: refer to teapots.c!

Try yourself!!!