Computer Graphics
Lighting
Outline
•Lighting
•Lighting models
•Ambient
•Diffuse
•Specular
•Surface Rendering Methods
What we know
• We already know how to render the world
from a viewpoint.
“Lighting”
• Two components:
– Lighting Model or
Shading Model - how
we calculate the intensity
at a point on the surface
– Surface Rendering
Method - How we
calculate the intensity at
each pixel
Jargon
• Illumination - the transport of light from a
source to a point via direct and indirect paths
• Lighting - computing the luminous intensity
for a specified 3D point, given a viewpoint
• Shading - assigning colors to pixels
• Illumination Models:
– Empirical - approximations to observed
light properties
– Physically based - applying physics
properties of light and its interactions with
matter
The lighting problem…
• What are we trying to
solve?
• Global illumination – the
transport of light within a
scene.
• What factors play a part in
how an object is “lit”?
• Let’s examine different
items here…
Two components
• Light Source Properties
– Color (Wavelength(s) of light)
– Shape
– Direction
• Object Properties
– Material
– Geometry
– Absorption
Global Effects
shadow
multiple reflection
translucent surface
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Local vs Global Rendering
• Correct shading requires a global
calculation involving all objects and light
sources
– Incompatible with pipeline model which shades
each polygon independently (local rendering)
• However, in computer graphics, especially
real time graphics, we are happy if things
“look right”
– Exist many techniques for approximating
global
effects
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Light Source Properties
• Color
– We usually assume the light has
one wavelength
• Shape
– point light source - approximate
the light source as a 3D point in
space. Light rays emanate in all
directions.
• good for small light sources
(compared to the scene)
• far away light sources?
Distributed Lights
• Light Source Shape continued
– distributed light source (not supported natively in
OpenGL) - approximating the light source as a 3D
object. Light rays usually emanate in specific
directions
• good for larger light sources
• area light sources
Light Source Direction
• In computer graphics, we usually treat lights
as rays emanating from a source. The
direction of these rays can either be:
– Omni-directional (point light source)
– Directional angle (spotlights)
– Directional (parallel rays)
Light Position
• We can specify the position of a light with
an x, y, and z coordinate.
– What are some examples?
– These lights are called positional lights
• Q: Are there types of lights that we can
simplify?
A: Yep! Think about the sun. If a light is significantly far
away, we can represent the light with only a direction vector.
These are called directional lights. How does this help?
Contributions from lights
• We will breakdown what a light does to an
object into three different components. This
APPROXIMATES what a light does. To
actually compute the rays is too expensive
to do in real-time.
– Light at a pixel from a light = Ambient +
Diffuse + Specular contributions.
– Ilight = Iambient + Idiffuse + Ispecular
Ambient Term - Background Light
• The ambient term is a HACK!
• It represents the approximate
contribution of the light to the
general scene, regardless of
location of light and object
• Indirect reflections that are too
complex to completely and
accurately compute
• Iambient = color
Diffuse Term
• Contribution that a light has on the
surface, regardless of viewing
direction.
• Diffuse surfaces, on a microscopic
level, are very rough. This means
that a ray of light coming in has an
equal chance of being reflected in
any direction.
• What are some ideal diffuse
surfaces?
Lambert’s Cosine Law
• Diffuse surfaces follow Lambert’s Cosine Law
• Lambert’s Cosine Law - reflected energy from a small
surface area in a particular direction is proportional to
the cosine of the angle between that direction and the
surface normal.
• Think about surface area and # of rays
Diffuse Term
• To determine how much of a diffuse contribution
a light supplies to the surface, we need the surface
normal and the direction on the incoming ray
• What is the angle between these two vectors?
• Idiffuse = kdIlightcos = kdIlight(N . L)
• Ilight = diffuse (intensity) of light
• kd [0..1] = surface diffuse reflectivity
• What CS are L and N in?
• How expensive is it?
Example
• What are the possible values for theta (and
thus the dot product?)
http://graphics.lcs.mit.edu/classes/6.837/F98/
Lecture18/Slide11.html
Normal for Triangle
n
plane
n ·(p - p0 ) = 0
p1
n = (p1 - p0 ) × (p2 - p0 )
normalize n  n/ |n|
p
p0
p2
Note that right-hand rule determines outward face
(programatically: ‘winding’ or order of vertices)
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Specular Reflection
• Specular contribution can be thought of as
the “shiny highlight” of a plastic object.
• On a microscopic level, the surface is very
smooth. Almost all light is reflected.
• What is an ideal purely specular reflector?
• What does this term depend on?
Viewing Direction
Normal of the Surface
Snell’s Law
• Specular reflection applies Snell’s Law.
 We assume l = r
Snell’s Law is for IDEAL surfaces
• Most surfaces are not ideal.
• Think about the amount of light reflected at
different angles.
N
R
L

V
Different for shiny vs. dull objects
Snell’s Law is for IDEAL surfaces
• Think about the amount of light reflected at
different angles.
N
R
L


V

Phong Model
Phong Reflection Model
• An approximation: set the intensity of specular
reflection proportional to (cos )shininess
• What are the possible values of cos ?
• What does the value of shininess mean?
• How do we represent shinny or dull surfaces using
the Phong model?
• Ispecular = ksIlight (cos )shininess = ksIlight (V.R)shininess
The Shininess Coefficient
• Values of a between 100 and 200 correspond to
metals
• Values between 5 and 10 give surface that look like
plastic
cosa 
-90
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
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How do we compute R?
• N*(N.L)
• R+L=2N(N.L)
• R = 2N(N.L)-L
L
N
R
N(N.L)
L
V


L V
H
L V
I specular  k s I light_ specularity  N  H 
shininess
Simplify this
• Instead of R, we
compute halfway
H
between L and V.
• We call this vector the
halfway vector, H. N
L
R
V


Combining the terms
• Ambient - the combination of light reflections
from various surfaces to produce a uniform
illumination. Background light.
• Diffuse - uniform light scattering of light rays on a
surface. Proportional to the “amount of light” that
hits the surface. Depends on the surface normal
and light vector.
• Sepecular - light that gets reflected. Depends on
the light ray, the viewing angle, and the surface
normal.
Ambient + Diffuse + Specular
Lighting Equation
I final  I ambientkambient  I diffusekdiffuseN  L   I speculark specularN  H 
shininess
I final 
lights1

l 0
I lambientkambient  I ldiffusekdiffuseN  L   I lspeculark specularN  H 
shininess
Ilambient = light source l’s ambient component
Ildiffuse = light source l’s diffuse component
Ilspecular = light source l’s specular component
kambient = surface material ambient reflectivity
N
R
L

kdiffuse = surface material diffuse reflectivity
kspecular = surface material specular reflectivity
shininess = specular reflection parameter (1 -> dull, 100+ -> very shiny)
V
Attenuation
• One factor we have yet to take into account
is that a light source contributes a higher
incident intensity to closer surfaces.
• What happens if we don’t do this?
f d  
1
a0  a1d  a2 d 2
Subtleties
• What’s wrong with:
1
f d  
a0  a1d  a2 d 2
What’s a good fix?


1

f d   min 1,
2 
 a0  a1d  a2 d 
Full Illumination Model
I final  I lambientkambient 
lights1

l 0

f dl  I ldiffusekdiffuseN  L   I lspeculark specular N  H 


1

f d   min 1,
2 
 a0  a1d  a2 d 
Run demo
shininess

Steps in OpenGL lighting
1.
2.
3.
4.
Enable lighting and select model
Specify normals
Specify material properties
Specify lights
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Normal for Triangle
n
plane
n ·(p - p0 ) = 0
p1
n = (p1 - p0 ) × (p2 - p0 )
normalize n  n/ |n|
p
p0
p2
Note that right-hand rule determines outward face
(programatically: ‘winding’ or order of vertices)
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X
Normals
• In OpenGL the normal vector is part of the state
• Set by glNormal*()
– glNormal3f(x, y, z);
– glNormal3fv(p);
• Usually we want to set the normal to have unit
length so cosine calculations are correct
– Length can be affected by transformations
– Note that scaling does not preserved length
– glEnable(GL_NORMALIZE) allows for
autonormalization at a performance penalty
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Shading
• Shading is how we “color” a triangle.
• Constant Shading
• Gouraud Shading
Constant Shading
•
•
•
•
•
•
Constant Intensity or Flat Shading
One color for the entire triangle
Fast
Good for some objects
What happens if triangles are small?
Sudden intensity changes at borders
Gouraud Shading
• Intensity Interpolation Shading
• Calculate lighting at the vertices. Then interpolate
the colors
Gouraud Shading
•
•
•
•
•
Relatively fast, only do three calculations
No sudden intensity changes
What can it not do?
What are some approaches to fix this?
Question, what is the normal at a vertex?
Enabling Shading
• Shading calculations are enabled by
– glEnable(GL_LIGHTING)
– Once lighting is enabled, glColor() ignored
• Must enable each light source individually
– glEnable(GL_LIGHTi) i=0,1…..
• Can choose light model parameters
– glLightModeli(parameter, GL_TRUE)
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• GL_LIGHT_MODEL_LOCAL_VIEWER do not use
simplifying distant viewer assumption in calculation
• GL_LIGHT_MODEL_TWO_SIDED shades both
sides of polygons independently
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Defining a Point Light Source
• For each light source, we can set an RGBA for the
diffuse, specular, and ambient components, and for the
position
GL float diffuse0[]={1.0, 0.0, 0.0, 1.0};
GL float ambient0[]={1.0, 0.0, 0.0, 1.0};
GL float specular0[]={1.0, 0.0, 0.0, 1.0};
Glfloat light0_pos[]={1.0, 2.0, 3,0, 1.0};
glEnable(GL_LIGHTING);
glEnable(GL_LIGHT0);
glLightv(GL_LIGHT0, GL_POSITION, light0_pos);
glLightv(GL_LIGHT0, GL_AMBIENT, ambient0);
glLightv(GL_LIGHT0, GL_DIFFUSE, diffuse0);
glLightv(GL_LIGHT0, GL_SPECULAR, specular0);
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Distance and Direction
• The source colors are specified in RGBA
• The position is given in homogeneous coordinates
– If w =1.0, we are specifying a finite location
– If w =0.0, we are specifying a parallel source
with the given direction vector
• The coefficients in the distance terms are by default
a=1.0 (constant terms), b=c=0.0 (linear and
quadratic terms). Change by
a= 0.80;
glLightf(GL_LIGHT0, GLCONSTANT_ATTENUATION, a);
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Spotlights
• Use glLightv to set
– Direction GL_SPOT_DIRECTION
– Cutoff GL_SPOT_CUTOFF
– Attenuation GL_SPOT_EXPONENT
• Proportional to cosa

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

Global Ambient Light
• Ambient light depends on color of light
sources
– A red light in a white room will cause a red
ambient term that disappears when the light is
turned off
• OpenGL also allows a global ambient term
that is often helpful for testing
– glLightModelfv(GL_LIGHT_MODEL_AMBIENT,
global_ambient)
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Moving Light Sources
• Light sources are geometric objects whose
positions or directions are affected by the modelview matrix
• Depending on where we place the position
(direction) setting function, we can
–
–
–
–
Move the light source(s) with the object(s)
Fix the object(s) and move the light source(s)
Fix the light source(s) and move the object(s)
Move the light source(s) and object(s) independently
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Material Properties
• Material properties are also part of the OpenGL
state and match the terms in the modified Phong
model
• Set by glMaterialv()
GLfloat ambient[] = {0.2, 0.2, 0.2, 1.0};
GLfloat diffuse[] = {1.0, 0.8, 0.0, 1.0};
GLfloat specular[] = {1.0, 1.0, 1.0, 1.0};
GLfloat shine = 100.0
glMaterialf(GL_FRONT, GL_AMBIENT, ambient);
glMaterialf(GL_FRONT, GL_DIFFUSE, diffuse);
glMaterialf(GL_FRONT, GL_SPECULAR, specular);
glMaterialf(GL_FRONT, GL_SHININESS, shine);
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Front and Back Faces
• The default is shade only front faces which works
correctly for convex objects
• If we set two sided lighting, OpenGL will shade
both sides of a surface
• Each side can have its own properties which are set
by using GL_FRONT, GL_BACK, or
GL_FRONT_AND_BACK in glMaterialf
back faces not visible
back faces visible
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Emissive Term
• We can simulate a light source in OpenGL
by giving a material an emissive component
• This component is unaffected by any
sources or transformations
GLfloat emission[] = 0.0, 0.3, 0.3, 1.0);
glMaterialf(GL_FRONT, GL_EMISSION, emission);
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