color

Lighting and Shading
Steve Lin
Department of Computer Science &
Institute of Multimedia Engineering
I-Chen Lin’CG Slides, Doug James’CG Slides,
Angel, Interactive Computer Graphics, Chap 6
Shirley, Fundamentals of Computer Graphics, Chap 9

Illumination and Shading
•Is it a ball or a plate
•What color should I set for each pixel
DCP4516 Introduction to Computer Graphics 2

Why Do We Need Shading
•Suppose we color a sphere model. We get
something like
•But we want
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Shading
•Why does the image of a real sphere look like
•Light-material interactions cause each point to
have a different color or shade
•Need to consider
–Light sources
–Material properties
–Location of the viewer
–Surface orientation
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Factors that affect the“color”of a pixel
•Light sources
–Emittance spectrum (color)
–Geometry (position and direction)
–Directional attenuation
•Objects’surface properties
–Reflectance spectrum (color)
–Geometry (position, orientation, and micro-
structure)
–Absorption
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Light and Matter
•Light strikes A
–Some reflected
–Some absorbed
•Some of reflected light strikes B
–Some reflected
–Some absorbed
•Some of reflected light reflected back to A and B,
and so on
•Rendering equation describes this recursive
process
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Rendering Equation
•The infinite reflection and absorption of light can be
described by the rendering equation
–[outgoing]-[incoming] = [emitted]-[absorbed]
–[outgoing] = [emitted] + [reflected] (+[transmitted])
–Cannot be solved in general
–Ray tracing is a special case for perfectly reflecting surfaces
•Rendering equation is global and includes
–Shadows
–Multiple reflection from object to object
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Global Effects
shadow
transmission
multiple reflection
translucent surface
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Local vs Global Illumination
•Correct shading requires a global calculation
–Incompatible with a pipeline model which shades
each polygon independently (local rendering)
•However, in computer graphics, especially
real time graphics, we are happy if things
“look right”
–many techniques for approximating global effects
exist
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Local Illumination
•Adequate for real-time graphics.
•No inter-reflection, no refraction, no realistic
shadow ….
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Light Sources
•General light sources are difficult to simulated
–because we must integrate light coming from all points
on the source
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Simple Light Sources
•Point source
–Model with position and color
–Distant source = infinite distance away (parallel)
•Spotlight
–Restrict light from ideal point source
•Ambient light
–Same amount of light everywhere in scene
–Can model contribution of many sources and reflecting
surfaces
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Surface Types
•The smoother a surface, the more reflected
light is concentrated in the direction
•A very rough surface scatters light in all
directions
smooth surface
rough surface
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Phong Reflection (Lighting) Model
•A simple model that can be computed rapidly
•Has three components
–Ambient
–Diffuse
–Specular
•Uses four vectors
–To source l
–To viewer v
–Normal n
–Perfect reflector r
r = 2 (l · n ) n- l
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Ambient Light
•The result of multiple interactions between
(large) light sources and the objects in the
environment.
•I a = k a L a
ambient light intensity
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Diffuse Reflection
•Light scatters equally in all directions
•Reflected intensities vary with the direction
of the light.
•Lambertian Surface
–Perfect diffuse reflector
•I d = k d (l·n) L d
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Specular Surfaces
•Most surfaces are neither perfectly diffuse nor
perfectly specular (ideal reflectors)
•Incoming light reflects in concentrated directions
close to the direction of a perfect reflection
specular
highlight
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Modeling Specular Relections
•Phong model
I s = k s L s (r·v) α
= k s L s cos α Φ
shininess coefficient
reflected
intensity incoming intensity
absorption coefficient
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The Shininess Coefficient α
•Values of αbetween 100 and 200 correspond to
metals
•Values between 5 and 10 give surfaces that look
like plastic
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Distance Terms
•Account for attenuation
•Original: Inversely proportional to the square of
the distance d between light source and surface
•Modified: add a factor of the form 1/(a + bd +cd 2 )
to the diffuse and specular terms
•The constant and linear terms soften the effect
of the point source
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Adding up the Components
•A primitive virtual world with lighting can be
shaded by combining the three light
components:
•I = I ambient
+ I diffuse
+ I specular
= k a
L a
+ k d
(l · n) L d
+ k s
L s
(v · r ) α
diffuse
diffuse
+
specular
diffuse
+
ambient
DCP4516 Introduction to Computer Graphics 21

Coefficients
•3 color channels and 3 surface types
•9 coefficients for each point light source
–L ra
, L rd
, L rs
, L ga
, L gd
, L gs
, L ba
, L bd
, L bs
•Material properties
–9 absorption coefficients
•k ra , k rd , k rs , k ga , k gd , k gs , k ba , k bd , k bs
–Shininess coefficient α
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Modified Phong Model
•Problem: In the specular component of
Phong model, it requires the calculation of a
new reflection vector and view vector for
each vertex
r = 2 (l · n ) n - l
•Blinn suggested an approximation using the
halfway vector that is more efficient
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The Halfway Vector
•h is the normalized vector halfway between
l and v
h = ( l + v )/ | l + v |
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Using the Halfway Angle
•Replace (v · r ) α by (n · h ) b
•b is chosen to match shininess
•Note that halfway angle is half of angle
between r and v if vectors are coplanar
l
n h
φ Θ-φ
θ θ Φ
r
v
2
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Blinn lighting model
•Resulting model is known as the modified
Phong or Blinn lighting model
•Specified in OpenGL standard and most
real-time applications
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Example
Teapots with
different
parameters.
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Computation of Vectors
•l and v : specified by the application
•r: computed from l and n
•Determine n
–OpenGL leaves determination of normal to
application; exception for GLU quadrics and Bezier
surfaces
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Plane Normals
•Equation of plane: ax+by+cz+d = 0
•Normal can be obtained by
n = (p 2 -p 0 ) × (p 1 -p 0 )
n
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Normal to Sphere
•Implicit function f(x,y.z)=0
•Normal given by gradient
•Sphere
–n = [∂f/∂x, ∂f/∂y, ∂f/∂z] T
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Parametric Form
•For sphere
x = x(u,v) = cos u sin v
y = y(u,v) = cos u cos v
z = z(u,v) = sin u
•Tangent plane determined by vectors
∂p/∂u = [∂x/∂u, ∂y/∂u, ∂z/∂u] T
∂p/∂v = [∂x/∂v, ∂y/∂v, ∂z/∂v] T
•Normal given by cross product
n = ∂p/∂u × ∂p/∂v
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What’s next
•So far, we know how to compute the color at
a point given lighting model, illumination
model, and surface normals
•The required computation can be huge if we
compute for every point on a surface
•Exploit efficiency by decomposing curved
surfaces into many small flat polygons
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Polygonal Shading
•Curved surfaces are approximated by polygons
•How do we shade
–Flat shading
–Interpolative shading
–Gouraud shading
–Phong shading (not Phong reflection model)
•Two questions:
–How do we determine normals at vertices
–How do we calculate shading at interior points
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Flat Shading:
•Normal: given explicitly before vertex
glShadeModel(GL_SMOOTH);
glNormal3f(nx, ny, nz);
glVertex3f(x, y, z);
•Shading constant across polygon
•Single polygon: first vertex
•Triangle strip: vertex n+2 for triangle n
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Flat Shading Assessment
•Inexpensive to compute
•Appropriate for objects with flat faces
•Less pleasant for smooth surfaces
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Flat Shading and Perception
•Lateral inhibition: exaggerates perceived
intensity
•Mach bands: perceived “stripes”along edges
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Interpolative Shading
•Enable with glShadeModel(GL_SMOOTH);
•Calculate color at each vertex
•Interpolate color in interior
•Compute during scan conversion
(rasterization)
•More expensive to calculate
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Gouraud Shading
•Special case of interpolative shading
•How do we calculate vertex normals
•Gouraud: average all adjacent face normals
•Requires knowledge
about which faces share
a vertex—adjacency info
DCP4516 Introduction to Computer Graphics 39

Gouraud Shading Algorithm
•Find average normal at each vertex
•Apply Phong reflection model at each vertex
•Linearly interpolate vertex shades (colors)
across each polygon I 1 (x 1 , y 1 )
I
I
I
a
b
s
y
y
x
1
1
b
1
y
1
y
1
x
2
4
a
I
y
y
I y
y
1
I
y
y
I y
y
1
I
x
x
I x
x
a
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s
s
b
2
4
s
2
4
b
1
1
s
s
s
a
I a (x a , y s )
I 2 (x 2 , y 2 )
I s (x s , y s )
I 3 (x 3 , y 3 )
I b (x b , y s )
I 4 (x 4 , y 4 )

Phong Shading
•Interpolate normals rather than colors
•Significantly more expensive
•Mostly done off-line (not supported in
OpenGL)
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Phong Shading Algorithm
•Find vertex normals
•Interpolate vertex normals across edges
•Find shades along edges
•Interpolate edge shades across polygons
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Polygonal Shading Summary
•Gouraud shading
–Set vertex normals
–Calculate colors at vertices
–Interpolate colors across polygon
•Must calculate vertex normals!
•Must normalize vertex normals to unit length!
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