Illumination

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Illumination Shading Comp 575 - Fall 2008
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What is a Shading Model?

• Model of how light interacts with materials
• We will discuss the common, heuristic shading
  models
• Flat
• Gouraud
• Phong
• Not physically based work well in practice and
  are common on most graphics boards

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Diffuse Objects

• For matte objects with no shininess
• Diffuse/matte objects are called Lambertian
• Shading does not vary with viewpoint
• Example a piece of paper, chalk board
• Reflected light is scattered equally in all
  directions

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Lambertian Surface

• Obeys Lamberts Law (from physics)
• The color, c, of a surface is proportional to
  the cosine of the angle between the surface
  normal and the direction of the light source

l
l
n
l
n
n
q
q
q
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Lambertian Surface

• Lamberts Law As the angle (q) between the
  surface normal (n) and the light direction (l)
  increases, the same amount of light (A) falls on
  a larger surface area (x) ? surface is dimmer
• Diffuse color is independent of the eye position
  
• As you move from the light location, you see more
  area, but the amount of light reflected at that
  angle per visible unit area of surface is
  proportionally less

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Diffuse Lighting Model
Lets define a lighting model that captures this
Angle between light and the normal
Light color 0,1 (RGB)
Avoid negative light when q gt 90
Diffuse reflectance color fraction of light
reflected from the surface (RGB)
l
n
What happens if light source is at infinity?
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Ambient Term

• Lambertian model produces black for any surface
  facing away from the light
• In reality, light bounces off walls, is scattered
  in the atmosphere, etc., so surfaces facing away
  from the light arent usually black
• Add an ambient light term for all other light
  (a hack)
• to ensure 0 ? c ? 1, ca cl ? (1,1,1)

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Phong Illumination

• What about highlights on shiny surfaces?
• Highlight moves with eye location
• Highlight is brightest when j is 0 c ? (cos j)p
  (v ? r)p

n
Reflected (r)
l
Viewer (v)
j
Specular Color
Phong exponent
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Specular Highlights
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Whats Happening to the Light
Less Shiny Surface
Dull Surface
Shiny Surface
Perfect Mirror
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Phong Exponent

• The exponent p controls the sharpness of the
  highlight larger p produces sharper highlight

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p 1
p 2
p 4
p 1
(cos j)p
p 4
p 32
p 8
p 16
p 16
p 64
p 256
p 64
p 128
p 256
0
j
0
90
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Phong Illumination Computing r

• How can we compute the reflection vector r?

n and l are unit vectors
n
r
s
-s
l
n(nl)
Solve for s
Substitute s
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Complete Illumination Equation

• The complete illumination equation models
• Ambient light
• Diffuse reflections
• Specular reflections
• We can combine all of these together into a
  single equation

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Multiple Light Sources

• Our current equation deals with a single light
  source
• How do we account for additional light sources?
• Compute dot products with each light and sum them
  up.

Original Equation
Factor out cl and add N lights
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Shadows

• What about shadows?
• If a point is visible from a light, illuminate
  it. If not, dont.
• Introduce a visibility term Si for each (point,
  light) pair.
• Si 0 if the point is not visible, Si 1 if it
  is visible

visibility term
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Multiple Light Sources
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RGB Colors

• Illumination of a point on a surface
• This equation computes one color channel
• Since we are working in RGB space, we need to
  compute the equation once each for red, green,
  and blue
• Also make sure you clamp all colors at 1

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Illumination vs. Shading

• Illumination of an entire surface is termed
  shading.
• Expensive to compute at every visible point (but
  we can do it, if desired)
• We have three basic options
• Per polygon (flat shading) entire polygon gets
  the same color
• Per vertex (Gouraud Shading) compute
  illumination at each vertex and interpolate
  vertex colors
• Per pixel (Phong Shading) interpolate vertex
  normals and compute illumination for each pixel

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Flat Shading

• Compute one normal for each polygon
• Assumes light is very distant
• Assumes polygon exactly represents the actual
  surface, not an approximation
• i.e. cube vs. cylinder
• Interpolation is not used
• Faceting occurs when used on approximating
  surfaces

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Flat Shading

• You get faceted images

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Gouraud Shading

• Compute the normal, ni, at each vertex
• Compute color at each vertex using the
  illumination model
• Interpolate colors across the polygon during scan
  conversion
• Assumes the polygons
• approximate a curved surface
• Problems?

n0
n1
n2
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Interpolating Colors
c1
y1
ca
cb
ys
cs
y2
c2
y3
c3
Same as interpolating z-values.
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Computing the Normal

• Often the polygon will come with normals
  associated with the vertices.
• How do we compute them if they are not given?
• First compute polygon normals for each polygon
• Given a polygon with vertices p0, p1, and p2
  (Assume the vertices are specified in
  counter-clockwise order)
• Compute two edge vectors, v0 and v1
• Take the cross product between vectors
• This gives the normal for the polygon
• Repeat this for each polygon

n v0 x v1
p0
v1 p2 - p0
v0 p1 - p0
p2
p1
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Computing the Normal (cont)

• For each vertex, find all polygons that contain
  the vertex
• for vertex v0, these are polygons p1, p2, p3, and
  p4
• Take the average of the polygon normals
• This gives the normal nv0 at
• the vertex
• Repeat this for each vertex

v3
nv0
n2
n3
p2
p0
v0
p3
p1
p4
v2
v4
n1
n4
v1
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Shading

• Now, with all vertex normals computed, we can
  shade using Gouraud shading
• Where does Gouraud shading fall short?
• Highlights on the interior of the polygon
• How can we handle those?
• Phong Shading

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Phong Shading

• Compute normal, ni, at each vertex
• Interpolate normals during scan conversion
• Compute color with the interpolated normals
• More expensive illumination is computed for
  every visible pixel instead of each vertex.
• Captures highlights in the middle of a polygon
• Looks smoother across edges
• In my opinion, well worth the
• extra computation.

n0
n1
n
n2
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Graphics Historical Note

• Who were Phong and Gouraud?
• PhD Students at the University of Utah in the 70s
• Much of what youre learning in this class was
  discovered at Utah in the 70s.
• For several years it was the only place to
  computer graphics research.

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Problems with Interpolated Shading

• Silhouettes
• Translucent materials
• Perspective distortion causes problems Imagine a
  polygon with 1 vertex at a very different depth
  than others
• Interpolation considers equal steps in y, but
  foreshortening produces unequal steps in depth
• Problem reduced by using many small polygons
• Orientation dependence for non-triangles
• Shared vertices on an edge

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Potential Problems

• If the surface normals fluctuate, the vertex
  normals may get interpolated incorrectly.

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Silhouettes Problem
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Cant Handle More Complicated Materials
Brushed Aluminum
Isotropic (Normal)
Satin
Velvet