Transcript CS430 Computer Graphics - Winona State University

CS430
Computer Graphics
Lighting and Shading
Chi-Cheng Lin, Winona State University
Topics
Introduction
 Geometric Model in Lighting
 Colored Surfaces and Lights
 Shading and Graphics Pipeline
 Flat Shading and Smooth Shading

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Introduction

Lighting
Process of computing the luminous
intensity reflected from a specific 3-D point

Shading
Process of assigning colors to pixels

Shading model dictates how light is
scattered or reflected from a surface
We will begin with achromatic light then
colored lights
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Introduction

Two types of light sources
Point light source
Ambient light

Light interacts surfaces in different ways
Absorbed by surface
Reflected by surface
Transmitted into the interior

What absorbs all of the incident
achromatic light?
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Introduction

Types of reflection of incident light
Diffuse scattering
Some of the incident light penetrates the
surface slightly and is re-radiated uniformly in all
directions
Scattering light interacts strongly with surface
 color is affected by nature of surface material
Specular reflections
Incident light does not penetrate the surface
Reflected directly from the surface
More mirror like and highly directional
Highlight, shiny, plastic like
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Introduction

Total light reflected from the surface in
a certain direction is the sum of
Diffuse components
Specular components

We calculate the size of each
component that reaches the eye for
each point of interest on surfaces
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Geometric Model in Lighting

Principle vectors to find amount of light
reaching the eye from a point P
m: normal vector of surface at P
v: from P to the eye
s: from P to light source
s
Angles between vectors are
calculated in the world
coordinates
 Is:
m
P
v
eye
intensity of light source
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 Id:
Diffuse Component
intensity of the diffused component
Scattering is uniform in all directions
Independent of v
unless m  v  0, where Id = 0 (why?)

Lambert’s law: brightness is proportional
to the area subtended (= fraction cos())
  0: brightness varies slightly with angle
  90°: brightness falls rapidly to 0
m
s

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Diffuse Component

ˆ
cos() = ˆs  m
 I d  I s  d max(( ˆ
ˆ ), 0 ),
s m
where  d  diffuse reflection

coefficien t
How do we calculate/obtain the value
for d ? By experiments.
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Specular Reflection
 Isp:
intensity of specular reflection
 Phong model is used to approximate
highlight
Amount of light reflected is greatest in the
direction of perfect mirror reflection, r
Amount of light reflected diminished
rapidly at the nearby angles
Beam pattern
r
m
s
P
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Specular Reflection
ˆ )m
ˆ ?
Remember r   s  2 ( s  m
 Amount of light reflected falls off as 
increases and is approximately cosf(),
where f is the Phong exponent

 I sp  I s  s (ˆ
ˆ )f ,
rv
where  s  specular
s

reflection
r
m

v
coefficien t
eye
Problem: expensive to compute as r has
to be found and normalized
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Specular Reflection

Solution (proposed by Jim Blinn)
Calculate h = s + v
Let  be the angle between h and m
Use  to calculate the falloff of specular
intensity as  has the same property as 
  , but can be compensated by different
=0 m =h
value of f
m h
s
s

v
v
ˆ m
 I sp  I s  s max(( h
ˆ ) f ,0 )
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Ambient Light

A uniform background glow in the
environment
Source is not situated at any particular place
Light spreads uniformly in all directions
 Ia:
intensity of light source
 Iaa is added to the light reaching the eye
a: ambient reflection coefficient
a is often the same as d
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Combining Light Contributions

I = Ia a + Id d  lambert + Isp s  phongf
lambert = max(( ˆs  m
ˆ ), 0 )
phong = max(( hˆ  m
ˆ ), 0 )

Implications for different points P on a facet
Ambient is not changed for different P
m is the same for all point on the facet
If the light is far far away, s will change slightly
as P changes  diffuse will change slightly on
different P
If the light or/and eye is/are close, s and h will
change a lot as P changes  specular changes
significantly over the facet
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Colored Surfaces and Lights

Colored surface
Ir = Iar ar + Idr dr  lambert + Ispr sr  phongf
Ig = Iag ag + Idg dg  lambert + Ispg sg  phongf
Ib = Iab ab + Idb db  lambert + Ispb sb  phongf
lambert and phong terms do not depends on
color component
 We have to define 9 reflection coefficients

Ambient and diffuse reflection are based on the
color of surface
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Colored Surfaces and Lights

Colored light (Isr, Isg, Isb)
If the color of a surface is (r, g, b), then it is
reasonable to set
(ar, ag, ab) = (dr, dg, db) = (rK, gK, bK),
where K is the fraction of light reflected
The diffusion of the surface =
(Isrdr, Isgdg, Isbdb) = (IsrrK, IsggK, IsbbK)

Example: white light
Isr = Isg = Isb = I, (r, g, b) = (0.3, 0.45, 0.25)
then diffusion = (0.3IK, 0.45IK, 0.25IK) 
the surface is seen as its color
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Colored Surfaces and Lights

Color of specular light
Often the same as that of light source

Example: sunlight
Highlight on plastic caused by sunlight is
white
Set (sr, sg, sb) = (s, s, s)
s = 0.5  slightly shiny
s = 0.9  highly shiny

Different coefficients are selected for
specific materials. (Fig 8.17)
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Shading and Graphics Pipeline
Vertices are sent down the pipeline
along with their associated normals
 All shading calculations are done on
vertices

v 1 , m1
v2, m2
v 0 , m0
VM
projection
matrix
clip
viewport
matrix
shading is
applied here
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Shading and Graphics Pipeline
Lights are objects and the positions of
light sources are also transformed by
the modelview matrix
 After all quantities are expressed in
camera coordinates, colors are attached
to vertices using the formula
 If an object is clipped, normals of newly
generated vertices are calculated by
interpolation

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Flat Shading and Smooth Shading

Polygonal face in 3D space
Individual face
Underlying surface approximated

Shading methods
Flat shading
Smooth shading
Gouraud shading
Phong shading
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Comparison of Shading Methods
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Flat Shading

Entire face is drawn with the same color

Lateral inhibition
When there is a discontinuity across an
object, the eye manufactures a Mach band
at the discontinuity and a vivid edge is seen

Specular highlights are rendered poorly
Either no highlight at all
Or highlight on the entire face
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Smooth Shading
Smooth shading computes colors at more
points on each face to de-emphasize
edges between adjacent faces
 Use linear interpolation
 Gouraud shading

Interpolate vertex colors

Phong shading
Interpolate vertex normals
Interpolate normal for each pixel
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Gouraud Shading
Used by OpenGL
 Example

color3
colora: by interpolating
color2
color3 and color4 colora
colorb
colorb: by interpolating color
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color1
color1 and color2
Colors of pixels on the horizontal line
segment is obtained by interpolating
colora and colorb

Does not picture highlights well
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Phong Shading
Compute normal at each pixel by
interpolating the normals at the vertices
 Apply the shading model to to every
point to find the color
 Example
m3

ma: by interpolating m3 and m4
mb: by interpolating m1 and m2
m2
Normals of pixels on the
ma
mb
horizontal line segment is
m4
m1
obtained by interpolating ma and mb
Colors of the pixels are then computed
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Phong Shading
Very smooth appearance
 Highlights are approximated better
 Principle drawback

Heavy computation  slow speed

Not supported by OpenGL
Can be approximated using texture
mapping

Phong shading  Phong model
Don’t be
confused!!
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