GR2
Advanced Computer Graphics
AGR
Lecture 5
Getting Started with OpenGL
A Simple Reflection Model
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What is OpenGL?

OpenGL provides a set of routines for
advanced 3D graphics
– derived from Silicon Graphics GL
– acknowledged industry standard, even on
PCs (OpenGL graphics cards available)
– integrates 3D drawing into X (and other
window systems such as Windows NT)
– draws simple primitives (points, lines,
polygons) but NOT complex primitives
such as spheres
– provides control over transformations,
lighting, etc
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Geometric Primitives
Defined by a group of vertices - for
example to draw a triangle:
glBegin (GL_POLYGON);
glVertex3i (0, 0, 0);
glVertex3i (0, 1, 0);
glVertex3i (1, 0, 1);
glEnd();


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See Chapter 2 of the OpenGL
Programming Guide
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Viewing

OpenGL maintains two matrix
transformation modes
– MODELVIEW
to specify modelling transformations, and
transformations to align camera
– PROJECTION
to specify the type of projection (parallel or
perspective) and clipping planes

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See Chapter 3 of OpenGL
Programming Guide
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OpenGL Utility Library (GLU)

Useful set of higher level utility routines
to make some tasks easier
– written in terms of OpenGL and provided
with the OpenGL implementation
– for example, gluLookAt() is a way of
specifying the viewing transformation

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See Appendix C of OpenGL
Programming Guide
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OpenGL Utility Toolkit (GLUT)
Set of routines to provide an interface to
the underlying windowing system - plus
many useful high-level primitives (even a
teapot - glutSolidTeapot()!)
 Improved version of the ‘aux’ library
described in Appendix E of the Guide
 Allows you to write ‘event driven’
applications

– you specify call back functions which are
executed when an event (eg window resize)
occurs
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How to Get Started

Look at the GR2 practicals page:
– http://www.scs.leeds.ac.uk/kwb/GR2/
practicals.html

Points you to:
– example programs
– information about GLUT
– information about OpenGL
– a simple exercise
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A Simple Reflection Model
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What is a Reflection Model?

A reflection model (also called lighting
or illumination model) describes the
interaction between light and a
surface, in terms of:
– surface properties
– nature of incident light

Computer graphics uses a
simplification of accurate physical
models
– objective is to mimic reality to an
acceptable degree
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Phong Reflection Model
The most common reflection model in
computer graphics is due to Bui-Tuong
Phong - in 1975
 Has proved an acceptable
compromise between simplicity and
accuracy
 Largely empirical

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Diffuse Reflection and Specular
Reflection - Phong Approach
white
light
specular reflection (white)
diffuse reflection
(yellow)
microscopic view
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yellow
pigment particles
Some light reflected
directly from surface.
Other light passes into
material. Particles of
pigment absorb certain
wavelengths from
the incident light, but
also scatter the light
through multiple
reflections - some
light emerges back
through surface as
diffuse reflection.
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Ambient Reflection
In addition to diffuse and specular
reflection, a scene will also include
ambient reflection
 This is caused by light falling on an
object after reflection off other
surfaces

– eg in a room with a light above a table,
the floor below the table will not be totally
black, despite having no direct
illumination - this is reflection of ambient
light
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Reflection Model - Ambient
Light
hemisphere
of ambient
light
surface
P
I ( )= Ka ( )Ia()
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Ia = Intensity of ambient light
Ka = Ambient-reflection
coefficient
I = Reflected intensity
= wavelength of light
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Reflection Model - Diffuse
Reflection
light
source
light
source
P
Light reflected equally in all
directions - intensity dependent
on angle  between light source
and surface normal
Lambert’s cosine law: I = I* cos 
where I* is intensity of light
source
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N

L
light
source
surface
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Reflection Model - Diffuse
Reflection
light
source
N
L

Light reflected equally
in all directions, with
intensity depending on
angle  between light and
surface normal:
I = Kd ( cos ) I*
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surface
I* = Intensity of light source
N = Surface normal
L = Direction of light source
Kd = Diffuse-reflection
coefficient
I = Reflected intensity
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Reflection Model - Diffuse
Reflection
light
source
N
L

surface
The angle between two vectors is given by
their dot product: cos  = L . N (assume L, N
are unit length)
 The coefficient Kd depends on the
wavelength of the incoming light
I (  ) = Kd() ( L . N ) I*()

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Reflection Model - Specular
Reflection
N
light
source
R
P
In perfect specular reflection, light is only
reflected along the unique direction symmetric
to the incoming light
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Reflection Model - Specular
Reflection
N
light
source
R
P
In practice, light is reflected within a small angle of
the perfect reflection direction - the intensity of the
reflection tails off at the outside of the cone. This
gives a narrow highlight for shiny surfaces, and a
broad highlight for dull surfaces.
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Reflection Model - Specular
Reflection

Thus we want to model intensity, I, as
a function of angle between viewer
and R, say , like this:
I

with a sharper peak for shinier surfaces, and broader peak
for dull surfaces.
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Reflection Model - Specular
Reflection
Phong realised this effect can be
modelled by:
(cos  )n
with a sharper peak for larger n

I
n=1
n=10
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
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Reflection Model - Specular
Reflection
eye
R
light
source
N
V 
L
surface
Intensity depends on
angle between eye and
reflected light ray:
I = Ks( cos )n I*
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n varies with material
large n : shiny
small n : dull
I* = Intensity of light source
V = View direction
R = Direction of perfect
reflected light
Ks = Specular-reflection
coefficient
I = Reflected intensity
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Reflection Model - Specular
Reflection
eye
R
V 
light
source
N
L
surface
Using cos = R . V (R, V unit vectors), we have:
I () = Ks ( R . V )n I()*
Note: Ks does not depend on the wavelength  - hence
colour of highlight is same as source
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Reflection Model Ambient, Diffuse and Specular
eye
R
V 
light
source
N
L

surface
I() = Ka()Ia() + ( Kd()( L . N ) + Ks( R . V )n ) I*()
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Reflection Model - Effect of
Distance
light
source
d
surface
The intensity of light reaching a surface
decreases with distance - so we use typically:
I*
K1 + K2*d + K3*d2
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K1, K2, K3 constant
- often K2=1, K3=0
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Final Reflection Model
eye
R
V 
light
source
N
L

d
surface
I() = Ka()Ia() + ( Kd()( L . N ) + Ks( R . V )n ) I*()
K1 + K2*d + K3*d2
This needs to be applied for every light source in the scene
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Phong Model in Practice
In practice, some simplifications are
made to the model for sake of
efficiency
 For example, ambient light is
sometimes assumed to be a constant
 Other simplifications are:

– lights at infinity
– simple colour model
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Practicalities - Effect of
Distance

There are advantages in assuming
light source and viewer are at infinity
– L and V are then fixed for whole scene
and calculations become simpler
Lights at infinity are called directional
lights
 Lights at a specified position are
called positional, or point, lights

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Practicalities - Calculating R
R + L = 2 ( N.L ) N
hence
R = 2 ( N.L )N - L
 In practice,
implementations often
compute H = ( L + V ) / 2
and replace (R.V) with (H.N)
N

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– these are not the same, but
compensation is made with
choice of n (angle between
N and H is half angle
between R and V)
R
V
R
R
L
N
H
L
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Practicalities - Calculating R
As noted, if viewer and light source
both sufficiently far from surface, then
V and L are constant over scene - and
also H
 Then, for nonplanar surfaces, the
calculation:
N.H
is faster than R . V because R needs to
be evaluated at each point in terms of
N.

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Practicalities - Effect of Colour
The Phong reflection model gives reflection
for each wavelength  in visible spectrum
 In practice, we assume light to be
composed as a mixture of RGB (red, green,
blue) components - and reflection model
is applied for each component
 Coefficients of ambient-reflection (Ka) and
diffuse-reflection (Kd) have separate
components for RGB
 Coefficient of specular-reflection (Ks) is
independent of colour
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
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Example - Ambient Reflection
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Example - Ambient and Diffuse
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Ambient, Diffuse and Specular
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