1. GR2 Advanced Computer Graphics AGR
Lecture 5
Getting Started with OpenGL
A Simple Reflection Model 1 1

2. 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 4 4

3. 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();
See Chapter 2 of the OpenGL Programming Guide 5 5

4. 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
See Chapter 3 of OpenGL Programming Guide 6 6

5. 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
See Appendix C of OpenGL Programming Guide 7 7

6. 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 8 8

7. How to Get Started Look at the GR2 practicals page: Points you to:
practicals.html
Points you to:
example programs
information about GLUT
information about OpenGL
a simple exercise

8. A Simple Reflection Model10 10

9. 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 11 11

10. 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 12 12

11. Diffuse Reflection and Specular Reflection - Phong Approach
white
light
specular reflection (white)
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.
diffuse reflection
(yellow)
yellow
pigment particles
microscopic view 13 13

12. 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 14 14

13. Reflection Model - Ambient Light
hemisphere
of ambient
light
surface P
Ia = Intensity of ambient light
Ka = Ambient-reflection
coefficient
I = Reflected intensity
= wavelength of light
I ( )= Ka ( )Ia() 15 15

14. Reflection Model - Diffuse Reflection
light
source
light
source P 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
light
source N L 
surface 16 16

15. Reflection Model - Diffuse Reflection
light
source N L 
surface
Light reflected equally
in all directions, with
intensity depending on
angle  between light and
surface normal:
I* = Intensity of light source
N = Surface normal
L = Direction of light source
Kd = Diffuse-reflection
coefficient
I = Reflected intensity
I = Kd ( cos ) I* 17 17

16. Reflection Model - Diffuse Reflection
light
source
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 N L 
surface
I (  ) = Kd() ( L . N ) I*() 18 18

17. Reflection Model - Specular Reflection
light
source R P
In perfect specular reflection, light is only
reflected along the unique direction symmetric
to the incoming light 19 19

18. Reflection Model - Specular Reflection
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. 20 20

19. 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.

20. 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 

21. Reflection Model - Specular Reflection
light
source N R
eye L V 
surface
Intensity depends on
angle between eye and
reflected light ray:
I* = Intensity of light source
V = View direction
R = Direction of perfect
reflected light
Ks = Specular-reflection
coefficient
I = Reflected intensity
I = Ks( cos )n I*
n varies with material
large n : shiny
small n : dull 21 23

22. Reflection Model - Specular Reflection
light
source N R
eye L V 
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 22 24

23. Ambient, Diffuse and Specular
Reflection Model -
Ambient, Diffuse and Specular
light
source N R
eye L  V 
surface
I() = Ka()Ia() + ( Kd()( L . N ) + Ks( R . V )n ) I*() 23 25

24. 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, K3 constant
- often K2=1, K3=0
K1 + K2*d + K3*d2 24 26

25. Final Reflection Model
light
source N R
eye L  V  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 27

26. 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 28

27. 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 27 29

28. 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)
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) N R R L N V H R L 28 30

29. 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. 29 31

30. 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 30 32

31. Example - Ambient Reflection

32. Example - Ambient and Diffuse

33. Ambient, Diffuse and Specular