1. SI23 Introduction to Computer Graphics
Lecture 13 – Simple Reflection Model

2. 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

3. Phong Reflection Model
The most common reflection model in computer graphics is due to Phong Bui-tuong - in 1975
Has proved an acceptable compromise between simplicity and accuracy
Largely empirical
It is a local reflection model – does not handle global effects of light reflecting between surfaces
Ray tracing and radiosity methods will handle this 12 12

4. 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

5. 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

6. 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

7. Ambient Lighting

8. 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

9. 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

10. 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

11. Ambient and Diffuse

12. 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

13. 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

14. 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.

15. 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 

16. 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

17. Reflection Model - Specular Reflection
light
source N R
eye L
Note: intensity
forms ‘ellipse’ shape 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

18. Ambient, Diffuse and Specular

19. 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

20. Example - Ambient Reflection

21. Example - Ambient and Diffuse

22. Ambient, Diffuse and Specular

23. 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

24. 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

25. Phong illumination model: Ks 0.0 to 1.0, Kd 0.0 to 1.0
(Ka = 0.7, n = 10.0) Ks Kd

26. Phong Illumination Model: Ks 0.0 to 1.0; n = 10.0 to 810.0
(Ka = 0.7, Kd = 1.0) n Ks

27. 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 in Phong model but …. 30 32

28. Specular Reflection in Reality
Really… specular reflection depends a little bit on:
Angle of incidence of light
Material proerties of surface
Thus OpenGL for example will allow different specular reflection coefficients in R,G, B channels

29. 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

30. Programming Reflection in OpenGL
Light sources
Read pp13-14 of guide
To set position
glLightfv(GL_LIGHT1, GL_POSITION, ptCoords)
To set colour
glLightfv(GL_LIGHT1, GL_DIFFUSE, rgba_colour)
Remember to activate lights (glEnable)
Surface Reflection
Read p15 of guide
To set material property – ie reflection coeffs (at each vertex of model)
glMaterialfv (GL_FRONT, GL_DIFFUSE, myDiffuse)
where
Glfloat myDiffuse[] = {0.8, 0.3, 0.4, 1.0}

31. Coursework 3
London Eye

32. Acknowledgements
Thanks to Alan Watt for the images