1. Advanced Computer Graphics
and
Virtual Environments
LIGHTING

2. Lecture overview Introduction to the lighting problem Ray tracing
Radiosity
Ronald: introduction lighting problem + basic principles of ray tracing
Romke: ray tracing optimization
Ralf/Maarten: radiosity

3. I – The lighting problem

4. complexity of interaction between light and objects in a scene
The lighting problem
Lighting scenes:
the major and central conceptual and practical problem of computer graphics
Reason:
complexity of interaction between light and objects in a scene
The lightning problem

5. Light: the fundamental equation
Input:
Emission (Φe)
In-scattering (Φi)
Output:
Streaming (Φs)
Out-scattering (Φo)
Absorption (Φa)
Input == output
Φe + Φi == Φs + Φo + Φa
Radiance equation:
Φ(p,ω) = emitted radiance +
total reflected radiance
- Radiance equation can be derived from fundamental light equation (after some simplifications and introduction of terms)
- The problem in CG boils down to solving Φ(p,ω) for all points and directions
Illustration of radiance equation

6. Four classes of solutions of radiance equation
LOCAL
GLOBAL
View dependent
“real-time” graphics
Ray tracing
Monte Carlo path tracing
View independent
“flat-shaded” graphics
Radiosity
Monte Carlo photo tracing
- (a) shows local illumination model for ray tracing
- (d) shows local illumination model for radiosity
- Local: no recursion; only look at light coming directly from light source (and ambient light)
The lighting problem

7. Rendered or real?
As pointed out, there are local and global solutions of the radiance equation. Global solutions can account for a much higher degree of ‘photo-reality’ than local solutions can. However, global solutions also take a lot more time to compute. The figures seen here are all computer-rendered (with rendering times of several hours).

8. II – Local Illumination

9. Local illumination model
We are looking for the intensity (Ir) radiating from an object (i.e. Φ(p,ω))
Three components Ir :
Ambient lighting
Specular lighting
Diffuse lighting
Ir = ambient + specular + diffuse
NB: Formally, we should split Ir into Ir,red, Ir,green and Ir,blue
- The total intensity radiating from an object consists of R,G and B component; for the sake of simplicity we ignore this fact for the moment
Local Illumination

10. Component 1: ambient lighting
Ambient light models global illumination
Each object is illuminated to a certain extent by “stray” light
Assumed constant across a whole scene (Ia)
Often used simply to make sure everything is lit, just in case something isn’t struck by light directly from a light source
Ir = kaIa
(ka : proportion of light reflected rather than absorbed by the material)
Actually we should distinguish between I[r,red], I[r,green] and I[r,blue].
Local illumination

11. Component 2: specular lighting
Perfect specular reflection 
Light
Glossy specular reflection
‘Shininess’ parameter m defines the degree of glossiness (Phong exponent)
Local illumination

12. Component 2: specular lighting
Imperfect specularity (Phong) E N H L
surface
N: surface normal
E: direction to eye
L: direction to light
H: bisects E and L
(halfway vector)
Ir = ksIi (h.n)m
ks : proportion of light reflected rather than absorbed by the material
m : Phong exponent(‘shininess’)
Local illumination

13. Component 3: diffuse lighting
Lambert’s Law
Diffuse reflector scatters light
Assume equality in all direction
Called Lambertian surface
Angle of incoming light is still critical
Local illumination

14. Component 3: diffuse lighting
L is the direction to the light
N is the surface normal
Incoming intensity of light is proportional to d
d is proportional to cos  = N.L
Ir = kdIi (n.l)
Local illumination

15. Local Illumination model - summary
Ir = ambient + diffuse + specular = Ir,a + Ir,d + Ir,s
Putting things together gives the following local illumination model:
Ir = kaIa + kdIi(n.l) + ksIi (h.n)m
An analogous model applies for multiple light sources
This model does however not yet account for global effects and shadows
Local Illumination

16. III – Ray Tracing

17. Ray Tracing
Basic principles
Accounts for:
Local illumination effects
Object inter-reflection (for specular surfaces only)
Transparency / ray transmission
Occlusion/shadows
Follows the rays in reverse (start at pixel in view plane)

18. Correct for non-visible lights
E: direction to eye
N: surface normal
L: direction to light
H: bisects E and L E L
surface
- Basically this is an extension to the local illumination model;
- Adjustment of the formula is quite straighforward (addition of S). Detecting object interference, however, can be quite hard/computational expensive
Ir = kaIa + S * Ii(kd(n.l)+ks(h.n)m
(S is a ‘shadow feeler’: 0 if light source not visible, 1 otherwise)
Ray Tracing

19. Adding reflection to the model
N: surface normal
E: direction to eye
L: direction to light
H: bisects E and L E L
surface
Ir = Ilocal + krIr
Ray Tracing

20. Adding transparency to the modelα T β
transparent
object
Snell’s Law
N: surface normal
E: direction to eye
L: direction to light
H: bisects E and L
R: direction of reflection
T: transmitted ray
η: index of
refraction
Ray tracing

21. Putting everything together
Illustration of the basic ray tracing model
Ray tracing

22. Summary
Recursive ray tracing is a good simulation of specular reflections
We’ve seen how the ray-casting can be extended to include shadows, reflections and transparent surfaces
Next:
Ray Tracing optimization
Radiosity ( )
Ray tracing