1. Illumination Models Chapter 14 Section 14.1 to 14.2
Some of the material in these slides may have been adapted from University of Virginia, MIT, MIT, Colby College, and Åbo Akademi University

2. What we will study Not much time is left for graphics
We will study two things
Lighting Models
Surface Rendering
If we have time we will talk about color models

3. Solving the Lighting Problem
We somewhat understand the perception of light (color)
We engineered a solution to representing and generating color using computers
We need to understand the interplay of light and objects

4. Lighting Remember, we know how to rasterize But …
Given a 3-D triangle and a 3-D viewpoint, we know how to compute pixel positions to represent a shape
But …
How bright should each pixel be?
What color should those pixels be?

5. Lighting
If we’re attempting to create a realistic image, we need to simulate the lighting of the surfaces in the scene
Fundamentally simulation of physics and optics
Computationally intensive
As you’ll see, we use a lot of approximations (a.k.a perceptually based hacks) to do this simulation fast enough

6. Images by Henrik Wann Jensen
Definitions
Illumination: the transport of energy from light sources to surfaces & points
Note: includes direct and indirect illumination
Images by Henrik Wann Jensen

7. Definition Illumination Model, A.K.A
Lighting model
Shading model
In terms of graphics, illumination is the process of computing the luminous intensity (i.e., outgoing light) at a particular 3-D point, usually on a surface
In some cases, shading model is defined differently as the process of computing colors

8. Goal of Illumination Model
Must derive computer models for ...
Emission at light sources
Scattering at surfaces
Reception at the camera
Desirable features …
Concise
Efficient to compute
“Accurate”

9. Illumination vs. Surface Rendering
Illumination model is an approximate mathematical model used to compute light intensity
Surface Rendering: The procedure of applying lighting model to obtain pixel intensities for all projected surfaces in the scene
A.K.A. surface shading (or just shading)
Realism involves
Accurate representation of objects
Accurate physical description of light effect on the scene

10. Light Sources vs. Reflecting Surface
Emits light energy
Reflecting Surface
Does not emit light
Reflects light
Object may be
Both source and reflecting surface
Example: Light bulb

11. Light Sources vs. Reflecting Surface
Point source
It is source that emits light equally in all directions from a single point
Simplest model
Dimension of light source is sufficiently small compared to illuminated objects
Far light sources
The sun can be accurately modeled as a point source

12. Light Sources vs. Reflecting Surface
Distributed light source
Light source dimensions are not small enough compared to illuminated objects
Modeled as accumulation of point sources on the surface of the light source
Accurate model for nearby sources
Fluorescent light

13. Light Sources vs. Reflecting Surface
Surface absorbs and reflects incident light
Diffuse Reflection
Light scattered by rough surface
Very rough surfaces tend to mainly diffuse light
Surface appears equally bright from all directions
Specular Reflection
Bright Spot
Occurs in addition to the diffuse reflection
More pronounced on polished surfaces
Diffuse Reflection
Specular Reflection

14. Basic Illumination Models
Simple and computationally efficient
Light source is considered point source specified by
Co-ordinates
Intensity
color
Reasonably good result
Intensity is computed based on optical surface properties
E.g. Glossy, opaque, transparent
Controls the amount of reflection and absorption

15. Ambient Light Objects not directly lit are typically still visible
e.g., the ceiling in this room, undersides of desks
This is the result of indirect illumination from emitters, bouncing off intermediate surfaces
Too expensive to calculate (in real time), so we use a hack called an ambient light source
No spatial or directional characteristics; illuminates all surfaces equally
Amount reflected depends on surface properties

16. Ambient Light It is indirect light comes from “everywhere” Idea
Calculate direct light only
Set indirect (ambient) light level to a constant Ia
Properties of Ambient light:
The amount of ambient light incident on every object is a constant for all surfaces and directions
No spatial or directional properties
The reflected light is constant, independent of viewing direction
The intensity of the reflected light depends on surface properties

17. Ambient Light If scene is only lit by Ambient source:
Light Position Not Important
Viewer Position Not Important
Surface Angle Not Important

18. Diffuse Reflection Ambient Light
Defined by ka, ambient diffuse reflection coefficient
Represents portion of reflected light
Between 0 and 1
Let a surface be exposed only to ambient light
Iambdiff be the intensity of the diffuse reflection at any point on the surface
Iambdiff = kaIa
where
ka [0,1] Ambient Reflection coefficient
Ia is the ambient light intensity
Produces a flat uninteresting shading

19. Diffuse Reflection Point Source
Want to model diffuse reflection from point sources
Ideal Diffuse reflector
Light is scattered equally to all directions irrespective of the direction of incident light
A.K.A Lambert Reflectors
An ideal diffuse reflector, at the microscopic level, is a very rough surface (real-world example: chalk, carpet, rough cloth)
Because of these microscopic variations, an incoming ray of light is equally likely to be reflected in any direction over the hemisphere

20. Diffuse Reflection Lambert’s Cosine Law
Ideal diffuse surfaces reflect according to Lambert’s cosine law:
The energy reflected by an infinitesimal surface element dA from a light source in a given direction is proportional to the cosine of the angle between that direction and the surface normal q dL dA
Surface

21. Diffuse Reflection Lambert’s Cosine Law
Note that the reflected intensity is independent of the viewing direction, but does depend on the surface orientation with regard to the light source

22. Diffuse Reflection Computing Diffuse Reflection
The angle between the surface normal and the incoming light is the angle of incidence:
Idiffuse = kd Ilight cos 
In practice we use vector arithmetic:
Idiffuse = kd Ilight (N • L)
where N, L are unit vectors L N 

23. Diffuse Reflection Sphere and a Point Source
Because diffuse reflection from point sources varies by angle of incidence, the sphere is NOT uniformly lit
Sphere seen at different lighting angles

24. Diffuse Reflection Combining Ambient and Point Source
Let’s assume that the reflection co-efficients of ambient and point sources are different
Additional parameter
More freedom to adjust lighting of the scene
Idiffuse = kaIa + kd Ilight (N • L)
where
kd, ka [0,1]
Remember: Viewer’s angle has no effect

25. Specular Reflection Shiny surfaces exhibit specular reflection
Polished metal
Glossy car finish
Apple
A light shining on a specular surface causes a bright spot known as a specular highlight
Where these highlights appear is a function of the viewer’s position, so, unlike diffuse reflection, specular reflectance is view dependent

26. Physics of Reflection on Perfect Surfaces
Reflection follows Snell’s Laws:
The incoming ray and reflected ray lie in a plane with the surface normal
The angle that the reflected ray forms with the surface normal equals the angle formed by the incoming ray and the surface normal:
(l)ight = (r)eflection

27. Geometry of Reflection Perfect Surfaces
Remember that N, L, and R are unit vectors
R is the reflection vector
We want to calculate R in terms of N and L because N and L are given values N R L qL qR
qL=qR

28. Geometry of Reflection Perfect Surfaces
Remember that |N| = |L| = 1
Hence cos(q) = N • L
Hence Lcos(q) = Ncos(q) = (N • L)L = (N • L)N N
(N.L)N R L
cos(qi)N qL qR
qL=qR

29. Geometry of Reflection Perfect Surfaces
2(N.L)N N R L qL qR
qL=qR

30. Geometry of Reflection Perfect Surfaces
L+R = 2(N.L)N L N R L q qL qR q
qL=qR

31. Geometry of Reflection Perfect Surfaces
R = 2(N.L)N  L
L+R = 2(N.L)N L N R L qL q qR q
qL=qR

32. Non-Ideal Specular Reflection
Snell’s law applies to perfect mirror-like surfaces, but aside from mirrors (and chrome) few surfaces exhibit perfect specularity
How can we capture the “softer” reflections of surface that are glossy rather than mirror-like?
One option: model the microgeometry of the surface and explicitly bounce rays off of it
Or …
Use approximate (and far simpler) models…

33. Non-Ideal Specular Reflection
Hypothesis: most light reflects according to Snell’s Law
But because of microscopic surface variations, some light may be reflected in a direction slightly off the ideal reflected ray
Hypothesis: as we move from the ideal reflected ray, some light is still reflected
We have angular falloff

34. Non-Ideal Specular Reflection
An illustration of this angular falloff:
How might we model this falloff?

35. Specular Reflection Phong’s Model
Let V be the viewing Vector
Let f be the angle between the viewing vector V and the reflection vector R
Let q be the light incident angle
The intensity at a viewing a
angle f is proportional to
[cos(f)] ns v

36. Specular Reflection Phong’s Model
ns is the specular reflection parameter
Close to 0 for dull surfaces
Remember diffuse reflection !!
Larger for shiny surfaces (e.g. 100)
For a perfect mirror, what is the value of ns?
[cos(f)] ns f

37. Shiny Vs Dull Surface

38. Specular Reflection Phong’s Model
Fresnel’s laws from physics: the light is not reflected 100% (some is absorbed, some reflected back).
The amount of absorption is dependent on the incident angle q
Use the specular reflection co-efficeint W(q) to quantify this:
Ispec = W(q)Il
Final form of Phong’s model
Depends on
Incident light
angle
Depends on
Viewer’s angle

39. Specular Reflection Phong’s Model
As we can see, W(q) is almost constant
W(q) is usually approximated by by
a constant ks
Approximate Phong’s model
Using Vector Arithmetic…

40. Specular Reflection Phong’s Model Examples
These spheres illustrate the Phong model as L and nshiny are varied
Varying L
Varying nshiny
Which sphere is most shiny?

41. Combining Everything We want simple analytic model: From:
diffuse reflection +
specular reflection
From:
Multiple Light Sources
Ambient light
Surface

42. Combining Everything Single Light Sourceq q L f V
Surface

43. Combining Everything Single Light Source
Sum diffuse, specular, and ambient

44. Combining Everything Multiple Light Source
Surface

45. Attenuation If the light source is at distance d
Light power loses its amplitude with 1/d2
Problem: simple point-source illumination model does not always produce realistic pictures with 1/d2
Objects are usually illuminated from multiple sources
Model too simple to represent lighting effect
too much intensity variations when d is small
very little variation when d is large.
Simple solution: Use linear or quadratic attenuation function…

46. Attenuation Use the a0, a1, and a2 to adjust the seen E.g.
Adjust a0 to prevent f(d) from becoming too large when d is small
Adjust the a0, a1, and a2 so that the light intensity does not go above the maximum allowed levels of the display device
Combined illumination model for m point sources…

47. Color Consideration
We can assume that any color consists of 3 components: Red, Green, and Blue
Different reflection coefficient per color
Different attenuation function per color
For example, for the blue color,
We will talk about color models in detail if we have time

48. Transparency
Intensity equations must be modified to include contributions from light passing through the surface.
Both diffuse and specular transmission can take place at the surfaces of a transparent object
I.e. Light passes through the abject is also subjected to and specular like transmission
Realistic transparency effects are modeled by considering light refraction.

49. Transparency Refraction
Snell’s Law N L Qi T Qr hr hi
Refractive index is a function of the color

50. Transparency Refraction
T is the unit vector in the refraction direction qr

51. Transparency Refraction
What we see is what comes out of the transparent object N L Qi T Qr hr hi T`
The path is shifted

52. Transparency Simplifying Refraction
Computing the path shift is expensive
Assume that there is no shift  hi = hr  Qi = Qr
We still have to account for
reflection off the transparent object
Partial light absorption when passing
through the transparent object
Let kt be the transparency factor
Hence (1-kt)is the opacity factor
I = (1-kt)Irefl + ktItrans
Where I is the combined viewed light intensity
of the point P on the surface P
Irefl
Itrans

53. Shadow Different from Shading Basic idea
Apply hidden surface method with light source at view position
Shadowed surface = surface cannot be seen from the light source
Apply shading pattern to these areas
How to generate shading pattern
E.g. apply only ambient light and combine it with texture
We will talk about texture if we have time