lec 7 - Illumination models

Question 1

What are some examples of different types of surfaces?

Answer 1

1. Self luminous example is some kinds of jelly fish that glow in dark or radioactive isotopes
2. Transparent refractive, – glass or water
3. Transparent translucent – light interacts in more complex way, e.g scatters.
4. reflection, either
   a. diffuse (body reflection), e.g. carpet
   b. specular (surface reflection), e.g. polished steel.

Question 2

What are isotropic surfaces?

Answer 2

In isotropic surfaces the relationship between the incoming (or incident) and outgoing (or reflected) direction of light is the same over the whole surface (otherwise anisotropic).

Question 3

When do antistropic surfaces occur?

Answer 3

1. When certain kinds of material (such as velour) and certain rock or stone faces (look different depending on angle that you view them).
2. As a result of asymmetric microtexture.

Question 4

What is the difference between the shading model and the illumination model in rendering scenes?

Answer 4

The illumination model captures how light sources interacts with object surfaces.
The shading model determines how to render the faces of each polygon in the scene.
The illumination model is about determining how light
sources interacts with object surfaces whereas shading is about how to interpolate over the faces of polygons, given the illumination.

Question 5

In what ways does the shading model depend on the illumination model?

Answer 5

1. some shading models invoke an illumination model for every pixel (such as ray tracing),
2. others only use the illumination model for some pixels and then shade the remaining pixels by interpolation (such as Gouraud shading).

Question 6

How do simple illumination models work?

Answer 6

Simple illumination models do not consider shadows,

reflections or photon-based effects (such as radiosity).

Question 7

How does full ray tracing work?

Answer 7

In full ray tracing one considers all rays of light and their
recursive interaction between each object —very
computationally complex!

Question 8

What is ambient illumination?

Answer 8

light that comes uniformly from all directions.

Question 9

What is the formula for ambient illumination?

Answer 9

I = (Ia)(Ka)
Ia = intensity of the illumination
Ka = reflectivity (or albedo) of the surface—the fraction of the incoming light which the object reflects, near zero for black objects, near one for white objects.

Question 10

What is Lambertian (diffuse) reflection?

Answer 10

When a ray of light hits a surface, some fraction of it penetrates some way into the body of the object, where it is scattered (and may interact with coloured pigment particles). Eventually, some of the light is reradiated more-or-less uniformly in all directions. The brightness depends only on the angle between the
direction L to the light source and the surface normal N.

Question 11

What is the diffuse (or Lambertian) illumination equation?

Answer 11

I = (Ip) (Kd) cosθ or
I = (Ip) (Kd) ( N (dot product) L)
Ip = incoming light from the point light source
Kd = reflectivity (or albedo) of the surface
θ = the angle between the local surface normal, and the direction to the light source.
N = unit vector direction of normal
L = unit vector direction of light source

Question 12

Is Lambertian reflection dependent or independent of surface orientation with respect to the viewer?

Answer 12

independant.

Question 13

Explain why Lambertian reflection is independent of surface orientation with respect to the viewer.

Answer 13

For a given small surface patch, the amount of light radiated towards the viewer is greatest when the surface normal is pointing straight at the viewer, and falls off according to a cosine law as the surface slants away from the viewer.
However, at the same time, for a given visual angle subtended at the viewer, more of the surface is seen within that angle as the surface slants away from the viewer, again according to a cosine law.
These two effects exactly compensate, hence it’s independent.

Question 14

Is Lambertian reflection dependent or independent of the distance of the surface from the viewer?

Answer 14

independant.

Question 15

Explain why Lambertian reflection is independent of the distance of the surface from the viewer.

Answer 15

Likewise, as the surface moves further away from the viewer, the received light intensity falls off as an inverse-square law in distance.
However, for a given angle subtended at the viewer, the amount of surface included grows in proportion to the square of the distance.
These two effects also compensate, so that intensity of
Lambertian reflection is independent of the distance of the surface from the viewer.

Question 16

Is Lambertian reflection dependent or independent of the distance of the surface from the light source?

Answer 16

dependant.

Question 17

Explain why Lambertian reflection is dependent of the distance of the surface from the light source.

Answer 17

The intensity of the incoming light (and therefore of the
reflected light) does depend on the distance of the surface from the light source.
Physically, for a point light source, this dies off in inverse
proportion to the square of the distance.
However, if this physical law is followed in rendering, the
intensity seems to go down unrealistically fast. (This is because most real lighting is not from a single, ideal point source.)

Question 18

When does the effect of the distance from the light source in Lambertian reflection need to be corrected?

Answer 18

If the light source is sufficiently “distant”, then all parts of the object can be regarded as equally far from the light source, and therefore no such correction need be made.

Question 19

How can the effect of the distance from the light source in Lambertian reflection be corrected?

Answer 19

The effect of distance, the same for all points, can essentially be absorbed into the light-source intensity factor Ip.
Also using the formula 1/(C + U), where U is the light-source distance, and C is some constant offset.

Question 20

What is specular reflection?

Answer 20

When a ray of light hits a surface, some fraction of it is also reflected immediately at the outer boundary of the surface. This is the specular reflection and leads to highlights and glossiness.

Question 21

Why is specular reflection different from perfect reflection?

Answer 21

For most glossy surfaces, the reflected light is spread out (e.g. scratches in steel of texture in plastic), to a greater or lesser degree, from the direction of perfect reflection. This is caused by microscopic unevenness of the surface: there are a lot of little reflecting facets, whose normals vary from the overall surface normal.
The reflection is strongest in the direction of perfect reflection, and becomes weaker for directions away from this.

Question 22

What does the specular reflection exponent do?

Answer 22

It controls the degree of spread.

High values of n (maybe as much as 100 or 200) lead to a rapid fall-off and sharp highlights, corresponding to a very glossy surface, almost like a mirror.

Low values (as low as 1 or 2) lead to a slow fall-off and
spread-out, more diffuse highlights, a more matte surface appearance.

Question 23

Is specular reflection dependent or independent of Lambertian reflectivity?

Answer 23

specular reflection, being from the outer surface,

does not involve interaction with the body of the material, and so is independent of Lambertian reflectivity.

Question 24

Is specular reflection dependent or independent of material colour?

Answer 24

The colour of a specular reflection depends only on the colour of the incoming light, not on the colour of the material.
Example: coloured reflections on surface of steel.

Question 25

What is the formula for the phong illumination model (with cosine)?

Answer 25

Iλ = Iaλ ka Odλ + fatt Ipλ [kd Odλ cosθ +W(θ)(cosα)^n]
Iaλ = ambient light
ka = ambient light coefficient
Odλ = objects diffuse colour
fatt = the light source attenuation factor (a function of distance)
Ipλ = point light source
W(θ) = the fraction of specularly reflected light
n = the specular-reflection exponent

Question 26

What is the formula for the phong illumination model (without cosine)?

Answer 26

Iλ = Iaλ ka Odλ + fatt Ipλ [kd Odλ (N . L) + Ks (R . V)^n]
ks = specular reflection coefficient
Iaλ = ambient light
ka = ambient light coefficient
Odλ = objects diffuse colour
fatt = the light source attenuation factor (a function of distance)
Ipλ = point light source
kd = diffuse-reflection coefficient
W(θ) = the fraction of specularly reflected light
n = the specular-reflection exponent

Question 27

How to calculate the shading given multiple light sources?

Answer 27

If there are multiple light sources, then their contributions at any point on a surface add together, less any shadowing.