22_Illumination Model.pdf

ILLUMINATION

ILLUMINATION (LIGHTING)

ILLUMINATION MODEL

 A illumination model usually considers:

 Light attributes (light intensity, color, position, direction,

shape)

 Object surface attributes (color, reflectivity, transparency, etc)  Interaction among lights and objects (object orientation)

 Interaction between objects and eye (viewing dir.)

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ILLUMINATION CALCULATION



Local illumination:

the observer position, and the object material properties

ILLUMINATION MODELS



Global illumination:

interaction of light from all the surfaces in the scene

object 1

object 2 object 3

object 4

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BASIC LIGHT SOURCES

Point light Directional light

Light intensity can be independent or dependent of the distance between object and the light source

SIMPLE LOCAL ILLUMINATION

 It considers three types of light contribution to

compute the final illumination of an object

 Ambient

 Diffuse

 Specular

Final illumination of a point (vertex)

Illumination= ambient + diffuse + Specular

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AMBIENT LIGHT CONTRIBUTION

 Ambient light (background light): the combination of light reflections

from various surfaces in the surroundings yields to a uniform illumination called ambient light or background light

 very simple approximation of global illumination

 Independent of the light position, object orientation, observer’s

position or orientation – ambient light has no direction

object 1

object 2 object 3

AMBIENT LIGHTING EXAMPLE

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 Different objects can reflect different amounts of ambient

(different ambient reflection coefficient K_a, 0 <= K_a <= 1)

 So the amount of ambient light that can be seen from an

object is:

I_Ambient = I_a x K_a

I_a incident ambient light intensity

K_a ambient diffuse reflection constant I_Ambient reflected ambient light

The character of light reflected from a surface depends on the composition( i.e. monochromatic or achromatic),

1. direction and geometry of the light source 2. surface orientation and the

3. surface properties of the object.

They are of two types

1. Diffuse Reflection 2. Specular Reflection

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DIFFUSE LIGHT CONTRIBUTION

 Diffuse light: The illumination that a surface receives from a light

source and reflects equally in all direction

 Diffuse reflection is the reflection of light from an uneven or granular

surface such that an incident ray is seemingly reflected at a number of angles. It is the complement to specular reflection. If a surface is

completely non-specular, the reflected light will be evenly spread over the hemisphere surrounding the surface

DIFFUSE LIGHTING EXAMPLE

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DIFFUSE LIGHT CALCULATION

 Need to decide how much light the object point

receive from the light source – based on Lambert’s Law

DIFFUSE LIGHT CALCULATION (2)

 Lambert’s law: the radiant energy D that a

small surface patch receives from a light source is:

D = I x cos (q)

I: light intensity

q: angle between the light vector and the surface normal

N : surface normal

light vector (vector from object to light)

q

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 Like the ambient light case, different objects can reflect

different amount of diffuse light (different diffuse reflection coefficient K_d, 0 <= K_d <= 1))

 So, the amount of diffuse light that can be seen is:

IDiffuse = Kd I cos (q) Or

I_Diffuse = K_d I (N.L)

Diffuse light calculation (3)

q q

N

L cos(q) = N.L

SPECULAR LIGHT CONTRIBUTION

 The bright spot on the object

 The result of total reflection of the incident light in a concentrate region.

See nothing!

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SPECULAR LIGHT CALCULATION



How much reflection you can see

depends on where you are

The only position the eye can see specular from P if the object has an ideal reflection surface

But for a non-perfect surface you will

still see specular highlight when you move a little bit away from the ideal reflection Direction

q q

p

f

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PHONG MODEL FOR SPECULAR REFLECTION

 The angle φ is the viewing angle relative to the specular reflection direction.

 For mirrors (perfect reflector ) φ=0

 Acoording to Phong

Ispec ∞ 𝒄𝒐𝒔𝒏𝒔(φ)

 φ can be between 0 to 90

 Cos(φ) could be between 0 to 1

 n_s specular-reflection parameter is determined by the type of

 The intensity of specular reflection I_spec depends on

― Material properties of the surface

― Angle of incidence

― Polarization and color of the light

 Let W(θ)=specular reflection coefficients

 W(θ) tends to increase as the angle of incidence increases at θ=90 W(θ)=1 and all incidence light is reflected

 The variation of specular intensity with angle of incidence is described by Fresnels Laws of

Reflection.

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I_specular = W(θ).I .cosns(f)

W(θ): specular reflection coefficient I: light intensity

f: angle between V and R ie viewing angle relative to specular reflection direction R

N: surface normal at P

cosn_{(f): the larger is n, the smaller} is the cos value

cos(f) = V.R

I

= K

.I .(V.R)

PHONG SPECULAR REFLECTION MODEL

q q

p _f

Viewing

Reflection N

SPECULAR LIGHT CALCULATION (3)

 The effect of ‘n’ in the phong model

n = 10

n = 30

n = 90

n = 270

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 Transparent materials, such as glass, only exhibit appreciable specular reflections as θ approaches 90°. At θ = O°, about 4 percent of the

incident light on a glass surface is reflected.

 For most of the range of θ the reflected intensity is less than 10 percent of the incident intensity.

 For many opaque materials, specular reflection is nearly constant for all incidence angles.

 In this case, we can reasonably model the reflected light effects by replacing W(θ) with a constant specular-reflection coefficient k_s.

I_specular = W(θ).I .cosns(f)

Ispecular = KS.I .(V.R)ns

q q

Viewing

Reflection N

SUMMARY OF THE PHONG MODEL

 Light sources are assumed to be point sources

 Light sources and viewer are located at infinity

 Only the normal vector of a surface needs to be computed

 The diffuse and specular terms are modeled as local

components

 The color of the specular reflection is assumed to be

that of the light source

 ks is set to be a constant value independent of the surface

color

 The global term(ambient) is modeled as a constant

 Drawback:

For a single point source of light total reflection is combine of diffuse and specular

I=I_diff+I_spec

Illumination =ambient Light Ref+diffuse ref+specular Ref

Illumination=I_aK_a+I_a(K_d (N.L)+K_s (N.H)ns₎

Where

I_a=ambient Light

K_a,K_d,K_s are reflection Coefficients o<=k_a,k_s,k_d<=1

 If there are N lights

Total illumination for a point

COMBINED APPROACH

)]

)

(N.H

K

)

.

(

(K

[I

K

I





INTENSITY ATTENUATION

 As radiant energy from a point light source travels through

space, its amplitude is attenuated by the factor l/d2_{, where d is}

the distance that the light has traveled.

 Problem with our point light source

 Does not always produce realistic pictures, if we use the factor

l_/

d2 to attenuate intensities

 The factor l/d2 produces too much intensity variations when d is small, and  it produces very little variation when d is large. This is because real scenes

are usually not illuminated with point light sources.

 Solution

Nihar Ranjan Roy

 coefficients a₀,a₁ and a₂ can be varied to obtain a variety of lighting effects for a scene.

 We can limit the attenuation function to 1 by the following expression

 Thus our basic illumination model becomes

Where d_i is the distance traveled by the light from source i

2 2 1 0

1

)

(

d

a

d

a

a

d

f







)

1

,

1

min(

)

(

0

a

d

a

d

COLOR CONSIDERATION

 Yet in our illumination model we have considered white light.

 In order to consider color we should have the intensity equations in terms of color properties of light sources and object surfaces.

 For RGB model lets say k_dr, k_dg k_db be the diffuse coefficients of R G & B components.

 for a blue surface object k_dr =k_dg =0

Nihar Ranjan Roy

29 )] ) (N.H K ) . ( [(K )I f(d K I I n 1 i n i sbi abi i ab ab

B





 

 N L i

 In specular-reflection model, Phong set parameter k, to a

constant value independent of the surface color. This produces specular reflections that are the same color as the incident light (usually white), which gives the surface a plastic appearance.

 For a non-plastic material, the color of the specular reflection is a

function of the surface properties and may be different from both the color of the incident light and the color of the diffuse reflections.

 We can approximate specular effects on such surfaces by making

 Another method for setting surface color

 specify the components of diffuse and specular color vector for

each surface, while retaining the reflectivity coefficients as single-valued constants.

 For an RGB color representation, for instance, the

components of these two surface color vectors can be denoted as (S_dR,S_dC, S_dB) and (S_IR, S_rC, S_IB).

 The blue component of the reflected light is then calculated as

Nihar Ranjan Roy

31 ] ) (N.H S K ) . ( S [K I (d) f K I I n 1 i ns i sB s dB lBi i a aB B



 S_{dB d} N L_i

 Other color approaches

 represent any component of a color specification with its spectral wavelength λ.

 Intensity can be represented through









i

(d)

I

[K

S

(

.

)

K

S

(N.H

)

]

f

 



K

S

I

N

L

TRANSPARENCY

 A transparent surface, in general, produces both reflected and transmitted light. The relative

contribution of the transmitted light depends on the degree of transparency.

 When a transparent surface is to be modeled, the intensity equations must be modified to include

contributions from light passing through the surface  In most cases, the transmitted light is generated from

reflecting objects in back of the surface

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 Realistic transparency effects are modeled by

considering light refraction.

 When light is incident upon a transparent surface,

part of it is reflected and part is refracted.

 The direction of the refracted light specified by the

angle of refraction, is a function of the index of

refraction of each material and the direction of the incident light.

 Index of refraction for a material is defined as the ratio

 Angle of refraction θ_r, is calculated from the angle of incidence θ_i, the index of refraction η_i of the "incident" material (usually air), and the index of refraction η_r of the refracting material according to

 Sneil's law:

 We can combine the transmitted intensity I_Trans

through a surface from a background object with the reflected intensity I_reflec from the transparent surface using a transparency coefficient k_t We assign

parameter k_t a value between 0 and 1 to specify how much of the background light is to be transmitted. Total surface intensity is then calculated as

Nihar Ranjan Roy

35 ) sin( ) sin( _i r i

r _ q



WARN MODEL

 So far we have considered only point light sources.

 The Warn model provides a method for simulating studio lighting effects by

controlling light intensity in different directions.

 Light sources are modelled as points on a reflecting surface, using the Phong

model for the surface points.

 Then the intensity in different directions is controlled by selecting values for the

Phong exponent

 In addition, light controls,such as "barn doors" and spotlighting, used by studio

photographers can be simulated in the Warn model.

 Flaps are used to control the amount of light emitted by a source In various

directions. Two flaps are provided for each of the x, y, and z directions.

 Spotlights are used to control the amount of light emitted within a cone with