The Lighting Model - Hampden-Sydney Collegepeople.hsc.edu/faculty-staff/robbk/Coms331/Lectures... · The Lighting Model Lecture 15 Section 5.3 Robb T. Koether Hampden-Sydney College

The Lighting ModelLecture 15Section 5.3

Robb T. Koether

Hampden-Sydney College

Mon, Oct 3, 2011

Robb T. Koether (Hampden-Sydney College) The Lighting Model Mon, Oct 3, 2011 1 / 45

Outline

1 The Phong Lighting ModelAmbient ReflectionDiffuse ReflectionSpecular ReflectionEmissive Light

2 Assignment


Outline


2 Assignment


Shading Calculations

Example (The Material Properties)Let the position be P = (0,5,10).Let the surface normal be n = (0.8,0.6,0.0).Let us assume that the object has the following materialproperties.

Ambient reflection is (0.6,0.4,0.2).Diffuse reflection is (0.6,0.4,0.2).Specular reflection is (1.0,1.0,1.0).Shininess is 128.That is, the object is shiny brown.



Example (The Light Source)Let us assume that general ambient light is (0.2,0.2,0.2).Let LIGHT0 have the following properties.

Position is L = (10,10,0).Ambient light is (0.3,0.3,0.3).Diffuse light is (0.8,0.8,0.8).Specular light is (1.0,1.0,1.0).



Example (The Viewer)Let us assume that the viewer is located at V = (5,10,15).


Outline


2 Assignment


Computing Ambient Reflection

The ambient reflection depends onThe general ambient light inherent in the scene.

0 ≤ sa ≤ 1.

The ambient light from the light source.

0 ≤ La ≤ 1.

The ambient property of the surface.

0 ≤ ka ≤ 1.

The ambient reflection is computed as

ra = saka + Laka


The Shading Calculations

Example (Calculating Ambient Reflection)We have

sa = 0.2La = 0.3ka = (0.6,0.4,0.2)

Therefore, the ambient reflection is

saka + Laka = (0.3,0.2,0.1).

Original Ambient


Outline


2 Assignment


Point and Directional Sources

At each point of a surface, the light from a light source has adirection.

Point source - direction varies with position on surface.Directional source - direction does not vary with position on surface.

With a point source, the intensity may also depend on distancefrom the source if we enable attenuation.


Diffuse Relection

Intensity of reflected diffuse lightDepends on angle of incidence.Reflects equal in all directions. Therefore, it does not depend onthe viewer’s location.


Computing Diffuse Reflection

Let P be a point on the surface.We need to know two geometric facts.

The location of light source, as a vector l from P to the light source.The orientation of the surface, as a vector n normal to the surface.


Diffuse Reflection

Light Source n

lθ

P Surface


Lambert’s Law

Diffuse reflection is equal in intensity in all directions.However, the intensity depends on the angle of the incident light.Lambert’s law says that the intensity is proportional to the cosineof the angle of incidence (as measured down from the normal).


Lambert’s Law

nl

P Surface

θ

Small angle⇒ Large cosine⇒ Bright reflection


Lambert’s Law

n

l

P Surface

θ

Large angle⇒ Small cosine⇒ Dim reflection


Diffuse Reflection

If l and n are unit vectors, then the cosine of the angle betweenthem is

l · n = cos θ.

Two other factors are needed.Intensity of the incident light.

0 ≤ Ld ≤ 1.

Reflective property of the surface.

0 ≤ kd ≤ 1.


Diffuse Reflection

The formula for diffuse reflection is

rd = Ldkd(l · n).

Of course, if l · n < 0, then rd = 0.Why?



Example (Diffuse Reflection)We have

L− P = (10,5,−10)

l = (10,5,−10)/√

225= (2/3,1/3,−2/3)

n = (0.8,0.6,0.0)

l · n = 0.7333Ld = (0.8,0.8,0.8)

md = (0.6,0.4,0.2)



Example (Diffuse Reflection)The diffuse reflection is

Ldkd(l · n) = (0.3520,0.2347,0.1173).

Original Diffuse



Example (Ambient and Diffuse Reflection)Ambient and diffuse reflection combined is

(0.6520,0.4347,0.2173).

+

Ambient Diffuse


Outline


2 Assignment


Specular Reflection

The intensity of specular reflected light varies with viewingdirection as well as the direction of the light source.The maximum intensity is in the “ideal” direction, based on theprinciple that

Angle of reflection = Angle of incidence.


Blinn and Phong Lighting

OpenGL uses the Blinn lighting model of specular reflection.However, we will first study the Phong lighting model since itseems more natural.


Phong Lighting

The intensity of the reflection is a function of the angle betweenthe viewer and the ideal direction r of reflection of light from thelight source off the surface.


Phong Lighting

Light Source

Eye

n

l

vϕ

P Surface

r

θθ

IdealDirection


Phong Lighting

To compute r, note that r + l equals twice the projection of l onto n.

n

l rθθ

r l


Phong Lighting

The projection of l onto n is(l · nn · n

)n = (l · n)n.

Therefore,r + l = 2(l · n)n

andr = −l + 2(l · n)n.


Computing Specular Reflection

According to the Phong lighting model, the specular reflection isproportional to the cosine of the angle between v and r, raised tothe α power, where α is an integer between 0 and 128.This is calculated as

(cosϕ)α = (r · v)α.



Two other factors areIntensity of the incident light.

0 ≤ Ls ≤ 1.

Specular property of the surface.

0 ≤ ks ≤ 1.

Therefore, the formula for specular reflection is

rs = Lsks(r · v)α.



Of course, if l · n < 0 or if r · v < 0, then rs = 0.Why?



Example (Specular Reflection)Now we have

l = (2/3,1/3,−2/3)

n = (0.8,0.6,0.0)

V − P = (5,5,5)

v = (5,5,5)/√

75 =

(1√3,

1√3,

1√3

)r = −l + 2(l · n)n

=

(3875,4175,5075

)= (0.5067,0.5467,0.6667)

r · v = 0.9930



Example (Specular Reflection)And

α = 128Ls = 1.0ks = 1.0

Lsks(r · v)α = (0.4091,0.4091,0.4091)

Original Specular



Example (Total Reflection)Ambient, diffuse, and specular combined is

(1.0,0.8438,0.6264).

Compared to the inherent material color

(0.6,0.4,0.2).

+

Ambient Diffuse

+

Specular


Blinn Lighting

A slightly more efficient method is the Blinn lighting model.Let h be the halfway vector, the unit vector halfway between l andv.Then use h · n instead of r · v.

rs = Lsks(h · n)α.


Blinn Lighting

Light Source

Eye

n

l

v

P Surface

ωω

hζ


Blinn Lighting

How does h · n compare to l · v?If l, n, and v are coplanar, then the angle between h and n is halfof the angle between r and v.Why is Blinn lighting more efficient?h is computed as

h =l + v|l + v|

.

This is more efficient to compute than r.


Outline


2 Assignment


Emissive Lighting

Emissive “lighting” is light that emitted by the surface itself.It is used for objects that are meant to glow.It is independent of all light sources and directions.Let me be the intensity of the emissive light.


Computing the Shade of a Surface

The total reflection from a point is the sum of the ambient, diffuse,and specular reflections and the emissive light.

ke + saka + Laka + Ldkd(l · n) + Lsks(h · n)shiny .


Lighting in OpenGL

Since the ambient, diffuse, and specular reflections depend onlight sources, there is a separate contribution for each light source.OpenGL provides up to 8 light sources.Furthermore, there is a separate color component for each type oflight (red, green, blue).


The Lighting Model

The complete formula for the reflected shade (Ir , Ig , Ib) for 8 lightsis

Ir = ker + sar kar+

7∑i=0

(Lar kar + Ldr kdr (l · n) + Lsr ksr (h · n)shiny

)Ig = keg + sagkag+

7∑i=0

(Lagkag + Ldgkdg(l · n) + Lsgksg(h · n)shiny

)Ib = keb + sabkab+

7∑i=0

(Labkab + Ldbkdb(l · n) + Lsbksb(h · n)shiny

)


The Lighting Model

For each color, the computed value is “clamped” to the interval[0,1].If the value exceeds 1, then it is set to 1.


Outline


2 Assignment


Homework

HomeworkRead Section 5.3 – the Phong lighting model.


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The Lighting Model - Hampden-Sydney Collegepeople.hsc.edu/faculty-staff/robbk/Coms331/Lectures... · The Lighting Model Lecture 15 Section 5.3 Robb T. Koether Hampden-Sydney College