1. Lights in the Phong Model𝑹 𝑵 𝑳
1. How to compute these?
𝐼= 𝑘 𝑎 𝐿 𝑎 + 𝑘 𝑑 𝐿 𝑑 𝑁 ∙ 𝐿 + 𝑘 𝑠 𝐿 𝑠 𝑉 ∙ 𝑅 𝑛
2. What are these?

2. Light source direction: 𝐿
credit:
Look around you …
The light in Seattle: Indirect
background, … ambient
Sun light: Direct, very far away
coming from a constant direction (independent of where you are)
Light bulb at home: Direct
closer, shines from a fixed point
Light from the projector/desk lamp
How would you describe this?
credit:

3. What is Ambient Light? Not in the real world!
Implementation dependent!
constant color added to illumination results
Maya scene file
Ambient light
Material Property
Rendered image

4. What about the Sun?
How would you describe the incoming light source for this scene?

5. Directional Light Direction is: − 𝐿 No position!! (where is the Sun?)
− 𝑳
Direction is: − 𝐿
No position!! (where is the Sun?)
Light has no geometry and does not show up in final rendered image
Planes looks … flat 
Maya Scene
Rendered image
Directional Light

6. What about the Light Bulb?
How would you describe the light source of these scenes?

7. Point Light Position ( 𝑃 𝐿 ) For every visible position ( 𝑃 𝑖 )
Different 𝐿 𝑖 vector for each visible point
Position ( 𝑃 𝐿 )
For every visible position ( 𝑃 𝑖 )
𝐿 𝑖 = 𝑃 𝐿 − 𝑃 𝑖 is unique!
Illumination is a function of relative position to lights!
Maya Scene
Point Lights
Rendered image

8. Now, my desk lamp
How would you describe the light source of these scenes?

9. Spot Light Direction + Position: Pointing direction − 𝐿
As in point light, for each visible point 𝐿 𝑖 = 𝑃 𝐿 − 𝑃 𝑖 is unique!
Cone angle (θ) defines illumination range
𝑃 𝐿
Different 𝐿 𝑖 vector for each visible point
− 𝐿 θ

10. Rendered image
Cone boundaries
Maya Scene

11. Spotlight bounds Position: 𝑃 𝐿 Main direction:− 𝑳 𝝋: cone angleθ 𝝋
− 𝑳
𝑃 𝐿
Region: fully illuminated
Penumbra Region: gradual drop off 𝛂
Illumination at this point is 𝐼 𝑓
Position: 𝑃 𝐿
Main direction:− 𝑳
𝝋: cone angle
θ: regions of full illumination
𝛂: angle to position for illumination
If θ< 𝛂 < 𝝋 Illumination drops off according to:
𝐼 𝑓 = cos 𝛼 − cos 𝜑 2 cos 𝜃 2 − cos 𝜑 𝑝

12. Drop off behavior 𝐼 𝑓 = cos 𝛼 − cos 𝜑 2 cos 𝜃 2 − cos 𝜑 2 𝑝 P<1
Drop off p=1
p=20
p=30

13. No drop off
Penumbra region
scene

14. Implement Penumbra Regionθ 𝝋
− 𝑳 𝛂
𝑃 𝐿
A visible position 𝑃 𝑖
For a visible position: 𝑃 𝑖
𝐿 𝑖 = 𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒(𝑃 𝐿 − 𝑃 𝑖 )
cos(𝛼)= 𝐿 𝑖 ∙ 𝐿
If (cos(𝛼) > cos( 𝜃 2 )) // 𝛼 < 𝜃
Full illumination
else if (cos(𝛼) < cos( 𝜑 2 )) // 𝛼 > 𝜑
no illumination
else
Penumbra region

15. Distance Attenuation Illumination is a function of
d = distance between light and visible position!!
Physics tells us 𝐼∝ 1 𝑑 2
Did not follow physics in the rest of the model!
WAY too dark!!
Generally:
𝐼= 𝐼 𝐿 𝐶 0 + 𝐶 1 𝑑+ 𝐶 2 𝑑 2 + 𝐶 3 𝑑 3

16. How about 𝐼 𝐿 ? Let user specify each of the components! OpenGL: Maya:
Our ToyRayTracer:

17. General form of Phong
𝐼= 𝑖 𝐴𝑙𝑙 𝐿𝑖𝑔ℎ𝑡𝑠 𝑘 𝑎 𝐿 𝑎𝑖 + 𝐿 𝑑𝑖 𝐶 0 + 𝐶 1 𝑑+ 𝐶 2 𝑑 2 + 𝐶 3 𝑑 3 𝑘 𝑑 𝑁 ∙ 𝐿 𝑖 + 𝐿 𝑠𝑖 𝐶 0 + 𝐶 1 𝑑+ 𝐶 2 𝑑 2 + 𝐶 3 𝑑 3 𝑘 𝑠 𝑉 ∙ 𝑅 𝑖 𝑛
Our Ray Tracer implements:
𝐼= 𝑘 𝑎 + 𝑖 𝐴𝑙𝑙 𝐿𝑖𝑔ℎ𝑡𝑠 𝐿 𝑑𝑖 𝑘 𝑑 𝑁 ∙ 𝐿 𝑖 + 𝑘 𝑠 𝑉 ∙ 𝑅 𝑖 𝑛