Lights in the Phong Model

𝐼=𝑘𝑎 𝐿𝑎+𝑘𝑑𝐿𝑑 ( �̂� ∙ �̂� )+𝑘𝑠𝐿𝑠 (𝑉 ∙ �̂� )𝑛

2. What are these?

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1. How to compute these?

Light source direction: • 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: http://mynasadata.larc.nasa.gov/Radiation_Explanation.html

credit: http://www.truebeyonddesign.com/products-page/

http://www.apartmenttherapy.com/ny/lighting/best-product-tolomeo-desk-lamp-001066

What is Ambient Light?

• Not in the real world!• Implementation dependent!– constant color added to illumination results– Maya scene file

Ambient lightMaterial Property

Rendered image

What about the Sun?

• How would you describe the incoming light source for this scene?

http://www.planetware.com/picture/kansas-cottonwood-falls-tallgrass-prairie-national-preserve-flint-hills-national-prairie-us-ks108.htm

Directional Light• Direction is: • No position!! (where is the Sun?)• Light has no geometry and does not show up

in final rendered image• Planes looks … flat • Maya Scene

− �̂�

Directional Light

Rendered image

What about the Light Bulb?

• How would you describe the light source of these scenes?

http://home.cogeco.ca/~richardastro2/

http://companyofburninghearts.wordpress.com/2010/03/18/mystic-clusters/

Point Light• Position ()• For every visible position ()

• is unique!

• Illumination is a function of relative position to lights!

• Maya Scene

Different vector for each visible point

Rendered imagePoint Lights

Now, my desk lamp

http://0.tqn.com/d/drawsketch/1/0/N/J/eggsetup.jpg

http://www.mackayphotography.co.uk/light_pollution.htm

• How would you describe the light source of these scenes?

http://agreenliving.org/tag/concept-design/

http://www.how-to-refinish-hardwood-floors.wirze.com/

Spot Light• Direction + Position:– Pointing direction

– As in point light, for each visible point is unique!

– Cone angle (θ) defines illumination range

𝑃 𝐿

Different vector for each visible point

− �̂�θ

Rendered image

Maya Scene

Cone boundaries

Spotlight bounds– Position: – Main direction– : cone angle– θ: regions of full

illumination – angle to position

for illumination– If θ< < Illumination drops off according to:

θ𝝋− �̂�

𝑃 𝐿

Region: fully illuminated

Penumbra Region: gradual drop off

𝛂 Illumination at this point is

𝐼 𝑓=[ cos𝛼− cos 𝜑2cos 𝜃2− cos 𝜑

2]𝑝

Drop off behavior

𝐼 𝑓=[ cos𝛼− cos 𝜑2cos 𝜃2− cos 𝜑

2]𝑝

Drop off p=1

p=0.2

p=0.1

p=30p=20

P>1

P<1

scene

No drop off

Penumbra region

Implement Penumbra Region

• For a visible position:

• cos(

If (cos( > cos( // < Full illumination

else if (cos() < cos()) // > no illuminationelse Penumbra region

θ𝝋− �̂�

𝛂𝑃 𝐿

A visibleposition

Distance Attenuation• Illumination is a function of

• d = distance between light and visible position!!

• Physics tells us • Did not follow physics in the rest of the

model!– WAY too dark!!

• Generally:

d

𝐼=𝐼𝐿

𝐶0❑+𝐶1

❑𝑑+𝐶2❑𝑑2+𝐶3

❑𝑑3

How about ?

• Let user specify each of thecomponents!

Maya:

OpenGL:

Our ToyRayTracer:

General form of Phong

𝐼= ∑𝑖

𝐴𝑙𝑙 h𝐿𝑖𝑔 𝑡𝑠

𝑘𝑎𝐿𝑎𝑖+𝐿𝑑𝑖

𝐶0❑+𝐶1

❑𝑑+𝐶2❑𝑑2+𝐶3

❑𝑑3𝑘𝑑

( �̂� ∙𝐿𝑖)+𝐿𝑠𝑖

𝐶0❑+𝐶1

❑𝑑+𝐶2❑𝑑2+𝐶3

❑𝑑3𝑘𝑠 (𝑉 ∙𝑅𝑖 )

𝑛

Our Ray Tracer implements:

𝐼=𝑘𝑎+ ∑𝑖

𝐴𝑙𝑙 h𝐿𝑖𝑔 𝑡𝑠

𝐿𝑑𝑖 [𝑘𝑑 ( �̂� ∙𝐿𝑖)+𝑘𝑠 (𝑉 ∙𝑅𝑖 )𝑛 ]