0426.md

Lighting

The color of an object is based on:

1. The reflective properties of the object
2. The color, intensity, and location of any light sources

Types of Light Sources

• Ambient
  • General light in an image
  • Comes from all locations equally
• Point Light Source
  • Comes from a specific location (far away)

Phong Reflection Model

• Models real world reflection by breaking reflection into 3 parts
  • Ambient
  • Diffuse (point source)
  • Specular (point source)
• I = Ambient + Diffuse + Specular

Ambient Reflection

• A: Ambient light (0-255)
• Ka: constant of ambient reflection (0-1)
• Ambient = A*Ka

Diffuse Reflection

• Reflection of a point source
• Light is reflected back evenly in all directions
• Matte/dull objects

Calculation

• L: vector from the surface to the light (L-hat is normalized)
• θ: angle between N (normal vector to surface) and L
• cosθ = N-hat • L-hat
• P: point light color (0-255)
• Kd: constant of diffuse reflection (0-1)
• Diffuse = P*Kd*(N-hat • L-hat)

!reflection

Specular Reflection

• Reflects a point source in a specific direction
• Models glossy/shiny surfaces
• Strength of a specular reflection is based on:
  • The angle between R and V (α)
  • The angle between L and N (θ)

!specular

Calculation

• L: vector from the surface to the light (L-hat is normalized)
• θ: angle between N (normal vector to surface) and L
• α: angle between R and V (α)
• R: reflected vector from the surface

We want R-hat • V-hat.

R-hat = T + S
S = T - L-hat
R-hat = 2T - L-hat

cosθ = L • N
cosθ = |T| / |L|
cosθ = |T|

T = |T| * N

T-hat = (L-hat • N-hat) * N-hat
R-hat = 2 * (N-hat • L-hat) * N-hat - L-hat

cosα = (2 * (N-hat • L-hat) * N-hat - L-hat) • V-hat

Specular = P*Ks*[(2 * (N-hat • L-hat) * N-hat - L-hat) • V-hat]^x

x: arbitrary exponent used to simulate how quickly the reflection decreases

Color

I = Ambient + Diffuse + Specular
I = A*Ka + P*Kd*(N-hat • L-hat) + P*Ks*[(2 * (N-hat • L-hat) * N-hat - L-hat) • V-hat]^x

where I is a color.