chapter 6.1a

Objectives

Learn to shade objects so their images appear three-dimensional
Introduce the types of light-material interactions
Build a simple reflection model---the Phong model--- that can be used with real time graphics hardware

Why we need shading

Suppose we build a model of a sphere using many polygons and color it with glColor.
We get something like the top sphere
but we want the bottom

Shading

Why does the image of a real sphere look like
Light-material interactions cause each point to have a different color or shade
Need to consider
- Light sources
- Material properties
- Location of viewer
- Surface orientation

Scattering

Light strikes A
- Some scattered
- Some absorbed
Some of scattered light strikes B
- Some scattered

Some absorbed

Some of this scattered light strikes A and so on

Rendering Equation

The infinite scattering and absorption of light can be described by the rendering equation
- Cannot be solved in general
- Ray tracing is a special case for perfectly reflecting surfaces
Rendering equation is global and includes
- Shadows
- Multiple scattering from object to object

Global Effects

Local vs Global Rendering

Correct shading requires a global calculation involving all objects and light sources
- Incompatible with pipeline model which shades each polygon independently (local rendering)
However, in computer graphics, especially real time graphics, we are happy if things “look right”
- Many techniques exist for approximating global effects

Light-Material Interaction

Light that strikes an object is partially absorbed and partially scattered (reflected)
The amount reflected determines the color and brightness of the object
- A surface appears red under white light because the red component of the light is reflected and the rest is absorbed
The reflected light is scattered in a manner that depends on the smoothness and orientation of the surface

Light Sources

General light sources are difficult to work with because we must integrate light coming from all points on the

Simple Light Sources

Point source
- Model with position and color
- Distant source = infinite distance away (parallel)
Spotlight
- Restrict light from ideal point source
Ambient light
- Same amount of light everywhere in scene
- Can model contribution of many sources and reflecting surfaces

Surface Types

The smoother a surface, the more reflected light is concentrated in the direction a perfect mirror would reflected the light
A very rough surface scatters light in all directions

Phong Model

A simple model that can be computed rapidly
Has three components
- Diffuse
- Specular
- Ambient
Uses four vectors
- To source
- To viewer
- Normal
- Perfect reflector

Ideal Reflector

Normal is determined by local orientation
Angle of incidence, l = angle of reflection, r
The three vectors must be coplanar

Lambertian Surface

Perfectly diffuse reflector
Light scattered equally in all directions
Amount of light reflected is proportional to the vertical component of incoming light

Specular Surfaces

Most surfaces are neither ideal diffusers nor perfectly specular (ideal reflectors)
Smooth surfaces show specular highlights due to incoming light being reflected in directions concentrated close to the direction of a perfect reflection

Modeling Specular Reflections

Phong proposed using a term that dropped off as the angle between the viewer and the ideal reflection increased

The Shininess Coefficient

Values of a between 100 and 200 correspond to metals
Values between 5 and 10 give surface that look like plastic

Ambient Light

Ambient light is the result of multiple interactions between (large) light sources and the objects in the environment
Amount and color depend on both the color of the light(s) and the material properties of the object
Add k_a, I_a to diffuse and specular terms
- k_a is the reflection coefficient
- I_a is the intensity of ambient light

Distance Terms

The light from a point source that reaches a surface is inversely proportional to the square of the distance between them
We can add a factor of the form 1/(ad + bd +cd²) to the diffuse and specular terms
The constant and linear terms soften the effect of the point source

Light Sources

In the Phong Model, we add the results from each light source
Each light source has separate diffuse, specular, and ambient terms to allow for maximum flexibility even though this form does not have a physical justification
Separate red, green and blue components
Hence, 9 coefficients for each point source
- I_dr, I_dg, I_db, I_sr, I_sg, I_sb, I_ar, I_ag, I_ab

Material Properties

Material properties match light source properties
- Nine absorbtion coefficients
  - k_dr, k_dg, k_db, k_sr, k_sg, k_sb, k_ar, k_ag, k_ab

Adding up the Components

For each light source and each color component, the Phong model can be written (without the distance terms) as

I =k_d I_d l · n + k_s I_s (v · r )^a + k_a I_a

For each color component we add contributions from all sources

Example

Only differences in these teapots are the parameters in the Phong model