Modeling the Interaction of Light and Materials

When we "see" an object it is because light rays are hitting the surface at that point and are being reflected into your eye. The light that hits the surface can come from several places:

• Local: directly from a light source

• Reflected: light that has first reflected off one or more other objects

• Transmitted: if the surface is transparent, there may be light from a light soruce or another object that has been transmitted through the object.

In ray tracing, we treat these three cases separately even though from your eye's perspective light is light where ever it might come from. Note that each component of light (i.e red, green, and blue) are treated independently.

Local Component

The local component is modeled using 3 components:

• Ambient: This models the many light rays that are bouncing around a room resulting in a low key and essentially uniform light.
  • Approximates diffuse inter-object reflections. It is clearly an oversimplification of a process that is otherwise too difficult to model.
  • Assumes no external light source.
  • Non-directional, i.e. it impinges equally on all surfaces from all directions.
  • Results in a monochrome silhouette.
  • Intensity = k_a I_ac where
    • I_a is the intensity of the ambient light (independent of object)
    • k_a = ambient reflection coefficient 0 <= k_a <= 1 (dependent on material properties of surface)
    • c = color of surface (dependent on object)
• Diffuse: This models matte surfaces, that is, surfaces that tend to scatter light in all directions. This happens because the surface is not completely smooth. At the microscopic level there are many small bumps.
  • The intensity of the scattered light depends on the angle the incoming light ray has with respect to the surface of the object.

• Intensity = k_d I c (L * N) where
  • k_d = coefficient of diffuse reflection (of the object being intersected)
  • I = intensity of the light source
  • L = unit direction of the light source
  • N = unit surface normal at the point of intersection
  • c = color of surface (dependent on object)
• Specular: This models the sharp highlights one gets from very reflective or shiny surfaces.
  • The intensity of the light depends on the angle between the observer (V) and the direction of reflection (R).

• Intensity = k_s I (V * R)ⁿ where
  • k_s = coefficient of specular reflection (of the object being intersected)
  • I = intensity of the light source
  • V = unit direction of the viewer
  • R = unit direction of the reflected ray
  • n = specularity ( measure of the sharpness of the highlight). Can be in the range from 1 to several hundred.
  • Note: the color of the specular highlight is that of the light source and not the object.

• Total local light intensity is the sum of the above three components:
  • Intensity = k_a I_ac + k_d I c (L * N) + k_s I (V * R)ⁿ

DEMO: To experiment with these components, click Java Applet

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