# Lecture 13 - Light in Motion

## And Now from our Sponsor

1. Projects
2. Next Wednesday's class

# Surface Reflectances

According to Jim Kajiya, writing in the mid 1980s,, the Bidirectional Reflectance Distribution Function (BRDF) should tell the whole story. What is it, and where does it come from?

• R( incoming angle (2 dof), outgoing angle (2 dof), wavelength (1 dof) )
• incoming and outgoing angles: 0 < \theta < \pi/2, 0 < \phi < 2\pi
• wavelength 400 nm < \lambda < 700nm
• we won't even talk about sampling density (3.14 million values at 10 degree, 10 nm sampling)
• potentially also a function of distance along the surface (2 dof) and difference in surface normal (1 dof )
• if the surface varies, then also parameters that control variation

Maybe it could come from measurement

• even if you could measure it how would you encode the result

Maybe you could simulate the system

• just how complex is the system

Maybe you could find a simple model

• capturing only the important aspects of the system

## Smooth Surfaces

#### Surface reflectance

• For smooth surfaces the surface reflectance is mirror-like

#### Body reflectance

• just like selective absorption
• doesn't come out at the same place: Why doesn't it matter?
• edges of a surface

#### Lambertian reflectance

Lambert 1728-1777

Consider a small circular hole in the surface and ask how much light comes through it in different directions

• Assume light direction is completely randomized
• The directional factor is the cosine zenith angle

The luminance of light in any direction is constant.

When the volume immediately below the surface has spatial structure, the direction of light re-emitted through the surface is not necessarily isotropic.

#### The Moon

• What would the full moon look like if its surface were Lambertian?
• What does the full moon actually look like?