10. Dot product, cont.

• The following properties of dot product make it especially important for us:

  1. If u and v are of unit length (the length of 1), then u·v is the cos(a)

  2. The dot product is used extensively during diffuse lighting calculations. It is taken between a surface normal and the vector pointing toward a light source. When the angle is zero, the light intensity is at its maximum.

  3. The magnitude (length) of a vector is usually measured as

     • |v| = sqrt( v·v )

  4. If

     • u·v = 0

     then u and v are orthogonal (positioned at 90 degree angle)