Vectors

Vector Length
Figure 1 shows a fixed vector with the following
coordinates ie. components,
The magnitude (length) of the vector is, length = sqrt((ax * ax) + (ay * ay) + (az * az)) length = sqrt(9 + 1 + 4) = 3.742 As a shorthand notation the magnitude of a vector is written with two vertical lines,

Unit Vectors  Normalizing
Operations in 2D and 3D computer graphics are often performed using copies
of vectors that have been normalized ie. converted to unit vectors. For
example, the tutorial
"RSL: Edge Effects"
applies normalization before calculating the dot product of two vectors.
Normalizing a vector involves two steps: x = ax/a y = ay/a z = az/a As a "worked example" the vector shown in figure 1 has the xyz components of 3, 1, 2 and a length of 3.742. Therefore, a normalized copy of the vector will have components, x = 3.0 / 3.742 = 0.802 y = 1.0 / 3.742 = 0.267 z = 2.0 / 3.742 = 0.534 
© 2002 Malcolm Kesson. All rights reserved.