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 short-hand 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.