Motivation
The inverse square root of a floating point number is used in calculating a normalized vector. Since a 3D graphics program uses these normalized vectors to determine lighting and reflection, millions of these calculations must be done per second. Before the creation of specialized hardware to handle transform and lighting, software computations could be slow. Specifically, when the code was developed in the early 1990s, most floating point processing power lagged behind the speed of integer processing.
To normalize a vector, the length of the vector is determined by calculating its Euclidean norm: the square root of the sum of squares of the vector components. When each component of the vector is divided by that length, the new vector will be a unit vector pointing in the same direction.
- is the Euclidean norm of the vector, analogous to the calculation of the Euclidean distance between two points in Euclidean space.
- is the normalized (unit) vector. Using to represent ,
- , which relates the unit vector to the inverse square root of the distance components.
Quake III Arena used the fast inverse square root algorithm to speed graphics processing unit computation, but the algorithm has since been implemented in some dedicated hardware vertex shaders using field-programmable gate arrays (FPGA).
Read more about this topic: Fast Inverse Square Root
Famous quotes containing the word motivation:
“Self-determination has to mean that the leader is your individual gut, and heart, and mind or we’re talking about power, again, and its rather well-known impurities. Who is really going to care whether you live or die and who is going to know the most intimate motivation for your laughter and your tears is the only person to be trusted to speak for you and to decide what you will or will not do.”
—June Jordan (b. 1939)