Background Information and Techniques - Computer Animation: Algorithms and Techniques - page 481

FIGURE B.56
Computing Gauss-Legendre weights and abscissas.
B.8.2 Updating function values
Integrating ordinary differential equations (ODEs) in computer animation typically means that the
derivative function f 0 is available and that a numerical approximation to the function f is desired.
For example, in a physically based simulation, the time-varying acceleration of an object is computed
from the object's mass and the forces acting on the object in the environment. From the acceleration
(the derivative function), the velocity (the function) is numerically calculated over time. Similarly,