
Chapter
16
Numerical Methods
T
his chapter describes various numerical methods that are generally useful in
computer graphics. Many of these are specifically useful in real-time game
engines.
16.1 Systems of Equations
The two types of systems that arise often in graphics applications are linear systems
and polynomial systems. Linear systems are written in the form AX = b for n × n
matrix A and n ×1vectorsX and b. Both A and b are known. The unknowns are the
components of X. Polynomial systems are written in the form p
i
(X) =0 for 0 ≤i<n
for n × 1vectorX and where p
i
is a polynomial function.
16.1.1 Linear Systems
The standard approach to solving linear systems ...