GPU PRO 3

290 V 3D Engine Design

because i = j and n is the same. To simplify the 2A · B term, note that

n

X

i=0

~a

i

·

n

X

j=0

~a

j

=

n

X

i=0

~a

2

i

because i = j, n is the same, and (~a ·~a) = ||~a||

2

.

Moving ||B|| to the left, simplifying, and combining like terms, we get Equa-

tion (3.6).

Bibliography

[Iourcha et al. 09] Konstantine Iourcha, Jason C. Yang, and Andrew Pomianowski. “A

Directionally Adaptive Edge Anti-Aliasing Filter.” In Proceedings of the Conference

on High Performance Graphics, pp. 127–133. Edited by Stephen N. Spencer, David

McAllister, Matt Pharr, and Ingo Wald. New York: ACM, 2009.

[Larson et al. 98] Ron Larson, Robert P. Hostetler, and Bruce H. Edwards. ...