Game Development Reference
In-Depth Information
Vectors can be multiplied in several ways. The component product has no geo-
metric correlate:
=
a x
a y
a z
b x
b y
b z
a x b x
a y b y
a z b z
a
b
=
and the symbol shown is a personal convention.
The scalar product
a x
a y
a z
b x
b y
b z
·
=
a
·
b
=
+
+
a x b x
a y b y
a z b z
has the trigonometric form
a
·
b
=
a x b x +
a y b y +
a z b z =|
a
||
b
|
cos θ
where θ is the angle between the two vectors.
The vector product
×
=
a x
a y
a z
b x
b y
b z
a y b z
a z b y
a
×
b
=
a z b x
a x b z
a x b y
a y b x
has the trigonometric form
|
a
×
b
|=|
a
||
b
|
sin θ
and is non-commutative:
a
×
b
=−
b
×
a
D.2
Q UATERNIONS
A quaternion
cos 2
x sin 2
y sin 2
z sin 2
Search Nedrilad ::




Custom Search