Graphics Reference
In-Depth Information
•
If P and Q, with position vectors
p
and
q
, respectively, are two points on a line perpendicular
to a vector
v
, then
p
·
v
=
q
·
v
.
•
The vector product is non-commutative:
a
×
b
=−
b
×
a
but obeys the distributive law:
a
×
b
+
c
=
a
×
b
+
a
×
c
•
The triple product or box product is given by
x
a
y
a
z
a
a
·
b
×
c
=
b
·
c
×
a
=
c
·
a
×
b
=
x
b
y
b
z
b
x
c
y
c
z
c
•
The volume of a prism constructed from three vectors is given by
Volume
=
a
·
b
×
c
•
The vector triple product is given by
a
×
b
×
c
=
a
·
c
b
−
a
·
b
c
and
a
×
b
×
c
=
a
·
c
b
−
b
·
c
a
•
b
j
is
v
⊥
=−
The perpendicular to a vector
v
=
a
i
+
b
i
+
a
j
.
•
The magnitude of
v
⊥
equals the magnitude of
v
.
•
The perp product equals
a
⊥
·
b
=
a
b
sin
which equals the signed area of the parallelogram formed by
a
and
b
.
•
Two vectors can be linearly interpolated using
w
=
1
−
u
+
v
0
≤
≤
1
