Graphics Reference
In-Depth Information
Inner product:
3D vectors
a
=
a
1
e
1
+
a
2
e
2
+
a
3
e
3
b
=
b
1
e
1
+
b
2
e
2
+
b
3
e
3
a
·
b
=|
a
||
b
|
cos
β
=
a
1
b
1
+
a
2
b
2
+
a
3
b
3
.
Outer product:
2D vectors
a
=
a
1
e
1
+
a
2
e
2
b
=
b
1
e
1
+
b
2
e
2
a
1
a
2
a
∧
b
=
e
1
∧
e
2
.
b
1
b
2
Outer product:
3D vectors
a
=
a
1
e
1
+
a
2
e
2
+
a
3
e
3
b
=
b
1
e
1
+
b
2
e
2
+
b
3
e
3
c
=
c
1
e
1
+
c
2
e
2
+
c
3
e
3
a
1
a
2
a
2
a
3
a
3
a
1
a
∧
b
=
e
1
∧
e
2
+
e
2
∧
e
3
+
e
3
∧
e
1
b
1
b
2
b
2
b
3
b
3
b
1
a
1
a
2
a
3
a
∧
b
∧
c
=
b
1
b
2
b
3
e
1
∧
e
2
∧
e
3
c
1
c
2
c
3
|
a
∧
b
|=|
a
||
b
|
sin
β.
Geometric product
ab
=
a
·
b
+
a
∧
b
ba
=
a
·
b
−
a
∧
b
1
2
(
ab
a
·
b
=
+
ba
)
1
2
(
ab
∧
=
−
a
b
ba
).
Inverse of a vector
a
a
−
1
=
2
.
|
a
|
Duality
A
=
I
A
I
=
the local pseudoscalar
.
Reverse of a multivector
A
=
ab
A
†
=
ba
.
