3D Program
Common formulas
1
Two vectors
A
And
B
The scalar product
(
See chapter Fifth
):
A
B
A
B
A
B
A
B
X
X
Y
Y
Z
Z
2
Two vectors
A
And
B
The cross product
(
See chapter Fifth
):
A
B
I
A
A
B
B
J
A
A
B
B
K
A
A
B
B
I
J
K
A
A
A
B
B
B
Y
Z
Y
Z
X
Z
X
Z
X
Y
X
Y
X
Y
Z
X
Y
Z
Det
Det
Det
Det
4
Translation transformations,
T
T
X
Y
,
And
T
Z
Describe panning
(
See chapter II
):
X
Y
Z
T
T
T
X
Y
Z
X
Y
Z
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
5
Zoom transform,
S
S
X
Y
,
And
S
Z
Describe scaling
(
See chapter II
):
X
Y
Z
S
S
S
X
Y
Z
X
Y
Z
0
0
0
0
0
0
6
3D
Rotation transformation, Angle
,
And
Describe rotation
(
See chapter II
):
Left
:
-z->+x
Around
Y
+y->-z
Around
X
+x->+y
Around
Z
X
Y
Z
X
Y
Z
Cos
)
Sin
)
Sin
)
Cos
)
Cos
)
Sin
)
Sin
)
Cos
)
Cos
)
Sin
)
Sin
)
Cos
)
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
7
Perspective Transformations,
Focus
Specifies that the perspective is shortened (
Perspective foreshortening
）
(
See chapter II
):
X
Y
Z
Focus
X
Y
Z
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
/
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