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Expression 29: "R" Subscript, "X" "x" , Baseline equals "R" Subscript, "Z" "x" , Baseline
R
X
x
=
R
Z
x
equals
=
negative 47.6 5 6 3 0 4 2 2
−
4
7
.
6
5
6
3
0
4
2
2
negative 30.4 7 7 4 7 8 0 4 6 7
−
3
0
.
4
7
7
4
7
8
0
4
6
7
47.6 5 6 3 0 4 2 2
4
7
.
6
5
6
3
0
4
2
2
30.4 7 7 4 7 8 0 4 6 7
3
0
.
4
7
7
4
7
8
0
4
6
7
negative 47.6 5 6 3 0 4 2 2
−
4
7
.
6
5
6
3
0
4
2
2
negative 30.4 7 7 4 7 8 0 4 6 7
−
3
0
.
4
7
7
4
7
8
0
4
6
7
30.4 7 7 4 7 8 0 4 6 7
3
0
.
4
7
7
4
7
8
0
4
6
7
47.6 5 6 3 0 4 2 2
4
7
.
6
5
6
3
0
4
2
2
29
Expression 30: "R" Subscript, "X" "y" , Baseline equals "R" Subscript, "Z" "y" , Baseline cosine "t" Subscript, "x" , Baseline minus "R" Subscript, "Z" "z" , Baseline sine "t" Subscript, "x" , Baseline
R
X
y
=
R
Z
y
c
o
s
t
x
−
R
Z
z
s
i
n
t
x
equals
=
40.5 8 3 0 2 1 2 0 8 3
4
0
.
5
8
3
0
2
1
2
0
8
3
negative 34.3 3 3 1 9 1 1 8 8 9
−
3
4
.
3
3
3
1
9
1
1
8
8
9
negative 17.8 6 1 7 9 3 6 3 2
−
1
7
.
8
6
1
7
9
3
6
3
2
57.0 5 4 4 1 8 7 6 5 2
5
7
.
0
5
4
4
1
8
7
6
5
2
17.8 6 1 7 9 3 6 3 2
1
7
.
8
6
1
7
9
3
6
3
2
negative 57.0 5 4 4 1 8 7 6 5 2
−
5
7
.
0
5
4
4
1
8
7
6
5
2
34.3 3 3 1 9 1 1 8 8 9
3
4
.
3
3
3
1
9
1
1
8
8
9
negative 40.5 8 3 0 2 1 2 0 8 3
−
4
0
.
5
8
3
0
2
1
2
0
8
3
30
Expression 31: "R" Subscript, "X" "z" , Baseline equals "R" Subscript, "Z" "y" , Baseline sine "t" Subscript, "x" , Baseline plus "R" Subscript, "Z" "z" , Baseline cosine "t" Subscript, "x" , Baseline
R
X
z
=
R
Z
y
s
i
n
t
x
+
R
Z
z
c
o
s
t
x
equals
=
29.6 9 6 7 1 7 9 6 1 6
2
9
.
6
9
6
7
1
7
9
6
1
6
51.8 8 7 9 1 1 0 6 5 1
5
1
.
8
8
7
9
1
1
0
6
5
1
47.0 0 8 8 6 0 8 2 7 9
4
7
.
0
0
8
8
6
0
8
2
7
9
24.8 1 7 6 6 7 7 2 4 4
2
4
.
8
1
7
6
6
7
7
2
4
4
negative 47.0 0 8 8 6 0 8 2 7 9
−
4
7
.
0
0
8
8
6
0
8
2
7
9
negative 24.8 1 7 6 6 7 7 2 4 4
−
2
4
.
8
1
7
6
6
7
7
2
4
4
negative 51.8 8 7 9 1 1 0 6 5 1
−
5
1
.
8
8
7
9
1
1
0
6
5
1
negative 29.6 9 6 7 1 7 9 6 1 6
−
2
9
.
6
9
6
7
1
7
9
6
1
6
31
3. Rotation about Y axis:
3. Rotation about Y axis:
32
Expression 33: "R" Subscript, "Y" "x" , Baseline equals "R" Subscript, "X" "x" , Baseline cosine "t" Subscript, "y" , Baseline plus "R" Subscript, "X" "z" , Baseline sine "t" Subscript, "y" , Baseline
R
Y
x
=
R
X
x
c
o
s
t
y
+
R
X
z
s
i
n
t
y
equals
=
negative 37.5 6 4 7 1 5 1 0 7 6
−
3
7
.
5
6
4
7
1
5
1
0
7
6
negative 56.4 1 3 9 4 0 2 6 5 8
−
5
6
.
4
1
3
9
4
0
2
6
5
8
negative 37.9 6 1 5 4 3 7 2 1 4
−
3
7
.
9
6
1
5
4
3
7
2
1
4
negative 19.1 1 2 3 1 8 5 6 3 1
−
1
9
.
1
1
2
3
1
8
5
6
3
1
37.9 6 1 5 4 3 7 2 1 4
3
7
.
9
6
1
5
4
3
7
2
1
4
19.1 1 2 3 1 8 5 6 3 1
1
9
.
1
1
2
3
1
8
5
6
3
1
56.4 1 3 9 4 0 2 6 5 8
5
6
.
4
1
3
9
4
0
2
6
5
8
37.5 6 4 7 1 5 1 0 7 6
3
7
.
5
6
4
7
1
5
1
0
7
6
33
Expression 34: "R" Subscript, "Y" "y" , Baseline equals "R" Subscript, "X" "y" , Baseline
R
Y
y
=
R
X
y
equals
=
40.5 8 3 0 2 1 2 0 8 3
4
0
.
5
8
3
0
2
1
2
0
8
3
negative 34.3 3 3 1 9 1 1 8 8 9
−
3
4
.
3
3
3
1
9
1
1
8
8
9
negative 17.8 6 1 7 9 3 6 3 2
−
1
7
.
8
6
1
7
9
3
6
3
2
57.0 5 4 4 1 8 7 6 5 2
5
7
.
0
5
4
4
1
8
7
6
5
2
17.8 6 1 7 9 3 6 3 2
1
7
.
8
6
1
7
9
3
6
3
2
negative 57.0 5 4 4 1 8 7 6 5 2
−
5
7
.
0
5
4
4
1
8
7
6
5
2
34.3 3 3 1 9 1 1 8 8 9
3
4
.
3
3
3
1
9
1
1
8
8
9
negative 40.5 8 3 0 2 1 2 0 8 3
−
4
0
.
5
8
3
0
2
1
2
0
8
3
34
Expression 35: "R" Subscript, "Y" "z" , Baseline equals negative "R" Subscript, "X" "x" , Baseline sine "t" Subscript, "y" , Baseline plus "R" Subscript, "X" "z" , Baseline cosine "t" Subscript, "y" , Baseline
R
Y
z
=
−
R
X
x
s
i
n
t
y
+
R
X
z
c
o
s
t
y
equals
=
negative 41.7 3 6 2 0 2 1 3 3
−
4
1
.
7
3
6
2
0
2
1
3
3
negative 20.9 4 5 1 5 0 4 2 8 4
−
2
0
.
9
4
5
1
5
0
4
2
8
4
55.1 3 5 0 8 4 3 5 2 3
5
5
.
1
3
5
0
8
4
3
5
2
3
34.3 4 4 0 3 2 6 4 7 7
3
4
.
3
4
4
0
3
2
6
4
7
7
negative 55.1 3 5 0 8 4 3 5 2 3
−
5
5
.
1
3
5
0
8
4
3
5
2
3
negative 34.3 4 4 0 3 2 6 4 7 7
−
3
4
.
3
4
4
0
3
2
6
4
7
7
20.9 4 5 1 5 0 4 2 8 4
2
0
.
9
4
5
1
5
0
4
2
8
4
41.7 3 6 2 0 2 1 3 3
4
1
.
7
3
6
2
0
2
1
3
3
35
Expression 36: "V" Subscript, "x" , Baseline equals "R" Subscript, "Y" "x" , Baseline plus "L" Subscript, "x" , Baseline
V
x
=
R
Y
x
+
L
x
equals
=
negative 37.5 6 4 7 1 5 1 0 7 6
−
3
7
.
5
6
4
7
1
5
1
0
7
6
negative 56.4 1 3 9 4 0 2 6 5 8
−
5
6
.
4
1
3
9
4
0
2
6
5
8
negative 37.9 6 1 5 4 3 7 2 1 4
−
3
7
.
9
6
1
5
4
3
7
2
1
4
negative 19.1 1 2 3 1 8 5 6 3 1
−
1
9
.
1
1
2
3
1
8
5
6
3
1
37.9 6 1 5 4 3 7 2 1 4
3
7
.
9
6
1
5
4
3
7
2
1
4
19.1 1 2 3 1 8 5 6 3 1
1
9
.
1
1
2
3
1
8
5
6
3
1
56.4 1 3 9 4 0 2 6 5 8
5
6
.
4
1
3
9
4
0
2
6
5
8
37.5 6 4 7 1 5 1 0 7 6
3
7
.
5
6
4
7
1
5
1
0
7
6
36
Expression 37: "V" Subscript, "y" , Baseline equals "R" Subscript, "Y" "y" , Baseline plus "L" Subscript, "y" , Baseline
V
y
=
R
Y
y
+
L
y
equals
=
40.5 8 3 0 2 1 2 0 8 3
4
0
.
5
8
3
0
2
1
2
0
8
3
negative 34.3 3 3 1 9 1 1 8 8 9
−
3
4
.
3
3
3
1
9
1
1
8
8
9
negative 17.8 6 1 7 9 3 6 3 2
−
1
7
.
8
6
1
7
9
3
6
3
2
57.0 5 4 4 1 8 7 6 5 2
5
7
.
0
5
4
4
1
8
7
6
5
2
17.8 6 1 7 9 3 6 3 2
1
7
.
8
6
1
7
9
3
6
3
2
negative 57.0 5 4 4 1 8 7 6 5 2
−
5
7
.
0
5
4
4
1
8
7
6
5
2
34.3 3 3 1 9 1 1 8 8 9
3
4
.
3
3
3
1
9
1
1
8
8
9
negative 40.5 8 3 0 2 1 2 0 8 3
−
4
0
.
5
8
3
0
2
1
2
0
8
3
37
Expression 38: "V" Subscript, "z" , Baseline equals "R" Subscript, "Y" "z" , Baseline plus "L" Subscript, "z" , Baseline
V
z
=
R
Y
z
+
L
z
equals
=
negative 1.7 3 6 2 0 2 1 3 3 0 4
−
1
.
7
3
6
2
0
2
1
3
3
0
4
19.0 5 4 8 4 9 5 7 1 6
1
9
.
0
5
4
8
4
9
5
7
1
6
95.1 3 5 0 8 4 3 5 2 3
9
5
.
1
3
5
0
8
4
3
5
2
3
74.3 4 4 0 3 2 6 4 7 7
7
4
.
3
4
4
0
3
2
6
4
7
7
negative 15.1 3 5 0 8 4 3 5 2 3
−
1
5
.
1
3
5
0
8
4
3
5
2
3
5.6 5 5 9 6 7 3 5 2 3 3
5
.
6
5
5
9
6
7
3
5
2
3
3
60.9 4 5 1 5 0 4 2 8 4
6
0
.
9
4
5
1
5
0
4
2
8
4
81.7 3 6 2 0 2 1 3 3
8
1
.
7
3
6
2
0
2
1
3
3
38
Expression 39: "P" Subscript, "x" , Baseline equals "v" left parenthesis, 0 , 0 , 0 , right parenthesis . "x"
P
x
=
v
0
,
0
,
0
.
x
equals
=
negative 1.5 1 8 9 0 4 1 0 9 5 9
−
1
.
5
1
8
9
0
4
1
0
9
5
9
39
Expression 40: "P" Subscript, "y" , Baseline equals "v" left parenthesis, 0 , 0 , 0 , right parenthesis . "y"
P
y
=
v
0
,
0
,
0
.
y
equals
=
negative 2.4 5 9 1 7 8 0 8 2 1 9
−
2
.
4
5
9
1
7
8
0
8
2
1
9
40
Controls
Controls
Hide this folder from students.
41
Back Axes
Back Axes
Hide this folder from students.
52
Faces & Wireframe
Faces & Wireframe
Hide this folder from students.
56
Points
Points
Hide this folder from students.
62
Normals
Normals
Hide this folder from students.
70
Shading & Colors
Shading & Colors
Hide this folder from students.
85
Front Axes
Front Axes
Hide this folder from students.
100
Axis Numbers
Axis Numbers
Hide this folder from students.
104
sources:
https://www.cs.uic.edu/~jbell/CourseNotes/ComputerGraphics/3DTransforms.html
.
https://www.geeksforgeeks.org/back-face-detection-method/#
https://www.gabrielgambetta.com/computer-graphics-from-scratch/03-light.html
https://education.siggraph.org/static/HyperGraph/scanline/visibility/backface.htm
sources: https://www.cs.uic.edu/~jbell/CourseNotes/ComputerGraphics/3DTransforms.html. https://www.geeksforgeeks.org/back-face-detection-method/# https://www.gabrielgambetta.com/computer-graphics-from-scratch/03-light.html https://education.siggraph.org/static/HyperGraph/scanline/visibility/backface.htm
112
113
powered by
powered by
camera (move)
light
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"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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