Monge’s projection
Revolution
1. revolution
1.1. l
p
1
l
A'
A"
l'
l"
A
=
p
2
'
X
12
=
p
1
"
D: A, l
p
1
,
j
1
, j
2
1. revolution
1.1. l
p
1
l
e
A
e
"
A
A'
A"
l'
l"
A
=
p
2
'
X
12
=
p
1
"
D: A, l
p
1
,
j
1
, j
2
e
A
l
e
A
A
1. revolution
1.1. l
p
1
l
e
A
e
"
A
A'
A"
S"
A
l'
=S'
A
l"
S
A
A
=
p
2
'
X
12
=
p
1
"
D: A, l
p
1
,
j
1
, j
2
e
A
l
e
A
A
S
A
=l
e
A
1. revolution
1.1. l
p
1
l
e
A
e
"
A
r
A
o'
A
r
A
A'
A"
S"
A
l'=S'
A
l"
S
A
A
o
A
=
p
2
'
X
12
=
p
1
"
D: A, l
p
1
,
j
1
, j
2
e
A
l
e
A
A
S
A
=l
e
A
r
A
=
AS
A
1. revolution
1.1. l
p
1
l
e
A
e
"
A
j
1
r
A
o'
A
r
A
A'
1
A'
A"
1
A"
S"
A
l'=S'
A
j
1
l"
S
A
A
A
1
o
A
=
p
2
'
X
12
=
p
1
"
D: A, l
p
1
,
j
1
, j
2
e
A
l
e
A
A
S
A
=l
e
A
r
A
=
AS
A
A
1
– revolved point A through
j
1
1. revolution
1.1. l
p
1
l
e
A
e
"
A
j
1
j
2
r
A
o'
A
r
A
A'
1
A'
A'
2
A"
1
A"
A"
2
S"
A
l'=S'
A
j
1
j
2
l"
S
A
A
A
1
A
2
o
A
=
p
2
'
X
12
=
p
1
"
D: A, l
p
1
,
j
1
, j
2
e
A
l
e
A
A
S
A
=l
e
A
r
A
=
AS
A
A
1
– revolved point A through
j
1
A
2
– revolved point A through
j
2
1. revolution
1.1. l
p
1
l
A
e
A
e
"
A
A
1
A
2
j
1
j
2
r
A
o
A
o'
A
r
A
A'
1
A'
A'
2
A"
1
A"
A"
2
S"
A
l'=S'
A
j
1
j
2
l"
S
A
=
p
2
'
X
12
=
p
1
"
D: A, l
p
1
,
j
1
, j
2
e
A
l
e
A
A
S
A
=l
e
A
r
A
=
AS
A
A
1
– revolved point A through
j
1
A
2
– revolved point A through
j
2
Monge’s projection
True length by revolution
1.2. Obtain the true length of segment AB
D: A,B
A'
B"
A"
B'
=
p
2
'
X
12
=
p
1
"
D: A,B
l
p
1
B
l
A'
B"
A"
B'
=l'
l"
=
p
2
'
X
12
=
p
1
"
1.2. Obtain the true length of segment AB
e
"
A
D: A,B
l
p
1
B
l
o'
A
r
A
A'
1
A'
B"
A"
A"
1
B'=l'
l"
=B"
1
=B'
1
S"
A
=S'
A
B
1
=B
e
A
l
e
A
A
r
A
=
AS
A
A
1
– revolved point A
line A
1
B
1
is a frontal line, parallel to
vertical projection plane
~
~
=
p
2
'
X
12
=
p
1
"
1.2. Obtain the true length of segment AB
A"
1
e
"
A
D: A,B
l
p
1
B
l
B
1
=B
e
A
l
e
A
A
r
A
=
AS
A
o'
A
r
A
A'
1
A'
B"
A"
B'=l'
l"
=B"
1
=B'
1
S"
A
=S'
A
~
~
=
p
2
'
X
12
=
p
1
"
1.2. Obtain the true length of segment AB
A
1
– revolved point A
line A
1
B
1
is a frontal line, parallel to
vertical projection plane
1.3. Obtain the true size of quadrangle ABCD
D:
a
=ABCD,
ap
2
B'
A'
B"
A"
C"
D"
a
"
D'
C'
=
p
2
'
X
12
=
p
1
"
D:
a
=ABCD,
ap
2
l
p
2
A
l
B'
A'
B"
l'
A"
=l"
C"
D"
a
"
D'
C'
=
p
2
'
X
12
=
p
1
"
1.3. Obtain the true size of quadrangle ABCD
D:
a
=ABCD,
ap
2
l
p
2
A
l
A
1
=A
B'
A'
=A'
1
B"
l'
A"=l"
=A"
1
C"
D"
a
"
D'
C'
=
p
2
'
X
12
=
p
1
"
1.3. Obtain the true size of quadrangle ABCD
D:
a
=ABCD,
ap
2
l
p
2
A
l
A
1
=A
B'
1
B'
A'=A'
1
B"
l'
A"=l"=A"
1
C"
D"
a
"
D'
C'
B"
1
e
'
B
a
"
1
B
e
B
e
B
l
a
1
ll
p
1
B
1
e
B
~
~
=
p
2
'
X
12
=
p
1
"
1.3. Obtain the true size of quadrangle ABCD
D:
a
=ABCD,
ap
2
l
p
2
A
l
A
1
=A
a
1
ll
p
1
B
e
B
e
B
l
B
1
e
B
B'
1
B'
A'=A'
1
B"
l'
A"=l"=A"
1
C"
D"
a
"
C'
1
D'
C'
B"
1
C"
1
e
'
C
e
'
B
a
"
1
~
~
~
=
p
2
'
X
12
=
p
1
"
1.3. Obtain the true size of quadrangle ABCD
D:
a
=ABCD,
ap
2
l
p
2
A
l
A
1
=A
a
1
ll
p
1
B
e
B
e
B
l
B
1
e
B
B'
1
B'
A'=A'
1
B"
l'
A"=l"=A"
1
C"
D"
a
"
C'
1
D'
1
D'
C'
B"
1
C"
1
D"
1
e
'
C
e
'
D
e
'
B
a
"
1
~
~
~
~
=
p
2
'
X
12
=
p
1
"
1.3. Obtain the true size of quadrangle ABCD
D:
a
=ABCD,
ap
2
l
p
2
A
l
A
1
=A
a
1
ll
p
1
B
e
B
e
B
l
B
1
e
B
B'
1
B'
A'=A'
1
B"
l'
A"=l"=A"
1
C"
D"
a
"
C'
1
D'
1
D'
C'
B"
1
C"
1
D"
1
a
"
1
e
'
C
e
'
D
e
'
B
a
1
=A
1
B
1
C
1
D
1
ABCD
~
~
~
~
=
p
2
'
X
12
=
p
1
"
1.3. Obtain the true size of quadrangle ABCD
D:
a
=ABCD,
ap
2
l
p
2
A
l
A
1
=A
a
1
ll
p
1
B
e
B
e
B
l
B
1
e
B
a
1
=A
1
B
1
C
1
D
1
ABCD
B'
1
B'
A'=A'
1
B"
l'
A"=l"=A"
1
C"
D"
a
"
C'
1
D'
1
D'
C'
B"
1
C"
1
D"
1
a
"
1
e
'
C
e
'
D
e
'
B
a
1
ll
p
1
~
~
~
~
=
p
2
'
X
12
=
p
1
"
1.3. Obtain the true size of quadrangle ABCD
Monge’s projection
Polyhedrons
– pyramid
Polyhedrons
Pyramid
C"
B"
A"
W"
C'
A'
W'
B'
=
p
2
'
X
12
=
p
1
"
C"
a
"
B"
A"
W"
C'
A'
W'
1'
2'
3'
1"
2"
3"
B'
=
p
2
'
X
12
=
p
1
"
Polyhedrons
Pyramid
C"
a
"
B"
A"
W"
C'
A'
W'
1'
2'
3'
1"
2"
3"
B'
=
p
2
'
X
12
=
p
1
"
Polyhedrons
Pyramid
C"
a
"
B"
A"
W"
C'
B'
A'
W'
1'
2'
3'
1"
2"
3"
l"
t
'
A'
C'
e
A
"
A"
C"
e
1
"
1"
3"
e
3
"
A
A
B
C
W
1
1
3
2
3
=l'
C
=
p
2
'
X
12
=
p
1
"
Polyhedrons
Pyramid
C"
a
"
B"
A"
W"
C'
B'
A'
W'
1'
2'
3'
1"
2"
3"
l"
t
'
A'
C'
e
A
"
A"
C"
e
1
"
1"
3"
e
3
"
A
A
B
C
W
1
1
3
2
3
=l'
C
=
p
2
'
X
12
=
p
1
"
Polyhedrons
Pyramid