mathematics and art

N
A
T
I
O
N
A
L
S
C
I
E
N
C
E
F
O
U
N
D
A
T
I
O
N
n f
x
y
z
P(x,y,z)

P'(x',y',0)
picture plane z=0
eye of viewer
at E(0,0,–d)
EP'=〈x',y',d〉
EP=〈x,y,z+d〉
E
x
y
z
P
2
picture plane
P
1
P'
2
P'
1
123
-1
-2
M' N'
P' Q'
R' S'
T'
x'
y'

-1-2-3
1
CAT
FOOD
CAT
FOOD
y'
x'
surface parallel to picture plane
picture plane
perspective
image
viewer
P
1
P
2
P'
1
P'
2
123
-1
-2
x'
y'
-1-2-3
1

123
-1
-2
x'
y'
-1-2-3
1
-3
45-4-5
123
-1
-2
x'
y'
1
y'
2
y'
3
y'
picture plane
(front view)
image of box
(x,y,z)
(x,y,z+a)
(x,y-b,z)
a
b
z
d

edge of picture
plane z=0
y'
1
y'
2
y'
3
y
actual box
(side view)
line visible
line still visible
line still visible
line vanishes
infinite straight line L
edge of picture plane
vanishing point
ab
c
?
v

0
v
0
d
v
0
v
1
?
e
v
0
v
1
f
a
v
0
b
v
0
v
2
c
v
0
v
2
d