Graphics Reference
In-Depth Information
Figure 3.1.
A perspectivity between parallel
lines.
O
L
A
BC
L¢
A¢
B¢
C¢
L
B
O
V (vanishing
point on L)
C
A
L¢
B¢
W
A¢
C¢
Figure 3.2.
A perspectivity between
skew lines.
(vanishing
point on L¢)
vanishing line
horizon
plane
E¢
view
plane
O
O
L
2
D¢
D
L
1
object
plane
C¢
B¢
G
C
G¢
A¢
B
F
L
2
¢
A
object
plane
F¢
L
3
J
view
plane
L
4
L
4
¢
vanishing line
L
1
¢
L
3
¢
(a)
(b)
Figure 3.3.
A perspectivity between skew planes.
See Figure 3.3(a).
(1) The rectangle
ABCD
in the object plane gets mapped to the trapezoid
A
¢
B
¢
C
¢
D
¢
and the lines
L
1
and
L
2
through
A
,
C
and
B
,
D
, respectively, get mapped to the lines
L
1
¢
and
L
2
¢ through
A
¢,
C
¢ and
B
¢,
D
¢.
(2) The parallel lines
L
1
and
L
2
get mapped to lines that intersect at a point
E
¢ in
the view plane. The point
E
¢ has the property that
OE
¢ is parallel to the object plane.
