Graphics Reference
In-Depth Information
For example, suppose that the segment [
P
1
,
P
2
] is as shown in Figure 3.8(c). Here are
the computations one has to perform. Let
P
i
= (x
i
,y
i
) and let
C
= (xmax,ymin) be the
corner of the window also indicated in Figure 3.8(c). After checking that y
2
< ymin,
we must determine whether the vector
P
1
P
2
is above or below the vector
P
1
C
. This
reduces to determining whether the ordered basis (
P
1
C
,
P
1
P
2
) determines the standard
orientation of the plane or not. Since
PC
PP
Ê
Ë
ˆ
¯
1
(
)
(
)
-
(
)
(
)
<
det
=
x
max
-
x
y
-
y
y
min
-
y
12 1
0
x
-
x
,
12 1
12
P
1
P
2
is below
P
1
C
. We now know that we will have to compute the intersection of
[
P
1
,
P
2
] with both the left and bottom boundary of the window.
Algorithm 3.2.4.1 is an abstract program for the Nicholl-Lee-Nicholl algorithm in
the edge region case (
P
1
in the region shown in Figure 3.8(c)). We assume a window
[xmin,xmax] ¥ [ymin,ymax].
Figure 3.8.
Nicholl-Lee-Nicholl line clipping.
procedure
LeftEdgeRegionCase (
ref real
x1, y1, x2, y2;
ref boolean
visible)
begin
real
dx, dy;
if
x2 < xmin
then
visible :=
false
else if
y2 < ymin
then
LeftBottom (xmin,ymin,xmax,ymax,x1,y1,x2,y2,visible)
else if
y2 > ymax
then
begin
Algorithm 3.2.4.1.
The edge region case of the Nicholl-Lee-Nicholl line-clipping
algorithm.
