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1995-04-07
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376 lines
_,-'xxx
,,--'' xxxxx
<)-,, xxxxx things we're
eye --,_ xxxxx looking at
'-,_xxx
projection
rays
Figure 1
=======================================
|
|
|
a| _,-'xxx
,,--+' xxxxx
<)-,, | xxxxx things we're
eye --+_ xxxxx looking at
b| '-,_xxx
|
|
a and b are the projection points.
Figure 2
=======================================
- - - - - - -
| |
/| |
/ | |
/ | _-| | |
/ | _- | | |
/ |_- | | y'
/ _+ | | |
/ _- | | y |
/ _- | | | |
/b_- | | | |
/_-a | | | |
------------------ - - -
<---x'---->
<--------x------->
Figure 3
=======================================
World "y"
Coordinate
.
/|\ -+Eye "y" unit vector
| /|
| /
| / /
| a /\
| / / \
| / \
| O\ \
| \ \ o Point
| \ \ /
| b \ /
| \ \
| \ \|
| -+Eye "x" unit vector
|
|
----------------------->
World World "x" coordinate
origin
O is eye origin
a is EyeY dot R
b is EyeX dot R
Figure 3a
=======================================
a
<---. X
. /|\
|
. |
|
. |.
|
. | .
|
. | .
|
.| .
|
| .
|
| .
----------------------->
Y
a has a length of X dot Y
Figure 3b
=======================================
|
|x|
|x|
|xxx|
------+---+-------
xxx| |xxx-
x| |x-
|x-_ _-|
|xxx_-xx|
|xxx- -xx|
|x- -x|
' '
Figure 4
=======================================
m
/\
/ \
/ \
/ \
n/ \
\ \
\ \
\ \
\ \p
\ /
\ /
\ /
\ /
\/
o
Note: this figure should be 3 figures. In part a, you only see the above
polygon, filled. In part b, you see the polygon described as vectors.
E.G. I represented the polygon as vectors mn, then no, then op, then pm.
In c, I represented the polygon as vectors mn, no, mp and po.
Figure 5
=======================================
Figure 6 is a bit hard to draw (it's 3d)
=======================================
.... ...-
...# .--#
.##. -##+
#... #+-.
a b
Figure 7
=======================================
_______
| i /
| /
|i i/
| /
| /
| <
| i\
| \
| i \
-------
The i's mark where the in side of an edge is.
This figure is a bit different from the original one, but it's
good anyway.
Figure 8
=======================================
Figure 9 a bit hard to draw because of the circle
=======================================
outside
/\ /\ /\
/ \ / \ /| \
/ \ / \ / | \
/ \ / \ / | \
/ inside \ |/ \| |/ | \|
/ \ +- -+ +- | -+
. | .
. | .
a b . | .
.| . c
\/
Figure 10
=======================================
________
| \
| \
|-> / |
| / | in /
| +- / | /
| |\ / | /
| / | /
| / | /
| / | /
| / "mixed" | /
|/ |/
.
..
. . "mixed"
. .
. .
. .
. out.
Figure 11
=======================================
a_,-'\
_,-' \b
| \
| \
| | 1
| |
| |
|___________|
a_,-'\
_,-' \b
|'--, \
| '--,,__\
| |
| | 2
| |
|___________|
|'--,
| '--,,__
| |
| | 3
| |
|___________|
Note: edges a and b are the "green" edges of the text.
Figure 12
=======================================
/ \
/ \
/ \ -+
/\| \/|
/ -+ \
/ \
/ \
\ /
\ /
\ -+ /
\/| /
\ /\|
\ / -+
\ /
Figure 13
=======================================
c
/\
/ \
/ \
/ \
/ \
/ \
b/ \
'-,_ P \
'+----+----+n
m '-,_ \
'-,_ \
'-+a
(A simplified version of the real figure)
Figure 14
=======================================
c
\ .
|\ .
| \ .<--- clipping plane
| \.
| +m
| .\
| . \
\ . \
d \ . \b
\ . |
\. |
n+ | <----- polygon
.\ |
. \ |
. \|
. |a
(A simplified version of the real figure)
Start with point a. Trivially accept vector ab (it's on the correct
side of the clipping plane). bc is cut to becom bm. cd is trivially
rejected. da is clipped at n and na is kept. Since we just
re-entered the acceptance region, link m and n to form the vector mn.
The complete clipped polygon is mnba.
Figure 15
=======================================
This:
.
.
. /
./|
/ |<---- polygon
/.|
/ .|
/ |
/ |
/ |.
/ |.
\ | .<---- clipping plane
\ |.
\ |.
\ |
\ |
\.|
\|
.\
.
.
clips to:
/
/|
/ |
||
||
|
|
.
.
.<---- there is a degenerate edge here
.
.
|
|
||
\|
\
Figure 16
=======================================
