Graphics Reference
In-Depth Information
2
4
3
5
cos h
ðx
1
bÞ
a
y
1
¼ c þ a
2
4
3
5
cos h
ðx
2
bÞ
a
y
2
¼ c þ a
2
3
5
a
2
3
ðx
2
bÞ
a
ðx
1
bÞ
a
L ¼ a
4
4
5
sin h
sin h
2
3
q
L
sin h
ðx
2
x
1
Þ
2
a
2
4
5
ða
can be solved for numerically at this point
2
ðy
2
y
1
Þ
¼
2
Þ
a
0
@
1
A
0
@
1
A
sin h
x
2
a
x
1
a
M ¼
sin h
0
@
1
A
0
@
1
A
cos h
x
2
a
x
1
a
N ¼
cos h
(7.87)
0
1
M
N
@
A
tan h
1
if N > M m ¼
M
sin h
N
cos h
Q ¼
ðmÞ
¼
ðmÞ
2
4
0
@
1
A
3
5
L
Q
a
b ¼ a
sin h
1
m
0
@
1
A
N
M
tan h
1
i
f
M > N
m ¼
N
sin h
M
cos h
Q ¼
ðmÞ
¼
ðmÞ
2
0
1
3
L
Q
a
b ¼ a
4
@
A
5
cos h
1
m
A relaxation process is used as the second and final step in positioning the vertices. The effect of
gravity is ignored; it has been used implicitly in the formation of the catenary curves using the interior
vertices. The exterior vertices are initially positioned to affect a downward pull. The relaxation pro-
cedure repositions each vertex to satisfy unit distance from each of its neighbors. For a given vertex,
displacement vectors are formed to each of its neighbors. The vectors are added to determine the direc-
tion of the repositioning. The magnitude of the repositioning is determined by taking the square root of
Search WWH ::
Custom Search