三维管线建模Matlab仿真程序(只做到插值)
进程被枪毙了.心里不痛快.把做了一半的matlab仿真程序拿出来供大家拍拍砖吧.写得比较乱.有不明白的可以回复或是发邮件给我.我的邮件是
phoenix8848@gmail.com
1
clear;
2A
=
[
0
0
0
;
0.65
0.25
0.376
;
1
0
0
];R
=
0.25
*
1.414
;
3%calculate line vectors
4v
=
ones(
1
,
3
);%initial line vectors
5
for
i
=
1
:
2
6 v(i,:)
=
A(i
+
1
,:)
-
A(i,:);
7
end
8%calculate the interpolation angle
9ang
=
acos(
abs
(v(
1
,
1
)
*
v(
2
,
1
)
+
v(
1
,
2
)
*
v(
2
,
2
)
+
v(
1
,
3
)
*
v(
2
,
3
))
/
(sqrt(v(
1
,
1
)
^
2
+
v(
1
,
2
)
^
2
+
v(
1
,
3
)
^
2
)
*
sqrt(v(
2
,
1
)
^
2
+
v(
2
,
2
)
^
2
+
v(
2
,
3
)
^
2
)));
10%the dis pB
to
pAi
11d
=
R
*
tan
(ang
/
2
);
12%direction cosine of V(Ai
-
1
,Ai)
13cosa1
=
v(
1
,
1
)
/
sqrt(v(
1
,
1
)
^
2
+
v(
1
,
2
)
^
2
+
v(
1
,
3
)
^
2
);
14cosb1
=
v(
1
,
2
)
/
sqrt(v(
1
,
1
)
^
2
+
v(
1
,
2
)
^
2
+
v(
1
,
3
)
^
2
);
15cosc1
=
v(
1
,
3
)
/
sqrt(v(
1
,
1
)
^
2
+
v(
1
,
2
)
^
2
+
v(
1
,
3
)
^
2
);
16%interpolation start point
17b1
=
[A(
2
,
1
)
-
d
*
cosa1,A(
2
,
2
)
-
d
*
cosb1,A(
2
,
3
)
-
d
*
cosc1];
18%direction cosine of V(Ai,Ai
+
1
)
19cosa2
=
v(
2
,
1
)
/
sqrt(v(
2
,
1
)
^
2
+
v(
2
,
2
)
^
2
+
v(
2
,
3
)
^
2
);
20cosb2
=
v(
2
,
2
)
/
sqrt(v(
2
,
1
)
^
2
+
v(
2
,
2
)
^
2
+
v(
2
,
3
)
^
2
);
21cosc2
=
v(
2
,
3
)
/
sqrt(v(
2
,
1
)
^
2
+
v(
2
,
2
)
^
2
+
v(
2
,
3
)
^
2
);
22%interpolation
end
point
23b2
=
[A(
2
,
1
)
+
d
*
cosa2,A(
2
,
2
)
+
d
*
cosb2,A(
2
,
3
)
+
d
*
cosc2];
24%vector of angular bisector
25v0
=
sqrt(v(
1
,
1
)
^
2
+
v(
1
,
2
)
^
2
+
v(
1
,
3
)
^
2
);
26v1
=
[v(
1
,
1
) v(
1
,
2
) v(
1
,
3
)]
/
v0;
27v0
=
sqrt(v(
2
,
1
)
^
2
+
v(
2
,
2
)
^
2
+
v(
2
,
3
)
^
2
);
28v2
=
[v(
2
,
1
) v(
2
,
2
) v(
2
,
3
)]
/
v0;
29L0
=
[(
-
v1(
1
)
+
v2(
1
))
/
2
,(
-
v1(
2
)
+
v2(
2
))
/
2
,(
-
v1(
3
)
+
v2(
3
))
/
2
];
30%direction cosine of angular bisector
31cosa3
=
L0(
1
)
/
sqrt(L0(
1
)
^
2
+
L0(
2
)
^
2
+
L0(
3
)
^
2
);
32cosb3
=
L0(
2
)
/
sqrt(L0(
1
)
^
2
+
L0(
2
)
^
2
+
L0(
3
)
^
2
);
33cosc3
=
L0(
3
)
/
sqrt(L0(
1
)
^
2
+
L0(
2
)
^
2
+
L0(
3
)
^
2
);
34%calculate the center point of interpolation circle
35t
=
R
*
sec(ang
/
2
);
36p
=
[A(
2
,
1
)
+
cosa3
*
t,A(
2
,
2
)
+
cosb3
*
t,A(
2
,
3
)
+
cosc3
*
t];
37%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
38%calculate the normal vector of interpolation circle
39dx
=
[b1(
1
)
-
p(
1
) b1(
2
)
-
p(
2
) b1(
3
)
-
p(
3
)];
40dx
=
dx
/
sqrt(dx(
1
)
^
2
+
dx(
2
)
^
2
+
dx(
3
)
^
2
);
41dy
=
[b2(
1
)
-
p(
1
) b2(
2
)
-
p(
2
) b2(
3
)
-
p(
3
)];
42dy
=
dy
/
sqrt(dy(
1
)
^
2
+
dy(
2
)
^
2
+
dy(
3
)
^
2
);
43dz
=
[v(
1
,
2
)
*
v(
2
,
3
)
-
v(
2
,
2
)
*
v(
1
,
3
),v(
1
,
1
)
*
v(
2
,
3
)
-
v(
2
,
1
)
*
v(
1
,
3
),v(
1
,
1
)
*
v(
2
,
2
)
-
v(
2
,
1
)
*
v(
1
,
2
)];
44dz
=
dz
/
sqrt(dz(
1
)
^
2
+
dz(
2
)
^
2
+
dz(
3
)
^
2
);
45
46T
=
[dx;dy;dz];
47%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
48P
=
ones(
3
,
11
);
49delta
=
pi
*
0.5
/
10
;
50
for
i
=
0
:
10
51 m
=
[R
*
cos
(i
*
delta) R
*
sin
(i
*
delta)
0
];
52 P(:,i
+
1
)
=
T
'
*m'+p';
53
end
54plot3(P(
1
,:),P(
2
,:),P(
3
,:),
'
r+-',A(:,1),A(:,2),A(:,3),'b+-');
55
grid
on
;
56axis
on
;
57xlabel(
'
X');ylabel('Y');zlabel('z');
clear;2
A
=
[
0
0
0
;
0.65
0.25
0.376
;
1
0
0
];R
=
0.25
*
1.414
;3
%calculate line vectors4
v
=
ones(
1
,
3
);%initial line vectors5
for
i
=
1
:
2
6
v(i,:)
=
A(i
+
1
,:)
-
A(i,:);7
end
8
%calculate the interpolation angle9
ang
=
acos(
abs
(v(
1
,
1
)
*
v(
2
,
1
)
+
v(
1
,
2
)
*
v(
2
,
2
)
+
v(
1
,
3
)
*
v(
2
,
3
))
/
(sqrt(v(
1
,
1
)
^
2
+
v(
1
,
2
)
^
2
+
v(
1
,
3
)
^
2
)
*
sqrt(v(
2
,
1
)
^
2
+
v(
2
,
2
)
^
2
+
v(
2
,
3
)
^
2
)));10
%the dis pB
to
pAi11
d
=
R
*
tan
(ang
/
2
);12
%direction cosine of V(Ai
-
1
,Ai)13
cosa1
=
v(
1
,
1
)
/
sqrt(v(
1
,
1
)
^
2
+
v(
1
,
2
)
^
2
+
v(
1
,
3
)
^
2
);14
cosb1
=
v(
1
,
2
)
/
sqrt(v(
1
,
1
)
^
2
+
v(
1
,
2
)
^
2
+
v(
1
,
3
)
^
2
);15
cosc1
=
v(
1
,
3
)
/
sqrt(v(
1
,
1
)
^
2
+
v(
1
,
2
)
^
2
+
v(
1
,
3
)
^
2
);16
%interpolation start point17
b1
=
[A(
2
,
1
)
-
d
*
cosa1,A(
2
,
2
)
-
d
*
cosb1,A(
2
,
3
)
-
d
*
cosc1];18
%direction cosine of V(Ai,Ai
+
1
)19
cosa2
=
v(
2
,
1
)
/
sqrt(v(
2
,
1
)
^
2
+
v(
2
,
2
)
^
2
+
v(
2
,
3
)
^
2
);20
cosb2
=
v(
2
,
2
)
/
sqrt(v(
2
,
1
)
^
2
+
v(
2
,
2
)
^
2
+
v(
2
,
3
)
^
2
);21
cosc2
=
v(
2
,
3
)
/
sqrt(v(
2
,
1
)
^
2
+
v(
2
,
2
)
^
2
+
v(
2
,
3
)
^
2
);22
%interpolation
end
point23
b2
=
[A(
2
,
1
)
+
d
*
cosa2,A(
2
,
2
)
+
d
*
cosb2,A(
2
,
3
)
+
d
*
cosc2];24
%vector of angular bisector25
v0
=
sqrt(v(
1
,
1
)
^
2
+
v(
1
,
2
)
^
2
+
v(
1
,
3
)
^
2
);26
v1
=
[v(
1
,
1
) v(
1
,
2
) v(
1
,
3
)]
/
v0;27
v0
=
sqrt(v(
2
,
1
)
^
2
+
v(
2
,
2
)
^
2
+
v(
2
,
3
)
^
2
);28
v2
=
[v(
2
,
1
) v(
2
,
2
) v(
2
,
3
)]
/
v0;29
L0
=
[(
-
v1(
1
)
+
v2(
1
))
/
2
,(
-
v1(
2
)
+
v2(
2
))
/
2
,(
-
v1(
3
)
+
v2(
3
))
/
2
];30
%direction cosine of angular bisector31
cosa3
=
L0(
1
)
/
sqrt(L0(
1
)
^
2
+
L0(
2
)
^
2
+
L0(
3
)
^
2
);32
cosb3
=
L0(
2
)
/
sqrt(L0(
1
)
^
2
+
L0(
2
)
^
2
+
L0(
3
)
^
2
);33
cosc3
=
L0(
3
)
/
sqrt(L0(
1
)
^
2
+
L0(
2
)
^
2
+
L0(
3
)
^
2
);34
%calculate the center point of interpolation circle35
t
=
R
*
sec(ang
/
2
);36
p
=
[A(
2
,
1
)
+
cosa3
*
t,A(
2
,
2
)
+
cosb3
*
t,A(
2
,
3
)
+
cosc3
*
t];37
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%38
%calculate the normal vector of interpolation circle39
dx
=
[b1(
1
)
-
p(
1
) b1(
2
)
-
p(
2
) b1(
3
)
-
p(
3
)];40
dx
=
dx
/
sqrt(dx(
1
)
^
2
+
dx(
2
)
^
2
+
dx(
3
)
^
2
);41
dy
=
[b2(
1
)
-
p(
1
) b2(
2
)
-
p(
2
) b2(
3
)
-
p(
3
)];42
dy
=
dy
/
sqrt(dy(
1
)
^
2
+
dy(
2
)
^
2
+
dy(
3
)
^
2
);43
dz
=
[v(
1
,
2
)
*
v(
2
,
3
)
-
v(
2
,
2
)
*
v(
1
,
3
),v(
1
,
1
)
*
v(
2
,
3
)
-
v(
2
,
1
)
*
v(
1
,
3
),v(
1
,
1
)
*
v(
2
,
2
)
-
v(
2
,
1
)
*
v(
1
,
2
)];44
dz
=
dz
/
sqrt(dz(
1
)
^
2
+
dz(
2
)
^
2
+
dz(
3
)
^
2
);45
46
T
=
[dx;dy;dz];47
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%48
P
=
ones(
3
,
11
);49
delta
=
pi
*
0.5
/
10
;50
for
i
=
0
:
10
51
m
=
[R
*
cos
(i
*
delta) R
*
sin
(i
*
delta)
0
];52
P(:,i
+
1
)
=
T
'
*m'+p';
53
end
54
plot3(P(
1
,:),P(
2
,:),P(
3
,:),
'
r+-',A(:,1),A(:,2),A(:,3),'b+-');
55
grid
on
;56
axis
on
;57
xlabel(
'
X');ylabel('Y');zlabel('z');
附上以上程序在matlab6.5环境下的运行结果:
