5
5.1
1
2
3
tt[01]t=0t=1
1
2
3
4
5
6
1
2
3
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4
ctk c?


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1
2
1
0
1
2
2
0
1
2
5.2 Hermite
n+1np(t)
T·Mn
[ 0,1 ] t1)()()()(
000
111

CT
cba
cba
cba
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n

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p(0)p(1)p’(0)p’(1)Hermite
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0001
0100
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p
p
p
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n+1Pii = 0,1,…,nnBezier
Bernstein
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0
,
ttBPtP
n
i
nii
)(,tB ni
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BezierBezierBezier
1Beziern=1
P0P1
[ 0,1 ]t
01
11
1
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1
0
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1
0
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P
t
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i
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2
1
0
2
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2
0
2,

P
P
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i
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[ 0,1 ] t
0001
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3
2
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0
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P
P
P
P
ttt
tBPtBPtBPtBPtBPtP
i
ii
1
2
3
4
5
6
7
1
2
3
4
5
6
1Bezier
5-2
2Bezier
3Bezier
4Bezier
5.4 B
m + n + 1Pii = 0,1,…,m + nn
nBi(i = 0,1,…,m)Fl,n(t)B
m + 1BnB
nlttFPtP
n
l
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0
,,
nltjlntCntF n
ln
j
j
n
j
nl?1010)()1(!
1)(
0
1,
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iBBiB
Bi = 00B0B
n
l
nll tFPtP
0
,)()(
10 t
B
1B
10
0141
0303
0363
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6
1
)(
3
2
1
0
23


t
P
P
P
P
ttttP
2B
3B
1B
5-9
2B
3BBezier
5.5Coons
P(u,v)u,v [0,1]
P(u,0),P(u,1),P(0,v),P(1,v)
P(0,0),P(0,1),P(1,0),P(1,1)
HermiteCoons
TT VU M C MvuP?),(
]1[],1[ 2323 vvvVuuuU

0001
0100
1233
1122
M
u
v
C
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vv
vv
11101110
01000100
11101110
01000100
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1G 0PQ
2G 1PQ k
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qp vv 10?
5.6Bezier
1Bezier
(n+1) (m+1)Pij(i=0,1… n; j=0,1… m)
n mBezier
PijP(u,v)Pi0Pi1… Pim (i=0,1,… n)P0jP1j… Pnj
(j=0,1,… m)P(u,v){Pij}P(u,v){Pij} {Pij}P(u,v)
]1,0[,)()(),(,
0 0
,

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n
i
m
j
niij
16(3 3)Bezier

0001
0033
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1331
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2Bezier
BezierBezier
5-10
5.7B
(n+1) (m+1)Pij(i=0,1… n;
j=0,1… m)n mB
BezierB
]1,0[,)()(),(,
0 0
,

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n
i
m
j
niij
16(3 3)B

0141
0303
0363
1331
6
1
BM
TTBB VGMUMvuP?),(
123 uuuU123 vvvV?
33323130
23222120
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PPPP
PPPP
PPPP
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G
5-11