1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
|
#!/usr/bin/octave
function y = bspline3_weight_at(x)
onebysix= 1.0/6.0;
zwo = 2.0;
x=abs(x);
if (x <= 1.0 )
y = zwo / 3.0 - x * x * ( 1 - 0.5 * x );
elseif (x < zwo)
y = (zwo-x)*(zwo-x)*(zwo-x) * onebysix;
else
y =0.0;
endif
endfunction
function y = bspline3_iweight_at(x)
zwo = 2.0;
if (x < -2)
y = 0;
elseif ( x < -1 )
h = (zwo+x);
y = h * h * h * h / 24;
elseif (x <= 0.0 )
y = 0.5 + x * 2.0 / 3.0 - x * x * x / 3.0 - x*x*x*x/8;
elseif (x <= 1.0 )
y = 0.5 + x * 2.0 / 3.0 - x * x * x / 3.0 + x*x*x*x/8;
elseif (x < zwo)
h = (zwo-x);
y = 1 - h * h * h * h / 24;
else
y = 1;
endif
endfunction
function y = bspline3_dweight_at(x)
ax = abs(x);
if (ax <= 1.0)
y = (1.5 .* ax - 2) .* x;
elseif (ax <= 2.0)
if (x > 0)
y = -0.5 .* (2-ax) .* (2-ax) ;
else
y = 0.5 .* (2-ax) .* (2-ax) ;
endif
else
y = 0;
endif
endfunction
function y = bspline3_ddweight_at(x)
x=abs(x);
if (x>2.0)
y = 0.0;
elseif (x>1.0)
y = 2.0-x;
else
y = 3.0*x-2.0;
endif
endfunction
function y = bspline3_weight(x,d)
switch (d)
case -1
y = bspline3_iweight_at(x);
case 0
y = bspline3_weight_at(x);
case 1
y = bspline3_dweight_at(x);
case 2
y = bspline3_ddweight_at(x);
otherwise
y = 0;
endswitch
endfunction
function y = b11_10_10(x)
y = bspline3_weight(x-10, 1) * bspline3_weight(x-10, 1);
endfunction
function y = b11_10_11(x)
y = bspline3_weight(x-10, 1) * bspline3_weight(x-11, 1);
endfunction
function y = b11_20_20(x)
y = bspline3_weight(x-20, 1) * bspline3_weight(x-20, 1);
endfunction
function y = b20_10_11(x)
y = bspline3_weight(x-10, 2) * bspline3_weight(x-11, 0);
endfunction
function y = b20_10_10(x)
y = bspline3_weight(x-10, 2) * bspline3_weight(x-10, 0);
endfunction
function y = b20_0_1(x)
y = bspline3_weight(x, 2) * bspline3_weight(x-1, 0);
endfunction
function y = b02_29_28(x)
y = bspline3_weight(x - 29, 0) * bspline3_weight(x-27, 2);
endfunction
[v, ier, nfun, err] = quad ("b20_10_10", 0, 30);
"b20_10_10"
v
[v, ier, nfun, err] = quad ("b11_10_10", 0, 30);
"b11_10_10"
v
[v, ier, nfun, err] = quad ("b20_10_11", 0, 30)
[v, ier, nfun, err] = quad ("b11_10_11", 0, 30)
|
