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5584cee2 | 1 | .\" @(#)spline.1 6.1 (Berkeley) %G% |
30e5e182 | 2 | .\" |
5584cee2 | 3 | .TH SPLINE 1G "" |
30e5e182 KM |
4 | .AT 3 |
5 | .SH NAME | |
6 | spline \- interpolate smooth curve | |
7 | .SH SYNOPSIS | |
8 | .B spline | |
9 | [ option ] ... | |
10 | .SH DESCRIPTION | |
11 | .I Spline | |
12 | takes pairs of numbers from the standard input as abcissas and ordinates | |
13 | of a function. | |
14 | It produces a similar set, which | |
15 | is approximately equally spaced and | |
16 | includes the input set, on the standard output. | |
17 | The cubic spline output | |
18 | (R. W. Hamming, | |
19 | .ft I | |
20 | Numerical Methods for Scientists and Engineers, | |
21 | .ft R | |
22 | 2nd ed., 349ff) | |
23 | has two continuous derivatives, | |
24 | and sufficiently many points to look smooth when plotted, for | |
25 | example by | |
203f7bf7 | 26 | .IR graph (1G). |
30e5e182 KM |
27 | .PP |
28 | The following options are recognized, | |
29 | each as a separate argument. | |
30 | .TP 5 | |
31 | .B \-a | |
32 | Supply abscissas automatically (they are missing from | |
33 | the input); spacing is given by the next | |
34 | argument, or is assumed to be 1 if next argument is not a number. | |
35 | .TP 5 | |
36 | .B \-k | |
37 | The constant | |
38 | .IR k "" | |
39 | used in the boundary value computation | |
40 | .IP | |
41 | .if n .ig | |
42 | .ti +1.5i | |
43 | .ds ' \h'-\w'\(fm\(fm'u' | |
44 | .EQ | |
45 | .nr 99 \n(.s | |
46 | .nr 98 \n(.f | |
47 | 'ps 10 | |
48 | .ft I | |
49 | .ds 11 "y\(fm\(fm | |
50 | .nr 11 \w'\*(11' | |
51 | .ds 12 "\*' | |
52 | .nr 12 \w'\*(12' | |
53 | 'ps 8 | |
54 | .ds 13 "\fR0\fP | |
55 | .nr 13 \w'\*(13' | |
56 | .as 12 \v'18u'\s8\*(13\|\s10\v'-18u' | |
57 | 'ps 10 | |
58 | .nr 12 \n(12+\n(13+\w'\s8\|' | |
59 | .as 11 "\*(12 | |
60 | .nr 11 \w'\*(11' | |
61 | .ds 12 "\|\| | |
62 | .nr 12 \w'\*(12' | |
63 | .as 11 "\*(12 | |
64 | .nr 11 \w'\*(11' | |
65 | .ds 12 "\|=\| | |
66 | .nr 12 \w'\*(12' | |
67 | .as 11 "\*(12 | |
68 | .nr 11 \w'\*(11' | |
69 | .ds 12 "\|\| | |
70 | .nr 12 \w'\*(12' | |
71 | .as 11 "\*(12 | |
72 | .nr 11 \w'\*(11' | |
73 | .ds 12 "ky\(fm\(fm | |
74 | .nr 12 \w'\*(12' | |
75 | .as 11 "\*(12 | |
76 | .nr 11 \w'\*(11' | |
77 | .ds 12 "\*' | |
78 | .nr 12 \w'\*(12' | |
79 | 'ps 8 | |
80 | .ds 13 "\fR1\fP | |
81 | .nr 13 \w'\*(13' | |
82 | .as 12 \v'18u'\s8\*(13\|\s10\v'-18u' | |
83 | 'ps 10 | |
84 | .nr 12 \n(12+\n(13+\w'\s8\|' | |
85 | .as 11 "\*(12 | |
86 | .nr 11 \w'\*(11' | |
87 | .ds 12 ", | |
88 | .nr 12 \w'\*(12' | |
89 | .as 11 "\*(12 | |
90 | .nr 11 \w'\*(11' | |
91 | .ds 12 "\|\| | |
92 | .nr 12 \w'\*(12' | |
93 | .as 11 "\*(12 | |
94 | .nr 11 \w'\*(11' | |
95 | .ds 12 "\|\| | |
96 | .nr 12 \w'\*(12' | |
97 | .as 11 "\*(12 | |
98 | .nr 11 \w'\*(11' | |
99 | .ds 12 "\|\| | |
100 | .nr 12 \w'\*(12' | |
101 | .as 11 "\*(12 | |
102 | .nr 11 \w'\*(11' | |
103 | .ds 12 "y\(fm\(fm | |
104 | .nr 12 \w'\*(12' | |
105 | .as 11 "\*(12 | |
106 | .nr 11 \w'\*(11' | |
107 | .ds 12 "\*' | |
108 | .nr 12 \w'\*(12' | |
109 | 'ps 8 | |
110 | .ds 13 "n | |
111 | .nr 13 \w'\*(13' | |
112 | .as 12 \v'18u'\s8\*(13\|\s10\v'-18u' | |
113 | 'ps 10 | |
114 | .nr 12 \n(12+\n(13+\w'\s8\|' | |
115 | .as 11 "\*(12 | |
116 | .nr 11 \w'\*(11' | |
117 | .ds 12 "\|\| | |
118 | .nr 12 \w'\*(12' | |
119 | .as 11 "\*(12 | |
120 | .nr 11 \w'\*(11' | |
121 | .ds 12 "\|=\| | |
122 | .nr 12 \w'\*(12' | |
123 | .as 11 "\*(12 | |
124 | .nr 11 \w'\*(11' | |
125 | .ds 12 "\|\| | |
126 | .nr 12 \w'\*(12' | |
127 | .as 11 "\*(12 | |
128 | .nr 11 \w'\*(11' | |
129 | .ds 12 "ky\(fm\(fm | |
130 | .nr 12 \w'\*(12' | |
131 | .as 11 "\*(12 | |
132 | .nr 11 \w'\*(11' | |
133 | .ds 12 "\*' | |
134 | .nr 12 \w'\*(12' | |
135 | 'ps 8 | |
136 | .ds 13 "n\|\(mi\|\fR1\fP | |
137 | .nr 13 \w'\*(13' | |
138 | .as 12 \v'18u'\s8\*(13\|\s10\v'-18u' | |
139 | 'ps 10 | |
140 | .nr 12 \n(12+\n(13+\w'\s8\|' | |
141 | .as 11 "\*(12 | |
142 | .nr 11 \w'\*(11' | |
143 | .ds 11 \x'0'\fI\*(11\s\n(99\f\n(98 | |
144 | .ne 78u | |
145 | \*(11 | |
146 | 'ps \n(99 | |
147 | .ft \n(98 | |
148 | .EN | |
149 | .. | |
150 | .if t .ig | |
151 | .ce | |
152 | (2nd deriv. at end) = k*(2nd deriv. next to end) | |
153 | .. | |
154 | .IP | |
155 | .br | |
156 | is set by the next argument. | |
157 | By default | |
158 | .IR k "" | |
159 | = 0. | |
160 | .TP 5 | |
161 | .B \-n | |
162 | Space output points | |
163 | so that approximately | |
164 | .I n | |
165 | intervals occur between the lower and upper | |
166 | .I x | |
167 | limits. | |
168 | (Default | |
169 | .I n | |
170 | = 100.) | |
171 | .TP 5 | |
172 | .B \-p | |
173 | Make output periodic, i.e. match | |
174 | derivatives at ends. | |
175 | First and last input values should normally agree. | |
176 | .TP 5 | |
177 | .B \-x | |
178 | Next | |
179 | 1 (or 2) arguments are lower (and upper) | |
180 | .I x | |
181 | limits. | |
182 | Normally these limits are calculated from the data. | |
183 | Automatic abcissas start at lower limit | |
184 | (default 0). | |
185 | .SH "SEE ALSO" | |
203f7bf7 | 186 | graph(1G), plot(1G) |
30e5e182 KM |
187 | .SH DIAGNOSTICS |
188 | When data is not strictly monotone in | |
189 | .I x, | |
190 | .I spline | |
191 | reproduces the input without interpolating extra points. | |
192 | .SH BUGS | |
193 | A limit of 1000 input points is enforced silently. |