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1.1 root 1: .\" @(#)spline.1g 6.1 (Berkeley) 4/29/85
2: .\"
3: .TH SPLINE 1G "April 29, 1985"
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
26: .IR graph (1G).
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"
186: graph(1G), plot(1G)
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.
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