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1.1 root 1: .\" Copyright (c) 1990 Regents of the University of California.
2: .\" All rights reserved. The Berkeley software License Agreement
3: .\" specifies the terms and conditions for redistribution.
4: .\"
5: .\" @(#)spline.1 6.2 (Berkeley) 6/24/90
6: .\"
7: .TH SPLINE 1 "%Q"
8: .AT 3
9: .SH NAME
10: spline \- interpolate smooth curve
11: .SH SYNOPSIS
12: .B spline
13: [ option ] ...
14: .SH DESCRIPTION
15: .I Spline
16: takes pairs of numbers from the standard input as abcissas and ordinates
17: of a function.
18: It produces a similar set, which
19: is approximately equally spaced and
20: includes the input set, on the standard output.
21: The cubic spline output
22: (R. W. Hamming,
23: .ft I
24: Numerical Methods for Scientists and Engineers,
25: .ft R
26: 2nd ed., 349ff)
27: has two continuous derivatives,
28: and sufficiently many points to look smooth when plotted, for
29: example by
30: .IR graph (1G).
31: .PP
32: The following options are recognized,
33: each as a separate argument.
34: .TP 5
35: .B \-a
36: Supply abscissas automatically (they are missing from
37: the input); spacing is given by the next
38: argument, or is assumed to be 1 if next argument is not a number.
39: .TP 5
40: .B \-k
41: The constant
42: .IR k ""
43: used in the boundary value computation
44: .IP
45: .if n .ig
46: .ti +1.5i
47: .ds ' \h'-\w'\(fm\(fm'u'
48: .EQ
49: .nr 99 \n(.s
50: .nr 98 \n(.f
51: 'ps 10
52: .ft I
53: .ds 11 "y\(fm\(fm
54: .nr 11 \w'\*(11'
55: .ds 12 "\*'
56: .nr 12 \w'\*(12'
57: 'ps 8
58: .ds 13 "\fR0\fP
59: .nr 13 \w'\*(13'
60: .as 12 \v'18u'\s8\*(13\|\s10\v'-18u'
61: 'ps 10
62: .nr 12 \n(12+\n(13+\w'\s8\|'
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 "\|\|
74: .nr 12 \w'\*(12'
75: .as 11 "\*(12
76: .nr 11 \w'\*(11'
77: .ds 12 "ky\(fm\(fm
78: .nr 12 \w'\*(12'
79: .as 11 "\*(12
80: .nr 11 \w'\*(11'
81: .ds 12 "\*'
82: .nr 12 \w'\*(12'
83: 'ps 8
84: .ds 13 "\fR1\fP
85: .nr 13 \w'\*(13'
86: .as 12 \v'18u'\s8\*(13\|\s10\v'-18u'
87: 'ps 10
88: .nr 12 \n(12+\n(13+\w'\s8\|'
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 "\|\|
104: .nr 12 \w'\*(12'
105: .as 11 "\*(12
106: .nr 11 \w'\*(11'
107: .ds 12 "y\(fm\(fm
108: .nr 12 \w'\*(12'
109: .as 11 "\*(12
110: .nr 11 \w'\*(11'
111: .ds 12 "\*'
112: .nr 12 \w'\*(12'
113: 'ps 8
114: .ds 13 "n
115: .nr 13 \w'\*(13'
116: .as 12 \v'18u'\s8\*(13\|\s10\v'-18u'
117: 'ps 10
118: .nr 12 \n(12+\n(13+\w'\s8\|'
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 "\|\|
130: .nr 12 \w'\*(12'
131: .as 11 "\*(12
132: .nr 11 \w'\*(11'
133: .ds 12 "ky\(fm\(fm
134: .nr 12 \w'\*(12'
135: .as 11 "\*(12
136: .nr 11 \w'\*(11'
137: .ds 12 "\*'
138: .nr 12 \w'\*(12'
139: 'ps 8
140: .ds 13 "n\|\(mi\|\fR1\fP
141: .nr 13 \w'\*(13'
142: .as 12 \v'18u'\s8\*(13\|\s10\v'-18u'
143: 'ps 10
144: .nr 12 \n(12+\n(13+\w'\s8\|'
145: .as 11 "\*(12
146: .nr 11 \w'\*(11'
147: .ds 11 \x'0'\fI\*(11\s\n(99\f\n(98
148: .ne 78u
149: \*(11
150: 'ps \n(99
151: .ft \n(98
152: .EN
153: ..
154: .if t .ig
155: .ce
156: (2nd deriv. at end) = k*(2nd deriv. next to end)
157: ..
158: .IP
159: .br
160: is set by the next argument.
161: By default
162: .IR k ""
163: = 0.
164: .TP 5
165: .B \-n
166: Space output points
167: so that approximately
168: .I n
169: intervals occur between the lower and upper
170: .I x
171: limits.
172: (Default
173: .I n
174: = 100.)
175: .TP 5
176: .B \-p
177: Make output periodic, i.e. match
178: derivatives at ends.
179: First and last input values should normally agree.
180: .TP 5
181: .B \-x
182: Next
183: 1 (or 2) arguments are lower (and upper)
184: .I x
185: limits.
186: Normally these limits are calculated from the data.
187: Automatic abcissas start at lower limit
188: (default 0).
189: .SH "SEE ALSO"
190: graph(1), plot(1)
191: .SH DIAGNOSTICS
192: When data is not strictly monotone in
193: .I x,
194: .I spline
195: reproduces the input without interpolating extra points.
196: .SH BUGS
197: A limit of 1000 input points is enforced silently.
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