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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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