| 1 | .th SPLINE VI 10/20/73 |
| 2 | .sh NAME |
| 3 | spline \*- interpolate smooth curve |
| 4 | .sh SYNOPSIS |
| 5 | .bd spline |
| 6 | [ option ] ... |
| 7 | .sh DESCRIPTION |
| 8 | .it Spline |
| 9 | takes pairs of numbers from the standard input as abcissas and ordinates |
| 10 | of a function. |
| 11 | It produces a similar set, which |
| 12 | is approximately equally spaced and |
| 13 | includes the input set, on the standard output. |
| 14 | The cubic spline output |
| 15 | (R. W. Hamming, |
| 16 | .ft I |
| 17 | Numerical Methods for Engineers and Scientists, |
| 18 | .ft R |
| 19 | 2nd ed., 349ff) |
| 20 | has two continuous derivatives, |
| 21 | and sufficiently many points to look smooth when plotted, for |
| 22 | example by |
| 23 | .it plot |
| 24 | (I). |
| 25 | .s3 |
| 26 | The following options are recognized, |
| 27 | each as a separate argument. |
| 28 | .s3 |
| 29 | .lp +5 5 |
| 30 | \fBa\fR Supply abscissas automatically (they are missing from |
| 31 | the input); spacing is given by the next |
| 32 | argument, or is assumed to be 1 if next argument is not a number. |
| 33 | .s3 |
| 34 | .lp +5 5 |
| 35 | \fBn\fR Output approximately |
| 36 | .it n |
| 37 | points, where |
| 38 | .it n |
| 39 | is given by the next argument. |
| 40 | (Default |
| 41 | .it n |
| 42 | = 100.) |
| 43 | .s3 |
| 44 | .lp +5 5 |
| 45 | \fBp\fR Make output periodic, i.e. match |
| 46 | derivatives at ends. |
| 47 | First and last input values should normally agree. |
| 48 | .s3 |
| 49 | .lp +5 5 |
| 50 | \fBx\fR Next 1 (or 2) arguments are lower (and upper) \fIx\fR limits. |
| 51 | .i0 |
| 52 | .sh "SEE ALSO" |
| 53 | plot(I) |
| 54 | .sh AUTHOR |
| 55 | M. D. McIlroy |
| 56 | .sh BUGS |
| 57 | A limit of 1000 input points is enforced silently. |