CIRCLE-SPLINE, 2-D, 3-D Spline Curve Fitting

1 - Description of program or function: CIRCLE SPLINE is a library of routines used to generate Splines in both two and three dimensions. To use it, two subroutines, PTSMAK and PTSPAR must be called into a main program to either generate or input the data that are to be interpolated by the CIRCLE SPLINE routine. Because of the multi- dimensional generation, the x-, y-, and z-coordinates must always be available. If a two-dimensional spline is desired, the third coordinate should be set to zero and run through the subroutine. 2 - Method of solution: CIRCLE SPLINE generates a spline by constructing and connecting a series of circular arcs. Subroutine PTSMAK takes the coordinates of three successive data points, calculates the parametric location of the center of a circle of radius r, and places an arc through the three data points. Once the first arc has been generated, PTSMAK moves by increments along the curve to the next data point. For N data points, N-2 arcs are produced. Two arcs pass between each pair of data points, with the exception of the two end pairs. CIRCLE SPLINE blends successive pairs of arcs to fit a single curve between data points. This blending process is performed by linearly weighing the effect each arc has in the interval between the respective data points. The user controls the number of sub-points that are between data points and available for the blending process. 3 - Restrictions on the complexity of the problem: The CIRCLE SPLINE blending process develops errors if too many sub-points are used, and persistent errors occur in cases of extreme variation of curvature (as in a cigar-shaped ellipse)