NESC9602 CIRCLE SPLINE.

1. NAME OR DESIGNATION OF PROGRAM:  CIRCLE SPLINE.

3. 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.

4. 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 subpoints that are between data points and available for the blending process.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The CIRCLE SPLINE blending process develops errors if too many subpoints are used, and persistent errors occur in cases of extreme variation of curvature (as in a cigar-shaped ellipse).

6. TYPICAL RUNNING TIME:

7. UNUSUAL FEATURES OF THE PROGRAM

Because of the circular configuration in which it fits data, CIRCLE SPLINE is well-suited to machining processes.

8. RELATED AND AUXILIARY PROGRAMS

CIRCLE SPLINE uses the Los Alamos Common Graphics System CGS (PSR-0243) for plotting. CIRCLE SPLINE, which can be used effectively in both two and three dimensions, compares favorably with the Wilson-Fowler spline software - SPLPKG,  WFCMPR, WFAPPX (NESC 9736) - which can be used effectively only in two dimensions.

10. REFERENCES:

- R.M. Dolin and D.L. Jaeger :
  Examination of the Circle Spline Routine
  LA-10521-MS UC-32 (November 1985)
- R.M. Dolin and W.R. Oakes :
  A Comparison Between the Wilson-Fowler Spline and the Circle
  Spline Routines
  LA-10522-MS UC-32 (November 1985)
- M. Birgersson :
  CIRCLE SPLINE Tape Directory and Implementation Information
  NESC Note 87-42 (February 19, 1987)

11. MACHINE REQUIREMENTS

At NEA-DB a Tektronix 4014 graphics display and a laser printer LN03 were used to test the program.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  VMS 4.4.

The program was tested at NEA-DB using the proprietary  graphics package DISSPLA of ISSCO.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

15. NAME AND ESTABLISHMENT OF AUTHORS

     R.M. Dolin
     Analysis and Testing Group
     Los Alamos National Laboratory
     LOS ALAMOS, New Mexico. U. S. A.

File name	File description	Records
NESC9602_01.001	INFORMATION FILE	72
NESC9602_01.002	SOURCE PROGRAM	490
NESC9602_01.003	VAX COMMAND PROCEDURE	10