A general scheme for shape preserving planar interpolating curves

BIT Numerical Mathematics

Volumn 43, Issue 2, 2003, Pages 297-317

  Costantini, Paolo ^a   Sampoli, Maria Lucia ^a  

^a UNIVERSITY OF SIENA   (Italy)

Author keywords

Abstract schemes; Fairness functional; Interpolation; Shape preservation; Splines

Indexed keywords

EID: 4043107687     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026035128791     Document Type: Article

References (31)

1. I. Applegarth, P. D. Kaklis and S. Wahl, eds., Benchmark Tests on the Generation of Fair Shapes subject to Constraints, B. G. Teubner, Stuttgart, 2000.
2. 2 Shape-Preserving Parametric Planar Curve Interpolation, in Designing and Creating Shape-Preserving Curves and Surfaces, H. Nowacki and P. Kaklis, eds., B. G. Teubner, Stuttgart, 1998, pp. 89-98.
3. 3, in Designing and Creating Shape-Preserving Curves and Surfaces, H. Nowacki and P. Kaklis, eds., B. G. Teubner, Stuttgart, 1998, pp. 99-108.
4. R. Bellman and S. Dreyfus, Applied Dynamic Programming, Princeton University Press, New York, 1962.
5. E. W. Cheney and A. Goldstein, Proximity maps for convex sets, Proc. Amer. Math. Soc., 10 (1959), pp. 448-450.
6. P. Costantini, On monotone and convex spline interpolation, Math. Comp., 46 (1986), pp. 203-214.
7. P. Costantini, An algorithm for computing shape preserving splines of arbitrary degree, J. Comput. Appl. Math., 22 (1988), pp. 89-136.
8. P. Costantini, A general method for constrained curves with boundary conditions, in Multivariate Approximation: from CAGD to Wavelets, K. Jetter e F. I. Utreras, eds., World Scientific Publishing Co., Singapore, 1993, pp. 91-108.
9. P. Costantini, Abstract schemes for functional shape-preserving interpolation, in Advanced Course on FAIRSHAPE, J. Hoschek and P. Kaklis, eds., B. G. Teubner, Stuttgart, 1996, pp. 185-199.
10. P. Costantini, Boundary-valued shape-preserving interpolating splines, ACM Trans. Math. Software, 23:2 (1997), pp. 229-251.
11. P. Costantini, Algorithm 770: BVSPIS-A package for computing boundary-valued shape-preserving interpolating splines, ACM Trans. Math. Software, 23:2 (1997), pp. 252-254.
12. P. Costantini and F. Pelosi, Shape-preserving approximation by space curves, Numer. Algorithms, 27 (2001), pp. 237-264.
13. P. Costantini and M. L. Sampoli, Abstract schemes and constrained curve interpolation, in Designing and Creating Shape-Preserving Curves and Surfaces, H. Nowacki and P. Kaklis, eds., B. G. Teubner, Stuttgart, 1998, pp. 121-130.
14. 3 by abstract schemes, to appear in Curve and Surface Design: Saint-Malo 2002, T. Lyche, M.-L. Mazure and L. Schumaker, eds., Nashboro Press, Brentwood, 2003, pp. 93-102.
15. R. E. Carlson and F. N. Fritsch, Monotone piecewise cubic interpolation, SIAM J. Numer. Anal. 17 (1980), pp. 238-246.
16. 2 space curves, Computer Aided Design 30:10 (1998), pp. 813-822.
17. T. N. T. Goodman and K. Unsworth, Shape preserving interpolation by parametrically defined curves, SIAM J. Numer. Anal. 25 (1988), pp. 1451-1465.
18. J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design, AK Peters Ltd., Wellesley, 1993.
19. P. D. Kaklis and N. S. Sapidis, Convexity preserving polynomial splines of non uniform degree, Comput Aided Geom. Design 12 (1995), pp. 1-26.
20. 3, IMA J. Numer. Anal., 17 (1997), pp. 373-419.
21. B. Jüttler, Shape-preserving least-squares approximation by polynomial parametric spline curves, Comput. Aided Geom. Design 14 (1997), pp. 731-747.
22. R. Morandi, D. Scaramelli and A. Sestini, A geometric approach for knot selection in convexity-preserving spline approximation, in Curve and Surface Design, Saint Malo 1999. P. J. Laurent, P. Sablonniere, and L. L. Schumaker, eds., Vanderbilt University Press, Nashville, 2000, pp. 287-296.
23. B. Mulansky and J. W. Schmidt, Convex interval interpolation using three-term staircase algorithm, Numer. Math. 82 (1999), pp. 313-337.
24. B. Mulansky and J. W. Schmidt, Composition based staircase algorithm and constrained interpolation with boundary conditions, Numer. Math. 85 (2000), pp. 387-408.
25. H. Nowacki, J. Heimann, E. Melissaratos and S. H. Zimmermann, Experiences in curve fairing, in Advanced Course on FAIRSHAPE, J. Hoschek and P. Kaklis, eds., B. G. Teubner, Stuttgart, 1996, pp. 9-16.
26. F. P. Preparata and M. I. Shamos, Computational Geometry, Springer-Verlag, Berlin, New York, 1985.
27. M. L. Sampoli, Effective schemes for constrained curve construction, PhD Thesis, University of Milan, 1998.
28. W. Heßand J. W. Schimdt, Schwach verkoppelte Ungleichungssysteme und konvexe Spline-Interpolation, Elem. Math. 39 (1984), pp. 85-96.
29. J. W. Schimdt, On shape-preserving spline interpolation: Existence theorems and determination of optimal splines, in Approximation and Function Spaces, Vol. 22 PWN-Polish Scientific Publishers, Warsaw, 1989.
30. 3, Comput. Math. Appl. 31 (1996), pp. 67-79.
31. D. G. Schweikert, An interpolation curve using a spline in tension, J. Math. Phys., 45, (1966), pp. 312-317.