Shape-preserving approximation by space curves

Numerical Algorithms

Volumn 27, Issue 3, 2001, Pages 237-264

  Costantini, Paolo ^a   Pelosi, Francesca ^b  

^a UNIVERSITY OF SIENA   (Italy)

^b UNIVERSITY OF PADOVA   (Italy)

Author keywords

Best approximation; Discrete binormal; Discrete torsion; Shape preservation; Splines; Tension property

Indexed keywords

EID: 0035602389     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011895529998     Document Type: Article

References (22)

1. I. Applegarth, P.D. Kaklis and S. Wahl, Benchmark Tests on the Generation of Fair Shapes Subject to Constraints (Teubner, Stuttgart, 2000).
2. S. Asaturyan, P. Costantini and C. Manni, Local shape-preserving interpolation by space curves, IMA J. Numer. Anal. 21 (2001) 301-325.
3. P. Costantini, Shape-preserving interpolation with variable degree polynomial splines, in: Advanced Course on FAIRSHAPE, eds. J. Hoschek and P.D. Kaklis (Teubner, Stuttgart, 1996) pp. 87-114.
4. P. Costantini, Variable degree polynomial splines, in: Curves and Surfaces in Geometric Design, eds. P.J. Laurent, A. Le Méhauté and L.L. Schumaker (Vanderbilt Univ. Press, Nashville, TN, 1996) pp. 85-94.
5. P. Costantini, Curve and surface construction using variable degree polynomial splines, Comput. Aided Geom. Design 17 (2000) 419-446.
6. 3 shape-preserving interpolating space curves, Università di Torino, Quaderno del Dipartimento di Matematica n. 36/1999, to appear in Adv. Comput. Math.
7. T.N.T. Goodman, Total positivity and the shape of curves, in: Total Positivity and its Applications, eds. M. Gasca and C.A. Micchelli (Kluwer, Dordrecht, 1996) pp. 157-186.
8. T.N.T. Goodman and B.H. Ong, Shape-preserving interpolation by curves in three dimensions, in: Advanced Course on FAIRSHAPE, eds. J. Hoschek and P. Kaklis (Teubner, Stuttgart, 1996) pp. 40-46.
9. T.N.T. Goodman and B.H. Ong, Shape-preserving interpolation by space curves, Comput. Aided Geom. Design 15 (1997) 1-17.
10. 2 curves in three dimensions, in: Curves and Surfaces with Applications in CAGD, eds. A. Le Méhauté, C. Rabut and L.L. Schumaker (Vanderbilt Univ. Press, Nashville, TN, 1997) pp. 151-158.
11. 2 space curves, Comput. Aided Geom. Design 30 (1998) 813-822.
12. J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design (A.K. Peters, Wellesley, MA, 1993).
13. B. Jüttler, Shape preserving least-squares approximation by polynomial parametric spline curves, Comput. Aided Geom. Design 14 (1997) 731-747.
14. 3, IMA J. Numer. Anal. 17 (1997) 373-419.
15. P.D. Kaklis and D.G. Pandelis, Convexity preserving polynomial splines of non-uniform degree, IMA J. Numer. Anal. 10 (1990) 223-234.
16. M.I. Karavelas and P.D. Kaklis, Spatial shape-preserving interpolation using ν-splines, Numer. Algorithms 8 (2000).
17. B.I. Kvasov, Methods of Shape-Preserving Spline Approximation (World Scientific, Singapore, 2000).
18. 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, eds. P.-J. Laurent, P. Sablonniere and L.L. Schumaker (Vanderbilt Univ. Press, Nashville, TN, 2000) pp. 287-296.
19. H. Nowacki and P.D. Kaklis, Creating Fair and Shape-Preserving Curves and Surfaces (Teubner, Stuttgart, 1998).
20. F. Pelosi, SPA3D: Software documentation, Dipartimento di Matematica, Università di Siena, Rapporto n. 406 (August 2000).
21. R. Sauer, Differenzengeometrie (Springer, Berlin, 1970).
22. S.T. Tuohy, T. Maekawa, G. Shen and N.M. Patrikalakis, Approximation of measured data with interval B-splines, Comput. Aided Geom. Design 29 (1997) 791-799.