The interpolation of discrete spatial data -- a sequence of points and unit tangents -- by G^1 Pythagorean--hodograph (PH) quintic spline curves, under shape constraints, is addressed. To achieve this, a local Hermite scheme incorporating a tension parameter for each spline segment is employed, the imposed shape constraints being concerned with preservation of convexity at the knots and the sign of the discrete torsion over each spline segment. An asymptotic analysis in terms of the tension parameters is developed, and it is shown that satisfaction of the prescribed shape constraints can always be achieved for each spline segment by a suitable choice of the free angular parameters that characterize each PH quintic Hermite segment. In particular, it is proved that the CC criterion for specifying these free parameters ensures satisfaction of the desired shape--preserving properties, requiring only mild application of the tension parameters that does not compromise the overall fairness of the interpolant. The performance of the method is illustrated through some computed examples.

Rida T., F., C., M., Sampoli, M.L., A., S. (2015). Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves. IMA JOURNAL OF NUMERICAL ANALYSIS, 35(1), 478-498 [10.1093/imanum/drt072].

Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves

SAMPOLI, MARIA LUCIA;
2015-01-01

Abstract

The interpolation of discrete spatial data -- a sequence of points and unit tangents -- by G^1 Pythagorean--hodograph (PH) quintic spline curves, under shape constraints, is addressed. To achieve this, a local Hermite scheme incorporating a tension parameter for each spline segment is employed, the imposed shape constraints being concerned with preservation of convexity at the knots and the sign of the discrete torsion over each spline segment. An asymptotic analysis in terms of the tension parameters is developed, and it is shown that satisfaction of the prescribed shape constraints can always be achieved for each spline segment by a suitable choice of the free angular parameters that characterize each PH quintic Hermite segment. In particular, it is proved that the CC criterion for specifying these free parameters ensures satisfaction of the desired shape--preserving properties, requiring only mild application of the tension parameters that does not compromise the overall fairness of the interpolant. The performance of the method is illustrated through some computed examples.
2015
Rida T., F., C., M., Sampoli, M.L., A., S. (2015). Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves. IMA JOURNAL OF NUMERICAL ANALYSIS, 35(1), 478-498 [10.1093/imanum/drt072].
File in questo prodotto:
File Dimensione Formato  
IMA J Numer Anal_2015.pdf

non disponibili

Tipologia: PDF editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 504.43 kB
Formato Adobe PDF
504.43 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
sp-spline-rev.pdf

accesso aperto

Descrizione: This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record Rida T., F., C., M., Sampoli, M.L., & A., S. (2015). Shape-preserving interpolation of spatial data by Pythagorean-hodograph quintic spline curves. IMA JOURNAL OF NUMERICAL ANALYSIS, 35(1), 478-498 [10.1093/imanum/drt072]. is available online at: http://dx.doi.org/10.1093/imanum/drt072
Tipologia: Post-print
Licenza: PUBBLICO - Pubblico con Copyright
Dimensione 529.97 kB
Formato Adobe PDF
529.97 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/35604