Positive blending Hermite rational cubic spline fractal interpolation surfaces
Abstract Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function al...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chand, A. K. B. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
Fractal interpolation functions |
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| Anmerkung: |
© Springer-Verlag Italia 2014 |
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| Übergeordnetes Werk: |
Enthalten in: Calcolo - Springer Milan, 1964, 52(2014), 1 vom: 28. Jan., Seite 1-24 |
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| Übergeordnetes Werk: |
volume:52 ; year:2014 ; number:1 ; day:28 ; month:01 ; pages:1-24 |
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| DOI / URN: |
10.1007/s10092-013-0105-5 |
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| 520 | |a Abstract Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS. | ||
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| 650 | 4 | |a Blending functions | |
| 650 | 4 | |a Fractal interpolation surfaces | |
| 650 | 4 | |a Positivity | |
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10.1007/s10092-013-0105-5 doi (DE-627)OLC2069162249 (DE-He213)s10092-013-0105-5-p DE-627 ger DE-627 rakwb eng 510 VZ Chand, A. K. B. verfasserin aut Positive blending Hermite rational cubic spline fractal interpolation surfaces 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Italia 2014 Abstract Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS. Fractals Iterated function systems Fractal interpolation functions Blending functions Fractal interpolation surfaces Positivity Vijender, N. aut Enthalten in Calcolo Springer Milan, 1964 52(2014), 1 vom: 28. Jan., Seite 1-24 (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:52 year:2014 number:1 day:28 month:01 pages:1-24 https://doi.org/10.1007/s10092-013-0105-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_90 GBV_ILN_2088 GBV_ILN_4277 GBV_ILN_4318 AR 52 2014 1 28 01 1-24 |
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10.1007/s10092-013-0105-5 doi (DE-627)OLC2069162249 (DE-He213)s10092-013-0105-5-p DE-627 ger DE-627 rakwb eng 510 VZ Chand, A. K. B. verfasserin aut Positive blending Hermite rational cubic spline fractal interpolation surfaces 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Italia 2014 Abstract Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS. Fractals Iterated function systems Fractal interpolation functions Blending functions Fractal interpolation surfaces Positivity Vijender, N. aut Enthalten in Calcolo Springer Milan, 1964 52(2014), 1 vom: 28. Jan., Seite 1-24 (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:52 year:2014 number:1 day:28 month:01 pages:1-24 https://doi.org/10.1007/s10092-013-0105-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_90 GBV_ILN_2088 GBV_ILN_4277 GBV_ILN_4318 AR 52 2014 1 28 01 1-24 |
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10.1007/s10092-013-0105-5 doi (DE-627)OLC2069162249 (DE-He213)s10092-013-0105-5-p DE-627 ger DE-627 rakwb eng 510 VZ Chand, A. K. B. verfasserin aut Positive blending Hermite rational cubic spline fractal interpolation surfaces 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Italia 2014 Abstract Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS. Fractals Iterated function systems Fractal interpolation functions Blending functions Fractal interpolation surfaces Positivity Vijender, N. aut Enthalten in Calcolo Springer Milan, 1964 52(2014), 1 vom: 28. Jan., Seite 1-24 (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:52 year:2014 number:1 day:28 month:01 pages:1-24 https://doi.org/10.1007/s10092-013-0105-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_90 GBV_ILN_2088 GBV_ILN_4277 GBV_ILN_4318 AR 52 2014 1 28 01 1-24 |
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10.1007/s10092-013-0105-5 doi (DE-627)OLC2069162249 (DE-He213)s10092-013-0105-5-p DE-627 ger DE-627 rakwb eng 510 VZ Chand, A. K. B. verfasserin aut Positive blending Hermite rational cubic spline fractal interpolation surfaces 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Italia 2014 Abstract Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS. Fractals Iterated function systems Fractal interpolation functions Blending functions Fractal interpolation surfaces Positivity Vijender, N. aut Enthalten in Calcolo Springer Milan, 1964 52(2014), 1 vom: 28. Jan., Seite 1-24 (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:52 year:2014 number:1 day:28 month:01 pages:1-24 https://doi.org/10.1007/s10092-013-0105-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_90 GBV_ILN_2088 GBV_ILN_4277 GBV_ILN_4318 AR 52 2014 1 28 01 1-24 |
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10.1007/s10092-013-0105-5 doi (DE-627)OLC2069162249 (DE-He213)s10092-013-0105-5-p DE-627 ger DE-627 rakwb eng 510 VZ Chand, A. K. B. verfasserin aut Positive blending Hermite rational cubic spline fractal interpolation surfaces 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Italia 2014 Abstract Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS. Fractals Iterated function systems Fractal interpolation functions Blending functions Fractal interpolation surfaces Positivity Vijender, N. aut Enthalten in Calcolo Springer Milan, 1964 52(2014), 1 vom: 28. Jan., Seite 1-24 (DE-627)129456330 (DE-600)199549-2 (DE-576)014819511 0008-0624 nnns volume:52 year:2014 number:1 day:28 month:01 pages:1-24 https://doi.org/10.1007/s10092-013-0105-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_90 GBV_ILN_2088 GBV_ILN_4277 GBV_ILN_4318 AR 52 2014 1 28 01 1-24 |
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Abstract Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS. © Springer-Verlag Italia 2014 |
| abstractGer |
Abstract Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS. © Springer-Verlag Italia 2014 |
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Abstract Fractal interpolation provides an efficient way to describe data that have smooth and non-smooth structures. Based on the theory of fractal interpolation functions (FIFs), the Hermite rational cubic spline FIFs (fractal boundary curves) are constructed to approximate an original function along the grid lines of interpolation domain. Then the blending Hermite rational cubic spline fractal interpolation surface (FIS) is generated by using the blending functions with these fractal boundary curves. The convergence of the Hermite rational cubic spline FIS towards an original function is studied. The scaling factors and shape parameters involved in fractal boundary curves are constrained suitably such that these fractal boundary curves are positive whenever the given interpolation data along the grid lines are positive. Our Hermite blending rational cubic spline FIS is positive whenever the corresponding fractal boundary curves are positive. Various collections of fractal boundary curves can be adapted with suitable modifications in the associated scaling parameters or/and shape parameters, and consequently our construction allows interactive alteration in the shape of rational FIS. © Springer-Verlag Italia 2014 |
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Positive blending Hermite rational cubic spline fractal interpolation surfaces |
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https://doi.org/10.1007/s10092-013-0105-5 |
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Vijender, N. |
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