Convexity/Concavity and Stability Aspects of Rational Cubic Fractal Interpolation Surfaces
Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rat...
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Gespeichert in:
| Autor*in: |
Chand, A. K. B. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
fractal interpolation functions |
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| Anmerkung: |
© Springer Science+Business Media, LLC 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Computational mathematics and modeling - Springer US, 1990, 28(2017), 3 vom: 28. Juni, Seite 407-430 |
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| Übergeordnetes Werk: |
volume:28 ; year:2017 ; number:3 ; day:28 ; month:06 ; pages:407-430 |
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| DOI / URN: |
10.1007/s10598-017-9373-2 |
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| 520 | |a Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C1-smoothness of rational cubic FIFs render C1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. | ||
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| 700 | 1 | |a Navascués, M. A. |4 aut | |
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10.1007/s10598-017-9373-2 doi (DE-627)OLC2044593726 (DE-He213)s10598-017-9373-2-p DE-627 ger DE-627 rakwb eng 004 VZ Chand, A. K. B. verfasserin aut Convexity/Concavity and Stability Aspects of Rational Cubic Fractal Interpolation Surfaces 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2017 Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C1-smoothness of rational cubic FIFs render C1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. fractals fractal interpolation functions blending functions fractal interpolation surfaces convexity concavity Vijender, N. aut Navascués, M. A. aut Enthalten in Computational mathematics and modeling Springer US, 1990 28(2017), 3 vom: 28. Juni, Seite 407-430 (DE-627)130898163 (DE-600)1043251-6 (DE-576)034187774 1046-283X nnns volume:28 year:2017 number:3 day:28 month:06 pages:407-430 https://doi.org/10.1007/s10598-017-9373-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 28 2017 3 28 06 407-430 |
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10.1007/s10598-017-9373-2 doi (DE-627)OLC2044593726 (DE-He213)s10598-017-9373-2-p DE-627 ger DE-627 rakwb eng 004 VZ Chand, A. K. B. verfasserin aut Convexity/Concavity and Stability Aspects of Rational Cubic Fractal Interpolation Surfaces 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2017 Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C1-smoothness of rational cubic FIFs render C1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. fractals fractal interpolation functions blending functions fractal interpolation surfaces convexity concavity Vijender, N. aut Navascués, M. A. aut Enthalten in Computational mathematics and modeling Springer US, 1990 28(2017), 3 vom: 28. Juni, Seite 407-430 (DE-627)130898163 (DE-600)1043251-6 (DE-576)034187774 1046-283X nnns volume:28 year:2017 number:3 day:28 month:06 pages:407-430 https://doi.org/10.1007/s10598-017-9373-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 28 2017 3 28 06 407-430 |
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10.1007/s10598-017-9373-2 doi (DE-627)OLC2044593726 (DE-He213)s10598-017-9373-2-p DE-627 ger DE-627 rakwb eng 004 VZ Chand, A. K. B. verfasserin aut Convexity/Concavity and Stability Aspects of Rational Cubic Fractal Interpolation Surfaces 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2017 Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C1-smoothness of rational cubic FIFs render C1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. fractals fractal interpolation functions blending functions fractal interpolation surfaces convexity concavity Vijender, N. aut Navascués, M. A. aut Enthalten in Computational mathematics and modeling Springer US, 1990 28(2017), 3 vom: 28. Juni, Seite 407-430 (DE-627)130898163 (DE-600)1043251-6 (DE-576)034187774 1046-283X nnns volume:28 year:2017 number:3 day:28 month:06 pages:407-430 https://doi.org/10.1007/s10598-017-9373-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 28 2017 3 28 06 407-430 |
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10.1007/s10598-017-9373-2 doi (DE-627)OLC2044593726 (DE-He213)s10598-017-9373-2-p DE-627 ger DE-627 rakwb eng 004 VZ Chand, A. K. B. verfasserin aut Convexity/Concavity and Stability Aspects of Rational Cubic Fractal Interpolation Surfaces 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2017 Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C1-smoothness of rational cubic FIFs render C1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. fractals fractal interpolation functions blending functions fractal interpolation surfaces convexity concavity Vijender, N. aut Navascués, M. A. aut Enthalten in Computational mathematics and modeling Springer US, 1990 28(2017), 3 vom: 28. Juni, Seite 407-430 (DE-627)130898163 (DE-600)1043251-6 (DE-576)034187774 1046-283X nnns volume:28 year:2017 number:3 day:28 month:06 pages:407-430 https://doi.org/10.1007/s10598-017-9373-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 28 2017 3 28 06 407-430 |
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10.1007/s10598-017-9373-2 doi (DE-627)OLC2044593726 (DE-He213)s10598-017-9373-2-p DE-627 ger DE-627 rakwb eng 004 VZ Chand, A. K. B. verfasserin aut Convexity/Concavity and Stability Aspects of Rational Cubic Fractal Interpolation Surfaces 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2017 Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C1-smoothness of rational cubic FIFs render C1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. fractals fractal interpolation functions blending functions fractal interpolation surfaces convexity concavity Vijender, N. aut Navascués, M. A. aut Enthalten in Computational mathematics and modeling Springer US, 1990 28(2017), 3 vom: 28. Juni, Seite 407-430 (DE-627)130898163 (DE-600)1043251-6 (DE-576)034187774 1046-283X nnns volume:28 year:2017 number:3 day:28 month:06 pages:407-430 https://doi.org/10.1007/s10598-017-9373-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 28 2017 3 28 06 407-430 |
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Convexity/Concavity and Stability Aspects of Rational Cubic Fractal Interpolation Surfaces |
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Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C1-smoothness of rational cubic FIFs render C1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. © Springer Science+Business Media, LLC 2017 |
| abstractGer |
Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C1-smoothness of rational cubic FIFs render C1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. © Springer Science+Business Media, LLC 2017 |
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Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C1-smoothness of rational cubic FIFs render C1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. © Springer Science+Business Media, LLC 2017 |
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Convexity/Concavity and Stability Aspects of Rational Cubic Fractal Interpolation Surfaces |
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Vijender, N. Navascués, M. A. |
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10.1007/s10598-017-9373-2 |
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