Weighted Lupaş q –Bézier curves
This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions whic...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Han, Li-Wen [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016transfer abstract |
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| Schlagwörter: |
Lupaş q -analogue of Bernstein operator Weighted Lupaş q -Bernstein basis |
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| Umfang: |
12 |
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| Übergeordnetes Werk: |
Enthalten in: Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics - Hu, Xing ELSEVIER, 2015transfer abstract, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:308 ; year:2016 ; day:15 ; month:12 ; pages:318-329 ; extent:12 |
| Links: |
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| DOI / URN: |
10.1016/j.cam.2016.06.017 |
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ELV02974475X |
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| 520 | |a This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. | ||
| 520 | |a This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. | ||
| 650 | 7 | |a Conic sections |2 Elsevier | |
| 650 | 7 | |a Lupaş q -analogue of Bernstein operator |2 Elsevier | |
| 650 | 7 | |a Weighted Lupaş q -Bernstein basis |2 Elsevier | |
| 650 | 7 | |a Shape parameter |2 Elsevier | |
| 650 | 7 | |a Normalized totally positive basis |2 Elsevier | |
| 650 | 7 | |a Rational Bézier curve |2 Elsevier | |
| 700 | 1 | |a Wu, Ya-Sha |4 oth | |
| 700 | 1 | |a Chu, Ying |4 oth | |
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10.1016/j.cam.2016.06.017 doi GBVA2016012000011.pica (DE-627)ELV02974475X (ELSEVIER)S0377-0427(16)30288-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Han, Li-Wen verfasserin aut Weighted Lupaş q –Bézier curves 2016transfer abstract 12 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. Conic sections Elsevier Lupaş q -analogue of Bernstein operator Elsevier Weighted Lupaş q -Bernstein basis Elsevier Shape parameter Elsevier Normalized totally positive basis Elsevier Rational Bézier curve Elsevier Wu, Ya-Sha oth Chu, Ying oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:308 year:2016 day:15 month:12 pages:318-329 extent:12 https://doi.org/10.1016/j.cam.2016.06.017 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 308 2016 15 1215 318-329 12 045F 510 |
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10.1016/j.cam.2016.06.017 doi GBVA2016012000011.pica (DE-627)ELV02974475X (ELSEVIER)S0377-0427(16)30288-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Han, Li-Wen verfasserin aut Weighted Lupaş q –Bézier curves 2016transfer abstract 12 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. Conic sections Elsevier Lupaş q -analogue of Bernstein operator Elsevier Weighted Lupaş q -Bernstein basis Elsevier Shape parameter Elsevier Normalized totally positive basis Elsevier Rational Bézier curve Elsevier Wu, Ya-Sha oth Chu, Ying oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:308 year:2016 day:15 month:12 pages:318-329 extent:12 https://doi.org/10.1016/j.cam.2016.06.017 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 308 2016 15 1215 318-329 12 045F 510 |
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10.1016/j.cam.2016.06.017 doi GBVA2016012000011.pica (DE-627)ELV02974475X (ELSEVIER)S0377-0427(16)30288-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Han, Li-Wen verfasserin aut Weighted Lupaş q –Bézier curves 2016transfer abstract 12 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. Conic sections Elsevier Lupaş q -analogue of Bernstein operator Elsevier Weighted Lupaş q -Bernstein basis Elsevier Shape parameter Elsevier Normalized totally positive basis Elsevier Rational Bézier curve Elsevier Wu, Ya-Sha oth Chu, Ying oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:308 year:2016 day:15 month:12 pages:318-329 extent:12 https://doi.org/10.1016/j.cam.2016.06.017 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 308 2016 15 1215 318-329 12 045F 510 |
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10.1016/j.cam.2016.06.017 doi GBVA2016012000011.pica (DE-627)ELV02974475X (ELSEVIER)S0377-0427(16)30288-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Han, Li-Wen verfasserin aut Weighted Lupaş q –Bézier curves 2016transfer abstract 12 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. Conic sections Elsevier Lupaş q -analogue of Bernstein operator Elsevier Weighted Lupaş q -Bernstein basis Elsevier Shape parameter Elsevier Normalized totally positive basis Elsevier Rational Bézier curve Elsevier Wu, Ya-Sha oth Chu, Ying oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:308 year:2016 day:15 month:12 pages:318-329 extent:12 https://doi.org/10.1016/j.cam.2016.06.017 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 308 2016 15 1215 318-329 12 045F 510 |
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10.1016/j.cam.2016.06.017 doi GBVA2016012000011.pica (DE-627)ELV02974475X (ELSEVIER)S0377-0427(16)30288-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Han, Li-Wen verfasserin aut Weighted Lupaş q –Bézier curves 2016transfer abstract 12 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. Conic sections Elsevier Lupaş q -analogue of Bernstein operator Elsevier Weighted Lupaş q -Bernstein basis Elsevier Shape parameter Elsevier Normalized totally positive basis Elsevier Rational Bézier curve Elsevier Wu, Ya-Sha oth Chu, Ying oth Enthalten in North-Holland Hu, Xing ELSEVIER Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics 2015transfer abstract Amsterdam [u.a.] (DE-627)ELV013217658 volume:308 year:2016 day:15 month:12 pages:318-329 extent:12 https://doi.org/10.1016/j.cam.2016.06.017 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 308 2016 15 1215 318-329 12 045F 510 |
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Enthalten in Dielectric relaxation and microwave dielectric properties of low temperature sintering LiMnPO4 ceramics Amsterdam [u.a.] volume:308 year:2016 day:15 month:12 pages:318-329 extent:12 |
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This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. |
| abstractGer |
This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. |
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This paper is concerned with a new generalization of rational Bernstein–Bézier curves involving q -integers as shape parameters. A one parameter family of rational Bernstein–Bézier curves, weighted Lupaş q –Bézier curves, is constructed based on a set of Lupaş q -analogue of Bernstein functions which is proved to be a normalized totally positive basis. The generalized rational Bézier curve is investigated from a geometric point of view. The investigation provides the geometric meaning of the weights and the representation for conic sections. We also obtain degree evaluation and de Casteljau algorithms by means of homogeneous coordinates. Numerical examples show that weighted Lupaş q –Bézier curves have more modeling flexibility than classical rational Bernstein–Bézier curves and Lupaş q –Bézier curves, and meanwhile they provide better approximations to the control polygon than rational Phillips q –Bézier curves. |
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