Geometric shape analysis for convolution curve of two compatible quadratic Bézier curves
In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that ther...
Ausführliche Beschreibung
Autor*in: |
Lee, Ryeong [verfasserIn] |
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Englisch |
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2015transfer abstract |
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10 |
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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:288 ; year:2015 ; pages:141-150 ; extent:10 |
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DOI / URN: |
10.1016/j.cam.2015.04.012 |
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ELV034589910 |
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520 | |a In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. | ||
520 | |a In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. | ||
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10.1016/j.cam.2015.04.012 doi GBVA2015012000018.pica (DE-627)ELV034589910 (ELSEVIER)S0377-0427(15)00230-7 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Lee, Ryeong verfasserin aut Geometric shape analysis for convolution curve of two compatible quadratic Bézier curves 2015transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. Quadratic Bézier curve Elsevier Sign of curvature Elsevier Classification of shapes Elsevier Convolution curve Elsevier Tangent direction Elsevier Ahn, Young Joon 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:288 year:2015 pages:141-150 extent:10 https://doi.org/10.1016/j.cam.2015.04.012 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 288 2015 141-150 10 045F 510 |
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10.1016/j.cam.2015.04.012 doi GBVA2015012000018.pica (DE-627)ELV034589910 (ELSEVIER)S0377-0427(15)00230-7 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Lee, Ryeong verfasserin aut Geometric shape analysis for convolution curve of two compatible quadratic Bézier curves 2015transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. Quadratic Bézier curve Elsevier Sign of curvature Elsevier Classification of shapes Elsevier Convolution curve Elsevier Tangent direction Elsevier Ahn, Young Joon 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:288 year:2015 pages:141-150 extent:10 https://doi.org/10.1016/j.cam.2015.04.012 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 288 2015 141-150 10 045F 510 |
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10.1016/j.cam.2015.04.012 doi GBVA2015012000018.pica (DE-627)ELV034589910 (ELSEVIER)S0377-0427(15)00230-7 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Lee, Ryeong verfasserin aut Geometric shape analysis for convolution curve of two compatible quadratic Bézier curves 2015transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. Quadratic Bézier curve Elsevier Sign of curvature Elsevier Classification of shapes Elsevier Convolution curve Elsevier Tangent direction Elsevier Ahn, Young Joon 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:288 year:2015 pages:141-150 extent:10 https://doi.org/10.1016/j.cam.2015.04.012 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 288 2015 141-150 10 045F 510 |
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10.1016/j.cam.2015.04.012 doi GBVA2015012000018.pica (DE-627)ELV034589910 (ELSEVIER)S0377-0427(15)00230-7 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Lee, Ryeong verfasserin aut Geometric shape analysis for convolution curve of two compatible quadratic Bézier curves 2015transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. Quadratic Bézier curve Elsevier Sign of curvature Elsevier Classification of shapes Elsevier Convolution curve Elsevier Tangent direction Elsevier Ahn, Young Joon 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:288 year:2015 pages:141-150 extent:10 https://doi.org/10.1016/j.cam.2015.04.012 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 288 2015 141-150 10 045F 510 |
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10.1016/j.cam.2015.04.012 doi GBVA2015012000018.pica (DE-627)ELV034589910 (ELSEVIER)S0377-0427(15)00230-7 DE-627 ger DE-627 rakwb eng 510 510 DE-600 670 VZ 540 VZ 630 VZ Lee, Ryeong verfasserin aut Geometric shape analysis for convolution curve of two compatible quadratic Bézier curves 2015transfer abstract 10 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. Quadratic Bézier curve Elsevier Sign of curvature Elsevier Classification of shapes Elsevier Convolution curve Elsevier Tangent direction Elsevier Ahn, Young Joon 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:288 year:2015 pages:141-150 extent:10 https://doi.org/10.1016/j.cam.2015.04.012 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA AR 288 2015 141-150 10 045F 510 |
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Geometric shape analysis for convolution curve of two compatible quadratic Bézier curves |
abstract |
In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. |
abstractGer |
In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. |
abstract_unstemmed |
In this paper we consider the local and global geometric properties of the convolution curve of two compatible quadratic Bézier curves. We characterize all shapes of convolution curves using the ratios of lengths of the corresponding control polygon of two Bézier curves. Especially we show that there are only three cases in the classification of local shapes with respect to the tangent direction and sign of curvature at each endpoint of the convolution curve. This special property can be extended to the convolution curve of two compatible Bézier curves of any degree n . We also classify all cases of global shapes of the convolution curves using the local shapes. The geometric properties of convolution curves are also presented when the ratio is critical point. Some examples are given to illustrate our characterization. |
collection_details |
GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA |
title_short |
Geometric shape analysis for convolution curve of two compatible quadratic Bézier curves |
url |
https://doi.org/10.1016/j.cam.2015.04.012 |
remote_bool |
true |
author2 |
Ahn, Young Joon |
author2Str |
Ahn, Young Joon |
ppnlink |
ELV013217658 |
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hochschulschrift_bool |
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author2_role |
oth |
doi_str |
10.1016/j.cam.2015.04.012 |
up_date |
2024-07-06T21:29:47.617Z |
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1803866747822931968 |
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score |
7.397897 |