Approximating sets on a plane with optimal sets of circles
Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Lebedev, P. D. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2012 |
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| Schlagwörter: |
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| Anmerkung: |
© Pleiades Publishing, Ltd. 2012 |
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| Übergeordnetes Werk: |
Enthalten in: Automation and remote control - SP MAIK Nauka/Interperiodica, 1957, 73(2012), 3 vom: März, Seite 485-493 |
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| Übergeordnetes Werk: |
volume:73 ; year:2012 ; number:3 ; month:03 ; pages:485-493 |
| Links: |
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| DOI / URN: |
10.1134/S0005117912030071 |
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OLC2060901626 |
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| 520 | |a Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles. | ||
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10.1134/S0005117912030071 doi (DE-627)OLC2060901626 (DE-He213)S0005117912030071-p DE-627 ger DE-627 rakwb eng 000 620 VZ Lebedev, P. D. verfasserin aut Approximating sets on a plane with optimal sets of circles 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2012 Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles. Remote Control Convex Hull Bold Line Subgradient Method Perpendicular Bisector Ushakov, A. V. aut Enthalten in Automation and remote control SP MAIK Nauka/Interperiodica, 1957 73(2012), 3 vom: März, Seite 485-493 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:73 year:2012 number:3 month:03 pages:485-493 https://doi.org/10.1134/S0005117912030071 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 73 2012 3 03 485-493 |
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10.1134/S0005117912030071 doi (DE-627)OLC2060901626 (DE-He213)S0005117912030071-p DE-627 ger DE-627 rakwb eng 000 620 VZ Lebedev, P. D. verfasserin aut Approximating sets on a plane with optimal sets of circles 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2012 Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles. Remote Control Convex Hull Bold Line Subgradient Method Perpendicular Bisector Ushakov, A. V. aut Enthalten in Automation and remote control SP MAIK Nauka/Interperiodica, 1957 73(2012), 3 vom: März, Seite 485-493 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:73 year:2012 number:3 month:03 pages:485-493 https://doi.org/10.1134/S0005117912030071 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 73 2012 3 03 485-493 |
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10.1134/S0005117912030071 doi (DE-627)OLC2060901626 (DE-He213)S0005117912030071-p DE-627 ger DE-627 rakwb eng 000 620 VZ Lebedev, P. D. verfasserin aut Approximating sets on a plane with optimal sets of circles 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2012 Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles. Remote Control Convex Hull Bold Line Subgradient Method Perpendicular Bisector Ushakov, A. V. aut Enthalten in Automation and remote control SP MAIK Nauka/Interperiodica, 1957 73(2012), 3 vom: März, Seite 485-493 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:73 year:2012 number:3 month:03 pages:485-493 https://doi.org/10.1134/S0005117912030071 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 73 2012 3 03 485-493 |
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10.1134/S0005117912030071 doi (DE-627)OLC2060901626 (DE-He213)S0005117912030071-p DE-627 ger DE-627 rakwb eng 000 620 VZ Lebedev, P. D. verfasserin aut Approximating sets on a plane with optimal sets of circles 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2012 Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles. Remote Control Convex Hull Bold Line Subgradient Method Perpendicular Bisector Ushakov, A. V. aut Enthalten in Automation and remote control SP MAIK Nauka/Interperiodica, 1957 73(2012), 3 vom: März, Seite 485-493 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:73 year:2012 number:3 month:03 pages:485-493 https://doi.org/10.1134/S0005117912030071 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 73 2012 3 03 485-493 |
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10.1134/S0005117912030071 doi (DE-627)OLC2060901626 (DE-He213)S0005117912030071-p DE-627 ger DE-627 rakwb eng 000 620 VZ Lebedev, P. D. verfasserin aut Approximating sets on a plane with optimal sets of circles 2012 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2012 Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles. Remote Control Convex Hull Bold Line Subgradient Method Perpendicular Bisector Ushakov, A. V. aut Enthalten in Automation and remote control SP MAIK Nauka/Interperiodica, 1957 73(2012), 3 vom: März, Seite 485-493 (DE-627)129603481 (DE-600)241725-X (DE-576)015097315 0005-1179 nnns volume:73 year:2012 number:3 month:03 pages:485-493 https://doi.org/10.1134/S0005117912030071 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 AR 73 2012 3 03 485-493 |
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Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles. © Pleiades Publishing, Ltd. 2012 |
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Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles. © Pleiades Publishing, Ltd. 2012 |
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Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles. © Pleiades Publishing, Ltd. 2012 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2060901626</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502215019.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2012 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1134/S0005117912030071</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2060901626</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)S0005117912030071-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">000</subfield><subfield code="a">620</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lebedev, P. D.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Approximating sets on a plane with optimal sets of circles</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2012</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Pleiades Publishing, Ltd. 2012</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We study optimal networks on a plane. We generalize the Chebyshev center of a set on the case of several points. We propose numerical and analytic methods for finding a placement of a fixed number of points that minimizes the Hausdorff deviation of a given set from these points. We develop and experiment with software for computing a network of two or three points for the case of flat figures. We show examples of modeling optimal coverings of polyhedra by sets of one, two, or three circles. Based on these networks, we propose an approximation of flat, in general nonconvex, sets by collections of circles.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Remote Control</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convex Hull</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bold Line</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Subgradient Method</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Perpendicular Bisector</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ushakov, A. V.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Automation and remote control</subfield><subfield code="d">SP MAIK Nauka/Interperiodica, 1957</subfield><subfield code="g">73(2012), 3 vom: März, Seite 485-493</subfield><subfield code="w">(DE-627)129603481</subfield><subfield code="w">(DE-600)241725-X</subfield><subfield code="w">(DE-576)015097315</subfield><subfield code="x">0005-1179</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:73</subfield><subfield code="g">year:2012</subfield><subfield code="g">number:3</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:485-493</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1134/S0005117912030071</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">73</subfield><subfield code="j">2012</subfield><subfield code="e">3</subfield><subfield code="c">03</subfield><subfield code="h">485-493</subfield></datafield></record></collection>
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