Apollonian Packing of Circles within Ellipses
The purpose of a circle packing procedure is to fill up a predefined, geometrical, closed contour with a maximum finite number of circles. The subject has received considerable attention in pure and applied sciences and has proved to be highly effective in connection with many a problem in logistics...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/16/3/129 |
| _version_ | 1827751773776904192 |
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| author | Carlo Santini Fabio Mangini Fabrizio Frezza |
| author_facet | Carlo Santini Fabio Mangini Fabrizio Frezza |
| author_sort | Carlo Santini |
| collection | DOAJ |
| description | The purpose of a circle packing procedure is to fill up a predefined, geometrical, closed contour with a maximum finite number of circles. The subject has received considerable attention in pure and applied sciences and has proved to be highly effective in connection with many a problem in logistics and technology. The well-known Apollonian circle packing achieves the packing of an infinite number of mutually tangent smaller circles of decreasing radii, internal or tangent to the outer boundary. Algorithms are available in the literature for the packing of equal-radius circles within an ellipse for global optimization purposes. In this paper, we propose a new algorithm for the Apollonian packing of circles within an ellipse, based on fundamental numerical methods, granting suitable speed, accuracy and stability. The novelty of the proposed approach consists in its applicability to the Apollonian packing of circles within a generic, closed, convex contour, if the parametrization of its outer boundary is given. |
| first_indexed | 2024-03-11T07:02:52Z |
| format | Article |
| id | doaj.art-c09386bcdbf747c2a1cfd438269b6e43 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-11T07:02:52Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-c09386bcdbf747c2a1cfd438269b6e432023-11-17T09:08:55ZengMDPI AGAlgorithms1999-48932023-02-0116312910.3390/a16030129Apollonian Packing of Circles within EllipsesCarlo Santini0Fabio Mangini1Fabrizio Frezza2Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, ItalyDepartment of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, ItalyDepartment of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, ItalyThe purpose of a circle packing procedure is to fill up a predefined, geometrical, closed contour with a maximum finite number of circles. The subject has received considerable attention in pure and applied sciences and has proved to be highly effective in connection with many a problem in logistics and technology. The well-known Apollonian circle packing achieves the packing of an infinite number of mutually tangent smaller circles of decreasing radii, internal or tangent to the outer boundary. Algorithms are available in the literature for the packing of equal-radius circles within an ellipse for global optimization purposes. In this paper, we propose a new algorithm for the Apollonian packing of circles within an ellipse, based on fundamental numerical methods, granting suitable speed, accuracy and stability. The novelty of the proposed approach consists in its applicability to the Apollonian packing of circles within a generic, closed, convex contour, if the parametrization of its outer boundary is given.https://www.mdpi.com/1999-4893/16/3/129circle packingpacking of ellipsesApollonian packing |
| spellingShingle | Carlo Santini Fabio Mangini Fabrizio Frezza Apollonian Packing of Circles within Ellipses Algorithms circle packing packing of ellipses Apollonian packing |
| title | Apollonian Packing of Circles within Ellipses |
| title_full | Apollonian Packing of Circles within Ellipses |
| title_fullStr | Apollonian Packing of Circles within Ellipses |
| title_full_unstemmed | Apollonian Packing of Circles within Ellipses |
| title_short | Apollonian Packing of Circles within Ellipses |
| title_sort | apollonian packing of circles within ellipses |
| topic | circle packing packing of ellipses Apollonian packing |
| url | https://www.mdpi.com/1999-4893/16/3/129 |
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