The upper envelope of Voronoi surfaces and its applications:
Abstract: "Given a set S of sources (points or segments), we consider the surface that is the graph of the function [formula], for some metric p. This surface is closely related to the Voronoi diagram, Vor(S), of S under the metric p. The upper envelope of a set of these Voronoi surfaces, each...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Ithaca, New York
1991
|
| Series: | Cornell University <Ithaca, NY> / Department of Computer Science: Technical report
1191 |
| Subjects: | |
| Summary: | Abstract: "Given a set S of sources (points or segments), we consider the surface that is the graph of the function [formula], for some metric p. This surface is closely related to the Voronoi diagram, Vor(S), of S under the metric p. The upper envelope of a set of these Voronoi surfaces, each defined for a different set of sources, can be used to solve a number of problems, including finding the minimum Hausdorff distance between two sets of points or line segments under translation, and determining the optimal placement of a site with respect to sets of utilities We derive bounds on the number of vertices on the upper envelope of a collection of Voronoi surfaces, and provide efficient algorithms to calculate these vertices. We then discuss applications of the methods to the aforementioned problems. |
| Physical Description: | 33 S. |
Staff View
MARC
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| 100 | 1 | |a Huttenlocher, Daniel P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The upper envelope of Voronoi surfaces and its applications |c Daniel P. Huttenlocher ; Klara Kedem ; Micha Sharir |
| 264 | 1 | |a Ithaca, New York |c 1991 | |
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| 490 | 1 | |a Cornell University <Ithaca, NY> / Department of Computer Science: Technical report |v 1191 | |
| 520 | 3 | |a Abstract: "Given a set S of sources (points or segments), we consider the surface that is the graph of the function [formula], for some metric p. This surface is closely related to the Voronoi diagram, Vor(S), of S under the metric p. The upper envelope of a set of these Voronoi surfaces, each defined for a different set of sources, can be used to solve a number of problems, including finding the minimum Hausdorff distance between two sets of points or line segments under translation, and determining the optimal placement of a site with respect to sets of utilities | |
| 520 | 3 | |a We derive bounds on the number of vertices on the upper envelope of a collection of Voronoi surfaces, and provide efficient algorithms to calculate these vertices. We then discuss applications of the methods to the aforementioned problems. | |
| 650 | 4 | |a Computational geometry | |
| 650 | 4 | |a Voronoi polygons | |
| 700 | 1 | |a Kedem, Klara |e Verfasser |4 aut | |
| 700 | 1 | |a Šārîr, Mîkā |d 1950- |e Verfasser |0 (DE-588)138916675 |4 aut | |
| 810 | 2 | |a Department of Computer Science: Technical report |t Cornell University <Ithaca, NY> |v 1191 |w (DE-604)BV006185504 |9 1191 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-007066574 | ||
Record in the Search Index
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| any_adam_object | |
| author | Huttenlocher, Daniel P. Kedem, Klara Šārîr, Mîkā 1950- |
| author_GND | (DE-588)138916675 |
| author_facet | Huttenlocher, Daniel P. Kedem, Klara Šārîr, Mîkā 1950- |
| author_role | aut aut aut |
| author_sort | Huttenlocher, Daniel P. |
| author_variant | d p h dp dph k k kk m š mš |
| building | Verbundindex |
| bvnumber | BV010596248 |
| ctrlnum | (OCoLC)25776307 (DE-599)BVBBV010596248 |
| format | Book |
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| id | DE-604.BV010596248 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:55:40Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007066574 |
| oclc_num | 25776307 |
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| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 33 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| record_format | marc |
| series2 | Cornell University <Ithaca, NY> / Department of Computer Science: Technical report |
| spelling | Huttenlocher, Daniel P. Verfasser aut The upper envelope of Voronoi surfaces and its applications Daniel P. Huttenlocher ; Klara Kedem ; Micha Sharir Ithaca, New York 1991 33 S. txt rdacontent n rdamedia nc rdacarrier Cornell University <Ithaca, NY> / Department of Computer Science: Technical report 1191 Abstract: "Given a set S of sources (points or segments), we consider the surface that is the graph of the function [formula], for some metric p. This surface is closely related to the Voronoi diagram, Vor(S), of S under the metric p. The upper envelope of a set of these Voronoi surfaces, each defined for a different set of sources, can be used to solve a number of problems, including finding the minimum Hausdorff distance between two sets of points or line segments under translation, and determining the optimal placement of a site with respect to sets of utilities We derive bounds on the number of vertices on the upper envelope of a collection of Voronoi surfaces, and provide efficient algorithms to calculate these vertices. We then discuss applications of the methods to the aforementioned problems. Computational geometry Voronoi polygons Kedem, Klara Verfasser aut Šārîr, Mîkā 1950- Verfasser (DE-588)138916675 aut Department of Computer Science: Technical report Cornell University <Ithaca, NY> 1191 (DE-604)BV006185504 1191 |
| spellingShingle | Huttenlocher, Daniel P. Kedem, Klara Šārîr, Mîkā 1950- The upper envelope of Voronoi surfaces and its applications Computational geometry Voronoi polygons |
| title | The upper envelope of Voronoi surfaces and its applications |
| title_auth | The upper envelope of Voronoi surfaces and its applications |
| title_exact_search | The upper envelope of Voronoi surfaces and its applications |
| title_full | The upper envelope of Voronoi surfaces and its applications Daniel P. Huttenlocher ; Klara Kedem ; Micha Sharir |
| title_fullStr | The upper envelope of Voronoi surfaces and its applications Daniel P. Huttenlocher ; Klara Kedem ; Micha Sharir |
| title_full_unstemmed | The upper envelope of Voronoi surfaces and its applications Daniel P. Huttenlocher ; Klara Kedem ; Micha Sharir |
| title_short | The upper envelope of Voronoi surfaces and its applications |
| title_sort | the upper envelope of voronoi surfaces and its applications |
| topic | Computational geometry Voronoi polygons |
| topic_facet | Computational geometry Voronoi polygons |
| volume_link | (DE-604)BV006185504 |
| work_keys_str_mv | AT huttenlocherdanielp theupperenvelopeofvoronoisurfacesanditsapplications AT kedemklara theupperenvelopeofvoronoisurfacesanditsapplications AT sarirmika theupperenvelopeofvoronoisurfacesanditsapplications |