Timeline for Covering an arbitrary polygon with minimum number of squares
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| S Aug 4, 2017 at 14:23 | history | edited | Taras Banakh | CC BY-SA 3.0 |
removed deprecated (geometry) tag - see the tag info: http://mathoverflow.net/tags/geometry/info; if there are some other geometry-related tags which are suitable, please use some of them instead; addes a tag of computational geometry
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| S Aug 4, 2017 at 14:23 | history | suggested | Martin Sleziak |
removed deprecated (geometry) tag - see the tag info: http://mathoverflow.net/tags/geometry/info; if there are some other geometry-related tags which are suitable, please use some of them instead
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| Aug 4, 2017 at 14:21 | review | Suggested edits | |||
| S Aug 4, 2017 at 14:23 | |||||
| Mar 17, 2012 at 21:59 | comment | added | Chris | They can overlap. | |
| Mar 16, 2012 at 0:40 | comment | added | Joseph O'Rourke | There remains one additional under-specified aspect: May the squares overlap one another? Or are they to be arranged in a grid? | |
| Mar 15, 2012 at 15:37 | comment | added | Chris | Apologies for the lack of clarity on my question. The polygon I wish to cover can be any size and shape. My squares are always smaller than the main polygon and of a fixed size. Therefore one bounding square will not work. The squares must also be upright (i.e. they cant be rotated). The union of all my squares must cover the completely to main polygon and I'm looking to find the minimum number of squares. The union of squares can include points exterior to the polygon. | |
| Mar 15, 2012 at 14:09 | answer | added | Joseph O'Rourke | timeline score: 4 | |
| Mar 15, 2012 at 13:53 | comment | added | Lee Mosher | I agree with Joseph. Is the size of the squares fixed before the polygon is given? Are you allowing the squares to be rotated, or must they have sides parallel to the axes? | |
| Mar 15, 2012 at 13:50 | comment | added | Joseph O'Rourke | I think you need to sharpen the description of your problem: one large square can cover any polygon. Perhaps you mean: the union of the squares must be exactly the polygon, but no square can contain a point exterior to the polygon? | |
| Mar 15, 2012 at 13:41 | history | asked | Chris | CC BY-SA 3.0 |