Timeline for Covering convex polygons with inscribed disks
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 26, 2013 at 2:10 | comment | added | Yoav Kallus | As for efficiency of calculating this area at each step, it seems it should be too inefficient. If for some reason it is, I can think of many ways of approximating it cheaply. | |
| Jul 26, 2013 at 2:06 | comment | added | Yoav Kallus | For the circle circumscribing the region, this is also easy if you think about the three cases above. Obviously, this is not applicable for regions that abut the boundary of $P$. | |
| Jul 26, 2013 at 2:05 | comment | added | Yoav Kallus | In the generic case, your region will be bounded by three circles (possibly of zero curvature) that are tangent to each other. Calculating the area of this region is easy (think of the triangle formed by the centers minus the three circular sectors). Other cases that arise, but are not much harder: near corners of $P$ you will have a region bounded by two lines and a circle tangent to them; you will unavoidably have some regions bounded by a cycle of four tangent circles. | |
| Jul 26, 2013 at 1:35 | comment | added | Vidit Nanda | Thank you, this looks like a promising idea. Is it efficient to compute these areas at each step when deciding whether the area is bounded? Similarly, I'm not sure how to check effectively that the complement of some disks in a polytope is circumscribable by another disk. | |
| Jul 25, 2013 at 22:53 | history | edited | Yoav Kallus | CC BY-SA 3.0 |
added 102 characters in body
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| Jul 25, 2013 at 22:45 | history | answered | Yoav Kallus | CC BY-SA 3.0 |