Timeline for Biconvex Lens - an 'oriented' convex container for planar point sets
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 17, 2023 at 16:59 | comment | added | Nandakumar R | Thanks again. Found that a randomized incremental algorithm does indeed work for the least area containing ellipse - github.com/dorshaviv/lowner-john-ellipse. One would guess that the same algorithm with limited changes would find the least perimeter containing ellipse as well - a further guess here is that there being no closed form for the ellipse perimeter need not prevent us from finding a least perimeter ellipse. | |
| Apr 16, 2023 at 21:25 | comment | added | Joseph O'Rourke | It is known that a minimum area ellipse must touch at least three points. An analogous result for a minimum area lens would be a step forward. | |
| Apr 16, 2023 at 11:21 | comment | added | Nandakumar R | Thank you. But can one not think of some 'perturbative' approach - say find the smallest containing circle or ellipse first and then work from there towards the smallest lens? The smallest circle can be done in linear time; not sure about the smallest ellipse but it must be much less than n^6. | |
| Apr 12, 2023 at 19:31 | comment | added | Joseph O'Rourke | For a lens (equal radii), I count $6$ degrees-of-freedom (DOF) in the plane: $2 \times 2$ for the diameter endpoints, the common radius, and the "sector displacement": distance from the diameter $\pm$ to the circles. So not easy to pin all these DOFs down. | |
| Apr 11, 2023 at 9:42 | history | asked | Nandakumar R | CC BY-SA 4.0 |