Timeline for How to characterize the regularity of a polygon?
Current License: CC BY-SA 4.0
17 events
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| Dec 8, 2022 at 20:02 | comment | added | Per Alexandersson | @CaioTomás If you can see what's going on when printed on a monochrome printer, then you're ok. | |
| Dec 8, 2022 at 18:48 | comment | added | Caio Tomás | @JoshuaZ I like the idea of measuring the distance to angle bisector and or perp bisector. However, the distances I am working with are quite small (and theses distances would be even smaller) and I would like a metric that has a somewhat decent range (at least for hexagons), as I mentioned in a comment on Matt F.'s answer. Maybe I could do with your suggestion, but then I would have to think how to give weights in order to scale up the variations, which I am not willing to do right now. | |
| Dec 8, 2022 at 18:35 | comment | added | Caio Tomás |
@PerAlexandersson Will do, good advise! Do you have any suggestions to what kind of coloring scheme (or matplotlib colormap, since that's what I am using right now) is best suited for that?
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| Dec 8, 2022 at 18:24 | vote | accept | Caio Tomás | ||
| Dec 8, 2022 at 17:02 | answer | added | mr_e_man | timeline score: 7 | |
| Dec 8, 2022 at 7:19 | comment | added | Per Alexandersson | Side note: Please don't use red/green to distinguish features, use some colorblind friendly coloring scheme instead | |
| Dec 8, 2022 at 0:10 | comment | added | nathan.j.mcdougall | fisherzachary.github.io/public/r-output.html | |
| Dec 7, 2022 at 18:09 | history | became hot network question | |||
| Dec 7, 2022 at 14:01 | history | edited | user44143 |
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| Dec 7, 2022 at 12:08 | comment | added | JoshuaZ | Some more geometric options: The center always exists, and if a polygon is regular, then the angle bisectors and perp bisectors both go through it. Take center of mass and measure how far it is from these segments (either set or both). Another geometric option is to draw a "potential" incircle and circumcircle of the correct radius based on area, with the center of mass, and then somehow measure how much they fail to be the actual incircle and circumcircle (possibly by having the wrong amount of area left over.) For all these metrics, inequalities between them may be interesting. | |
| Dec 7, 2022 at 12:07 | answer | added | user44143 | timeline score: 14 | |
| Dec 7, 2022 at 12:04 | comment | added | JoshuaZ | A few thoughts which may not be applicable to your situation. One may want notions which are scale invariant, so that dilations of the polygon don't change how irregular it is. In which case $\sigma(D)/M$ where M is the maximum length of a side may be a useful metric. If one wants one that talks about angles, one option is to look at how big the standard deviation of the angles is (although this will be zero for all rectangles). Combinations (linear, products etc.) of these also make sense. | |
| Dec 7, 2022 at 11:51 | comment | added | guest | Too short for a full response: but the space of polygons of fixed length (up to rotation and translation) is double covered by the Grassmanian of planes which has a metric on it that you can use for measuring distance from a given polygon of fixed length to a regular polygon of the same length…but this is maybe not applicable to your setting as lengths can be variable | |
| Dec 7, 2022 at 11:06 | history | edited | YCor |
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| Dec 7, 2022 at 10:14 | history | edited | Caio Tomás | CC BY-SA 4.0 |
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| S Dec 7, 2022 at 10:09 | review | First questions | |||
| Dec 7, 2022 at 11:08 | |||||
| S Dec 7, 2022 at 10:09 | history | asked | Caio Tomás | CC BY-SA 4.0 |