Timeline for Explicit equation for border of the Minkowski sum of sets
Current License: CC BY-SA 4.0
6 events
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| Mar 12, 2022 at 16:57 | comment | added | Deane Yang | Another less direct way to do this is to use the support function, which is defined to be $$h(u) = sup_{x \in M} \frac{x\cdot u}{f(x)}$$ The support function of the sum is the sum of the support functions. So if it's feasible, you could compute the support functions from the $f$'s, add them, and then convert the sum of support functions back into the function $f$. Note that if $f$ defines a norm, then $h$ is the dual norm. | |
| Mar 11, 2022 at 9:43 | comment | added | Felix Benning | oh, the GJK algorithm was the right clue I think, in there is the gem that you just have to add together the corners of a polygon to get the polygon of the minkowski sum. That reduces the problem to a finite problem at least, proves my intuition in 2d and can be generalized to higher dimensions. Constructing a function from it is a bit more difficult but, it's a step. Thanks! @GeraldEdgar | |
| Mar 10, 2022 at 13:14 | comment | added | Gerald Edgar | I think you are right: there is no formula for this. Here is information on how hard it is to compute the Minkowski sum of two convex polygons in the plane: en.wikipedia.org/wiki/… | |
| Mar 10, 2022 at 13:01 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tag
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| Mar 10, 2022 at 10:11 | history | edited | Felix Benning | CC BY-SA 4.0 |
added 56 characters in body
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| Mar 10, 2022 at 9:32 | history | asked | Felix Benning | CC BY-SA 4.0 |