Timeline for Centroid of Minkowski sum
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 22 at 19:26 | comment | added | Iosif Pinelis | Do you have a response to the answer below? | |
| Mar 20 at 14:29 | comment | added | Iosif Pinelis | @IgorBelegradek : (i) Please look at this guideline: "avoid trying to answer questions which [...] request answers to multiple questions". (ii) The centroid (also known as center of mass, center of gravity, or barycenter) is a standard notion. Even though there are other points that can be assigned to a convex set, such as the Steiner point, they are definitely not the centroid. | |
| Mar 20 at 14:17 | history | edited | Martin Sleziak |
edited tags
|
|
| Mar 20 at 14:03 | comment | added | Igor Belegradek | continued: if you have no access to Schenider's book see p.222 in math.ucdavis.edu/~deloera/MISC/LA-BIBLIO/trunk/McMullen/…. | |
| Mar 20 at 14:00 | comment | added | Igor Belegradek | I don't think MO has "only one question per post rule". Do you define centroid as the center of gravity? In convex geometry one studies functions invariant under Minkowski addition. In particular, if $f$ is a function from the set of convex compact subsets of $\mathbb R^n$ into $\mathbb R^n$ such that $f$ is Minkowski additive, equivariant under rigid motions and continuous in the Hausdorff distance, then $f$ is the Steiner point (which is not always the same as the center of gravity). The result can be found, e.g. in the book [Schneider, Convex Bodies: The Brunn-Minkowski Theory, 2013]. | |
| Mar 20 at 12:48 | comment | added | Iosif Pinelis | There should be only one question in one post. | |
| Mar 20 at 12:48 | answer | added | Iosif Pinelis | timeline score: 2 | |
| Mar 20 at 4:58 | history | asked | F J | CC BY-SA 4.0 |