Timeline for Characterizing Convex Configurations of Quadrupels of Coplanar Points via Linear (In-)equalities between Distance Sums or Differences
Current License: CC BY-SA 3.0
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| Feb 17, 2013 at 10:14 | comment | added | Manfred Weis | My question also includes that the adjacency relation between sides (i.e. which triplets of distances correspond to adjacent edges) are given. It is fairly easy to determine convexity from triangle's areas (which can be calculated from side-lengths via the Heronic formula): if the area of the largest triangle equals the sum of the areas of the remaining ones, then the quadrilateral isn't convex. Concerning the triangulation of complete metric graphs, one might resort to triangle areas to decide whether two non-adjacent edges intersect. | |
| Feb 17, 2013 at 4:09 | comment | added | Włodzimierz Holsztyński | I think that I have an example of a convex, symmetric trapezoid, which has the six lengths the same as a not convex, symmetric quadrilateral, with two long sides of the same length as the diagonals of the trapezoid; and the six distances (δ δ a A b b) in each case are the same--there are 4 different distances, since there are two pairs of equal (symmetric) distances. * If I manage, I'll provide the details a bit later. | |
| Feb 17, 2013 at 2:12 | comment | added | Włodzimierz Holsztyński | It's an obligation to have doubts :-) I need to think more about this question. Sorry for a false start. | |
| Feb 17, 2013 at 2:10 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
added 395 characters in body
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| Feb 17, 2013 at 1:10 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
typo
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| Feb 17, 2013 at 1:07 | comment | added | Joseph O'Rourke | @Wlodzimierz: I do not doubt you, but could you please provide an example? | |
| Feb 17, 2013 at 0:56 | history | answered | Włodzimierz Holsztyński | CC BY-SA 3.0 |