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Re^3: Data visualisation. (updated)by LanX (Saint) |
on Jan 02, 2014 at 13:17 UTC ( [id://1068954]=note: print w/replies, xml ) | Need Help?? |
> I'm curious about your assertion that the general case isn't solveable in the general case if the data doesn't correspond to a planar map. It depends on the criteria you have on "displayable". If it's defined such that each edge-length has to be congruent to the distance in the matrix, you can simply follow the algorithm I sketched to see how each point's position is determined by the distance to 3 other points. I.e. the distance to all other points can't be randomly chosen.
Since I had differential geometry at university I know that there are "distance-true"¹ projections originating from non-plane spaces This is no contradiction, since this data still has to fit into aforementioned algorithm.
The projection won't be "angle"¹ or "surface"¹-true, which is a problem for maps but not for graphs.
I.a.W. the origin of the data doesn't need to be from a planar geometry but the graph needs to be I will try to update some WP links...
Cheers Rolf ( addicted to the Perl Programming Language) ¹) not sure about the appropriate English terminology. ²) remembered it wrong sorry, see Map_projection#Metric_properties_of_maps, and in hindsight it's obvious that projections can only preserve distances if the Pythagorean theorem holds. Though preserving size of areas and angles are no problem.
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