Talk:Peano curve
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Picture without explanation
editThough the article talks about Peano curves being more generally defined as any space filling curves, the construction is specifically of the "snake" displayed in the initial picture. The other curves (https://en.wikipedia.org/wiki/File:Peano_1.GIF and https://en.wikipedia.org/wiki/File:Peano_2.GIF) are just left in the article without explanation.
These should either be removed or discussed, no?
Why is it not injective
editCould we expand that by "because ..." ? Presumably Multiple points on the line map to the same point in the plane ? Does that apply to every point on the plane ? and how many points on the line correspond to them ? - Rod57 (talk) 18:37, 9 March 2015 (UTC)
There's some discussion at http://math.stackexchange.com/questions/29732/in-what-way-is-the-peano-curve-not-one-to-one-with-0-12 Kerrick Staley (talk) 02:25, 21 July 2016 (UTC)
How the Peano Curve can lead to an approximate but very fast solution to the Traveling Salesman Problem
editThe Traveling Salesman Problem (TSP) is NP-complete, or at least NP-hard, meaning that it cannot be solved exactly in polynomial time (there is no algorithmic solution having an execution time upper-bounded by n to the m, for problem size n and any positive integer m).
An example of an approximate solution is the one used by some nonprofit organizations that deliver food to shut-ins: the positions of the vertices (delivery locations) are plotted on a printed approximation to a space-filling curve (SFC) such as a Peano Curve, and the visit order is read out as the distances along the SFC.
One source of error in this approximate solution is the nature of a cartesian SFC approximation, where each plotted (x,y) vertex may be very close to up to four of the SFC points, depending on the relative sizes of the physical TSP and SFC points. This error would yield up to four candidates for the position of each vertex in the solution path.
Computer Graphics
editI need to download the peano curves but I can't download itt please help to download it VenkateshChowdary (talk) 14:31, 11 October 2017 (UTC)