Sorting a list of points based on their euclidean distance

Question

I need to take a list of random points and then sort them from least to greatest based on their Euclidean distance from a certain point. How would I do this?

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score 1 · Answer 1 · answered Feb 21 '15 at 17:17

1

pts = RandomReal[{0, 1}, {20, 2}];
ordered2 = pts[[Ordering[-Norm /@ (# - orig & /@ pts)]]]

ordered2 == ordered (* `ordered` from belisarius's answer *)
(* True *)

answered Feb 21 '15 at 17:17

kglr

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score 0 · Accepted Answer · answered Feb 21 '15 at 16:21

0

orig = {1, 1};
pts = RandomReal[{0, 1}, {20, 2}];
ordered = Sort[pts, Norm[#1 - orig] > Norm[#2 - orig] &]
Graphics[{PointSize[#[[1]] .01], Point@#[[2]]} & /@  Transpose[{Range@Length@pts, ordered}]]

Mathematica graphics

answered Feb 21 '15 at 16:21

Dr. belisarius

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Or SortBy[..., Norm[#-orig]&] – Szabolcs Feb 21 '15 at 16:22

score 0 · Answer 3 · edited Apr 13 '17 at 12:55

Using Sort with a custom ordering function forces quadratic complexity due to pairwise comparison^{(1)(2)(3)(4)(5)} and should be avoided whenever possible. Use SortBy instead, as Szabolcs comments.

orig = {1, 1};

pts = RandomReal[1, {50000, 2}];

Sort[pts, Norm[#1 - orig] > Norm[#2 - orig] &] // AbsoluteTiming // First

SortBy[pts, Norm[# - orig] &]                  // AbsoluteTiming // First

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0.011001

It is shorter to write too. :-) Ordering is slightly faster still but not as convenient to use.

Sorting a list of points based on their euclidean distance

3 Answers3