How can I make points equally spaced along any line?

Question

What I am looking for is something like the output of this code:

DiscretizeRegion[Line[{{0, 0}, {1, 0}, {1, 1}, {0, 1}}],
                 MaxCellMeasure -> {"Length" -> 0.1}]

but I just want to have a list of the points on this line.

Thanks

Does this answer your question? Generating evenly spaced points on a curve — Alexey Popkov, Jul 30 '22 at 02:33
Does this answer your question? Breaking a Kinked line into $(n-1)$ segments of equal Euclidean distance? — Michael E2, Jul 30 '22 at 02:57
Both of the threads linked above treat very general situations; I think it is worthwhile to consider a line segment as a very special case. — J. M.'s missing motivation, Jul 30 '22 at 14:29

score 8 · Answer 1 · answered Jul 30 '22 at 01:37

This is easily done with Subdivide[] and some deft use of dot products:

lineSubdivide[{p1_, p2_}, n_Integer?Positive] :=
    With[{t = Subdivide[n]}, Transpose[{1 - t, t}] . {p1, p2}]
{Graphics[Point[lineSubdivide[{{0, 0}, {1, 1}}, 10]], Axes -> True], 
 Graphics3D[Point[lineSubdivide[{{0, 0, 0}, {1, 1, 1}}, 10]]]}

subdivided lines in 2D and 3D

score 7 · Answer 2 · answered Jul 30 '22 at 05:55

Subdivide support multiple coordinate.

Subdivide[{0, 0, 0}, {1, 1, 1}, 10]

MeshPrimitives can get the coordinates. ( Here we do not use MeshCoordinates since it not always in order.)

reg = DiscretizeRegion[Line[{p1, p2}], 
   MaxCellMeasure -> {"Length" -> 1/5}];
MeshPrimitives[reg, 1][[;; , 1]]

How can I make points equally spaced along any line?

2 Answers2