In Mathematica we have ListSurfacePlot3D for reconstructing surface from list of points in 3D. But I can not find something similar if I want to reconstruct a curve instead of a surface. For example if I have this list of points:


Notice that the curve should be a closed loop as the first and last points are the same. I want to find a smooth curve that passes exactly through these points. Something like this:

enter image description here

Any suggestion how to do it?

  • 1
    $\begingroup$ Interpolate with option PeriodicInterpolation->True. $\endgroup$ Jul 12, 2020 at 12:54

1 Answer 1


Following Henrik's suggestion, how about

 ff = Interpolation[#, PeriodicInterpolation -> True] & /@ Transpose[dat];
{ListPointPlot3D[dat, PlotStyle -> Orange],
ParametricPlot3D[#[t] & /@ ff//Evaluate, {t, 1, Length[dat]}]}//
  Show[#,BoxRatios -> {1, 1, 1}, Axes -> None] &

enter image description here

Note that following the OP's request, you can encapsulate this into a function:

ListCurvePlot3D[dat_] := 
 Module[{t, ff = 
    Interpolation[#, PeriodicInterpolation -> True] & /@ 
  {ListPointPlot3D[dat, PlotStyle -> Orange], 
    ParametricPlot3D[#[t] & /@ ff // Evaluate, {t, 1, Length[dat]}]} //
  • $\begingroup$ OP mentions I want to find a smooth curve, but this has corners. Perhaps a BSplineFunction would be more appropriate? $\endgroup$
    – flinty
    Jul 12, 2020 at 12:56
  • $\begingroup$ There is no interpolation. The curve is not smooth. $\endgroup$ Jul 12, 2020 at 12:57
  • $\begingroup$ What is the purpose of PeriodicInterpolation -> True when it works exactly same without it? $\endgroup$ Jul 12, 2020 at 13:15
  • $\begingroup$ @azerbajdzan i/ I tend to listen to what Henrik says because he is very smart. ii/ I guess you requested the path to be periodic: the documentation states that if this option is used you can evaluate t at values higher than Length[dat] and remain on the curve. I assume that it means internally it is using periodic functions to do the interpolation. For instance {t, -5, Length[dat] + 5} $\endgroup$
    – chris
    Jul 12, 2020 at 13:21
  • $\begingroup$ I see... Now I wonder why they did not make one command like they did for surface. If we have ListSurfacePlot3D we could also have ListCurvePlot3D. Thanks. $\endgroup$ Jul 12, 2020 at 13:28

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