Your plot is made up internally by a sequence of points connected by straight-line segments, i.e., a Line
. It is continuous by definition. You can use Interpolation
to get a spline interpolation:
myPlot = ParametricPlot3D[{{t*Sin[2*t], t*Cos[2*t], t}}, {t, -2*Pi,
2*Pi}]
myLine = Cases[myPlot, _Line, {1, Infinity}]
Interpolation[Transpose[{myLine[[1, 1, All, -1]], myLine[[1, 1]]}],
Method -> "Spline"]
As for exporting to 3D applications, have you tried the dxf file format?
Export[NotebookDirectory[] <> "file.dxf", myPlot]