Take the following plot:
ParametricPlot3D[{{t*Sin[2*t], t*Cos[2*t], t}}, {t, -2*Pi, 2*Pi},
AxesLabel -> {x, y, z}, PlotRange -> {All},
PlotStyle -> Directive[RGBColor[0, 0, 0], Thickness[.01]],
PlotPoints -> 1000, MaxRecursion -> 15]
What is the most effective way to export this parametric plot as a continuous, 3D spline for use in other 3D applications such as Cinema4D? Is it possible to export it so that it’s continuous, or can it only be exported as a set of discrete points in 3D space?
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]