Space Curves

Implementation

Needs["Graphics`Colors`"]

Needs["CURVES3D`"]

Needs["CSPROGS`"]

dip[ins_][g_]:=$DisplayFunction[Insert[g,ins,{1,1}]]

Elliptical Helix

The elliptical helix is a typical example of a space
curve that can be nicely plotted with Mathematica.

ParametricPlot3D[Append[helix[2,1,0.5][t],
Red]//Evaluate,
{t,0,6Pi},Axes->None,
DisplayFunction->dip[Thickness[0.05]]];

Determining a space curve from its curvature and torsion

The fundamental theorem of space curves states that up to
a rigid motion a space curve is determined by its curvature
and torsion.  The function plotintrinsic3d constucts a space curve from its
curvature and torsion.  Here is an example of its use.

?plotintrinsic3d

plotintrinsic3d[{1&,Cos},{0,{0,0,0},{1,0,0},{0,1,0}},
{-2Pi,2Pi},DisplayFunction->dip[Thickness[0.02]]];