3D Extrusion Using the Frenet-Serret System
This Demonstration illustrates the conversion of a parametrized three-dimensional space curve into a three-dimensional surface.[more]
This can be done by using the built-in Mathematica command FrenetSerretSystem to extract the normal and binormal unit vectors and of the space curve.
The one-variable parametric equation of the space curve can be combined with the polar equation of the cross section .
The result is the two-variable parametric equation of a surface: .
In this Demonstration, a parametric space curve is defined, with the parameters determining the shape of the curve.[less]