3D Extrusion Using the Frenet-Serret System
3D Extrusion Using the Frenet-Serret System
This Demonstration illustrates the conversion of a parametrized three-dimensional space curve into a three-dimensional surface.
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.
ℬ
The one-variable parametric equation of the space curve can be combined with the polar equation of the cross section .
c(u)
r(v)
The result is the two-variable parametric equation of a surface: .
c(u)+r(v)((u)cosv+ℬ(u)sinv)
In this Demonstration, a parametric space curve is defined, with the parameters determining the shape of the curve.
{cos(nt),rsin(mt),zcos(t)}
{n,m,z}