def tangentVec(r,t):
return(diff(r,t)/norm(diff(r,t)))
def Plottangent(r,t,x,**kwarg):
var('U')
r0=r(t=x)
T=tangentVec(r,t)(t=x)
return parametric_plot3d(list(r0+T*U),(U,0,1),**kwarg)
def NormalVec(b,t):
return(diff(b,t)/norm(diff(b,t)))
def PlotUNormal(r,t,x,**kwarg):
var('U')
r0=r(t=x)
T=NormalVec(tangentVec(r,t),t)(t=x)
return parametric_plot3d(list(r0+T*U),(U,0,1),**kwarg)
def binormalVector(r,t):
return(tangentVec(r,t).cross_product(NormalVec(r,t)))
def Plotbinormal(r,t,x,**kwarg):
var('U')
r0=r(t=x)
T=binormalVector(r,t)(t=x)
return parametric_plot3d(list(r0+T*U),(U,0,1),**kwarg)
r(t)=[sin(t),cos(t),2*t]
a=parametric_plot3d(r(t),(t,-10,10),thickness=5)
b=Plottangent(r(t),t,-2,thickness=10,color='yellow')
c=PlotUNormal(r(t),t,-2,thickness=10,color='red')
d=Plotbinormal(r(t),t,-2,thickness=10,color='red')
d
