   
\tikzstyle{curves}=[
   smooth,samples=200,
   variable=\t,
   domain=0:4*pi,
   color=blue
]

\tikzstyle{rolling}=[
   color=brown
]

\tikzstyle{frenet}=[
   color=cyan
]
\tikzstyle{error}=[
   color=red,
   very thick,
   -latex
]
