// Use of the windingnumber for simple curves (NON CROSSED)
// The most fast and robust with Asymptote.
// Utilisation du nombre d'enroulement pour des courbes NON CROISÉES
// Le plus rapide et robuste avec Asymptote.

size(6cm,0, false);
import math;
import roundedpath;

bool counterclockwise(path g)
{
  // Return "true" if "g" (SIMPLE CURVE i.e. NON CROSSED) is counterclockwise
  // Retounre "true" si "g" (NON CROISÉ) est dans le sens contraire des aiguilles d'une montre  
  return windingnumber(g,inside(g)) > 0;
}

path counterclockdirected(path g)
{
  if (counterclockwise(g)) return g; else return reverse(g);
}

path p = (0,1)..(.8,1)..(.8,.6)..(.4,.6)..(.4,.2)..(.8,.2)..(.8,-.2)..(.4,-.2)..(.4,-.6)..(.8,-.6)..(.8,-1)..(0,-1)..cycle;

draw(counterclockdirected(reverse(p)),
     Arrow(Relative(.1)), BeginBar);
draw(counterclockdirected(p),
     Arrow(position=Relative(.2),FillDraw(red)), BeginBar);