shader sheet_occlusion2 (
  normal Normal=N,
  float Radius=0.05,

  output float Fac=1,
  output float Var=1
){
  // calculate angle of incidence
  float alpha = acos(dot(I,Normal));
  // treat front and back the same
  alpha = alpha > M_PI_2 ? M_PI - alpha : alpha;
  // calculate the non occluded fraction 
  Fac = cos(alpha) - 2 * Radius;
  // calculate the range of the visible normals
  if( Fac < 0 ){
    Fac = 0;
    Var = cos(alpha) / (2 * Radius);
  }
}