INTERFACE LR2Curve;

IMPORT  LR3, PZTypes;

FROM PZTypes IMPORT 
  FloatChain, FourierChain;
  
  TYPE 
  
   T <: Public;
 
  Public = OBJECT 
  
    METHODS 
  
    fMax(): CARDINAL;
     
      (* This object represents an arbitrary closed curve  of the form
          a_0 + \sum_{ i = 1}^{ fMax} ( a_i \cos(i \theta) + b_i \sin( i \theta))$
          where $a_i$ , $b_i$ are vectors of $R^2$ and $\theta$ 
          is an argument (modulo $2\pi$).
       *)
       
    mMin(): CARDINAL;
      (* The minimum number of samples needed to avoid aliasing, i.e. 
         $ mMin = 2 * fMax + 1 $
.       *)
       
    eval(theta : LONGREAL): LR3.T;
       (* Evaluates the point at an  arbitrary $\theta$;
          in $[0..2\pi]$
        *)   
       
    length(theta : LONGREAL): LONGREAL;
        (* Returns the length of the curve for argument in the range $[0..\theta]$ *)
        
    sample(theta : LONGREAL; n : CARDINAL): REF FloatChain;
        (*  $res[k] = eval(\theta + k 2 \pi / n, order), k = 0 .. n-1 $ *) 

    diff(order : CARDINAL) : T;  
        (* Evaluates the "order"th   derivative of the curve *)  
    
    init(READONLY F : FourierChain) : T;   

 
   (*  evalP(p: LR3.T) : LONGREAL;
         Evalutes the parameter associate at an point $p$. If $p$ is not 
           in the curve the returned parameter is NaN 
   *) 
   
  END; 
  
END LR2Curve.