-- File:	AppParCurves_Projection.cdl
-- Created:	Thu Jun 24 16:27:02 1993
-- Author:	Modelistation
--		<model@nonox>
---Copyright:	 Matra Datavision 1993


generic class Projection from AppParCurves
    	    	    (MultiLine   as any;
    	    	     ToolLine    as any)   -- as ToolLine(MultiLine)


    ---Purpose: This algorithm uses the algorithms LeastSquare, 
    --          ResConstraint and a Projection method to approximate a set 
    --          of points (AppDef_MultiLine) with a minimization of the
    --          sum(square(|F(i)-Qi|)) by changing the parameter. 



uses Vector                    from math, 
     MultiCurve                from AppParCurves,
     HArray1OfConstraintCouple from AppParCurves


raises OutOfRange from Standard,
       NotDone    from StdFail


private class ProLeastSquare instantiates LeastSquare from AppParCurves
    	(MultiLine, ToolLine);
	
private class ProConstraint instantiates ResolConstraint from AppParCurves
    	(MultiLine, ToolLine);

private class ProFunction instantiates Function from AppParCurves
    	(MultiLine, ToolLine, ProLeastSquare, ProConstraint);


is

    Create(SSP: MultiLine; FirstPoint, LastPoint: Integer;
    	   TheConstraints: HArray1OfConstraintCouple;
    	   Parameters: in out Vector; Deg: Integer; 
    	   Tol3d, Tol2d: Real; NbIterations: Integer = 200)
	---Purpose: Tries to minimize the sum (square(||Qui - Bi*Pi||)) 
	--          where Pui describe the approximating Bezier curves'Poles 
	--          and Qi the MultiLine points with a parameter ui.
	--          In this algorithm, the parameters ui are the unknowns.
	--          The tolerance required on this sum is given by Tol.
	--          The desired degree of the resulting curve is Deg.
	--          SSP is returned with the new parameter.

    returns Projection from AppParCurves;
    
    
    IsDone(me)
	---Purpose: returns True if all has been correctly done.	

    returns Boolean
    is static;
    
    
    Value(me)
    	---Purpose: returns all the Bezier curves approximating the
    	--          MultiLine SSP after minimization of the parameter.

    returns MultiCurve from AppParCurves
    raises NotDone from StdFail
    is static;
    
    
    Error(me; Index: Integer)
	---Purpose: returns the difference between the old and the new 
	--          approximation.
	--          An exception is raised if NotDone.
	--          An exception is raised if Index<1 or Index>NbParameters.

    returns Real
    raises NotDone from StdFail,
    	   OutOfRange from Standard
    is static;
    

    MaxError3d(me)
    	---Purpose: returns the maximum difference between the old and the 
    	--          new approximation.

    returns Real
    raises NotDone from StdFail
    is static;


    MaxError2d(me)
    	---Purpose: returns the maximum difference between the old and the 
    	--          new approximation.

    returns Real
    raises NotDone from StdFail
    is static;


    AverageError(me)
       ---Purpose: returns the average error between the old and the
       --          new approximation.

    returns Real
    raises NotDone from StdFail
    is static;


fields

SCU:          MultiCurve from AppParCurves;
ParError:     Vector from math;
AvError:      Real;
MError3d:     Real;
MError2d:     Real;
Done:         Boolean;

end Projection from AppParCurves;