-- Created on: 1991-09-20
-- Created by: Laurent PAINNOT
-- Copyright (c) 1991-1999 Matra Datavision
-- Copyright (c) 1999-2012 OPEN CASCADE SAS
--
-- The content of this file is subject to the Open CASCADE Technology Public
-- License Version 6.5 (the "License"). You may not use the content of this file
-- except in compliance with the License. Please obtain a copy of the License
-- at http://www.opencascade.org and read it completely before using this file.
--
-- The Initial Developer of the Original Code is Open CASCADE S.A.S., having its
-- main offices at: 1, place des Freres Montgolfier, 78280 Guyancourt, France.
--
-- The Original Code and all software distributed under the License is
-- distributed on an "AS IS" basis, without warranty of any kind, and the
-- Initial Developer hereby disclaims all such warranties, including without
-- limitation, any warranties of merchantability, fitness for a particular
-- purpose or non-infringement. Please see the License for the specific terms
-- and conditions governing the rights and limitations under the License.



generic class Function from AppParCurves (
    	    	    	      MultiLine  as any;
			      ToolLine   as any; -- as ToolLine(MultiLine)
    	    	    	      Squares    as any;
			      ResolCons  as any)

    inherits MultipleVarFunctionWithGradient from math

    ---Purpose: This function inherits MultipleVarFunctionWithGradient to be 
    --          used in the mathematical algorithm BFGS.
    --          It computes the value of the function 
    --          F=sum(||Qui - B*Pi||)2 where Pi are Poles of the Bezier curves 
    --          approximating the given MultiLine SSP and ui the parameters 
    --          associated to the points Qi of SSP.
    --          It also computes the gradient for values ui of the parameter.


uses MultiCurve                from AppParCurves, 
     HArray1OfConstraintCouple from AppParCurves,
     Constraint                from AppParCurves,
     Vector                    from math, 
     Matrix                    from math,
     HArray1OfInteger          from TColStd

is

    Create(SSP: MultiLine; FirstPoint, LastPoint: Integer;
    	   TheConstraints: HArray1OfConstraintCouple;
    	   Parameters: Vector; Deg: Integer)
       ---Purpose: initializes the fields of the function. The approximating
       --          curve has the desired degree Deg.

    returns Function from AppParCurves;
    
    
    NbVariables(me)
    	---Purpose: returns the number of variables of the function. It 
    	--          corresponds to the number of MultiPoints.

    returns Integer
    is static;
    
    

    Perform(me: in out; X: Vector)
    	---Purpose: this method is used each time Value or Gradient is
    	--           needed.
    
    is static protected;


    Value(me: in out; X: Vector; F: out Real) 
    	---Purpose: this method computes the new approximation of the 
    	--          MultiLine
    	--          SSP and calculates F = sum (||Pui - Bi*Pi||2) for each 
    	--          point of the MultiLine.
    
    returns Boolean
    is static;


    Gradient(me: in out; X: Vector; G: out Vector)
    	---Purpose: returns the gradient G of the sum above for the 
    	--          parameters Xi.

    returns Boolean
    is static;
    
    
    Values(me: in out; X: Vector; F: out Real; G: out Vector)
    	---Purpose: returns the value F=sum(||Pui - Bi*Pi||)2.
    	--          returns the value G = grad(F) for the parameters Xi.

    returns Boolean
    is static;
    
    
    
    NewParameters(me)
    	---Purpose: returns the new parameters of the MultiLine.
    	---C++: return const&
    returns Vector
    is static;


    CurveValue(me: in out)
    	---Purpose: returns the MultiCurve approximating the set after
    	--          computing the value F or Grad(F).
    	---C++: return const&
    returns MultiCurve from AppParCurves
    is static;
    

    Error(me; IPoint, CurveIndex: Integer)
    	---Purpose: returns the distance between the MultiPoint of range 
    	--          IPoint and the curve CurveIndex.
    
    returns Real
    is static;


    MaxError3d(me)
    	---Purpose: returns the maximum distance between the points
    	--          and the MultiCurve.

    returns Real
    is static;
    
    MaxError2d(me)
    	---Purpose: returns the maximum distance between the points
    	--          and the MultiCurve.

    returns Real
    is static;

    
    FirstConstraint(me; TheConstraints: HArray1OfConstraintCouple;
    	    	    FirstPoint: Integer)
	---Purpose:

    returns Constraint from AppParCurves
    is static;
    
    
    LastConstraint(me; TheConstraints: HArray1OfConstraintCouple;
    	    	   LastPoint: Integer)
	---Purpose:

    returns Constraint from AppParCurves
    is static;
    
    
fields

Done:           Boolean;
MyMultiLine :   MultiLine;
MyMultiCurve:   MultiCurve from AppParCurves;
Degre:          Integer;
myParameters:   Vector;
FVal:           Real;
ValGrad_F:      Vector from math;
MyF:            Matrix from math;
PTLX :          Matrix from math;
PTLY :          Matrix from math;
PTLZ :          Matrix from math;
A:              Matrix from math;
DA:             Matrix from math;
MyLeastSquare : Squares;
Contraintes:    Boolean;
NbP:            Integer;
NbCu:           Integer;
Adeb:           Integer;
Afin:           Integer;
tabdim:         HArray1OfInteger from TColStd;
ERR3d:          Real;
ERR2d:          Real;
FirstP:         Integer;
LastP:          Integer;
myConstraints:  HArray1OfConstraintCouple from AppParCurves;

end Function;