-- Created on: 1991-04-11
-- Created by: Laurent PAINNOT
-- Copyright (c) 1991-1999 Matra Datavision
-- Copyright (c) 1999-2014 OPEN CASCADE SAS
--
-- This file is part of Open CASCADE Technology software library.
--
-- This library is free software; you can redistribute it and / or modify it
-- under the terms of the GNU Lesser General Public version 2.1 as published
-- by the Free Software Foundation, with special exception defined in the file
-- OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
-- distribution for complete text of the license and disclaimer of any warranty.
--
-- Alternatively, this file may be used under the terms of Open CASCADE
-- commercial license or contractual agreement.

package AppParCurves 

    ---Purpose: Parallel Approximation in n curves.
    -- This package gives all the algorithms used to approximate a MultiLine
    -- described by the tool MLineTool. 
    -- The result of the approximation will be a MultiCurve. 
    
uses  math, FEmTool,  gp, TColgp, StdFail, TColStd, TCollection, Standard, MMgt, GeomAbs, 
      PLib

is

    enumeration Constraint is
    	NoConstraint,
	PassPoint,
        TangencyPoint,
        CurvaturePoint
    end Constraint;
---Purpose:
-- -   NoConstraint: this point has no constraints.
-- -   PassPoint: the approximation curve passes through this point.
-- -   TangencyPoint: this point has a tangency constraint.
-- -   CurvaturePoint: this point has a curvature constraint.




    deferred generic class MLineTool;    --- Template


    class MultiPoint;

    class MultiCurve;

    class MultiBSpCurve;

    class ConstraintCouple;


-- Algorithms:
    
    
    generic class LeastSquare;
     	---Purpose: computes in parallel the least square resolution of a 
     	--          set of points (MultiLine). The result is a 
     	--          set of Bezier curves (MultiCurve).
 
    generic class ResolConstraint;
    	---Purpose: computes the approximating resolution with constraints
    	--          starting from a guess solution issued, for example, 
    	--          from the least squares.
    	--          It uses the Uzawa method from the mathematical package.


    generic class Function;


    generic class BSpFunction;
    

    generic class Gradient,  Gradient_BFGS, ParLeastSquare, ResConstraint, ParFunction;
    	---Purpose: computes the approximation of a MultiLine by the
    	--          search for a new parameters to minimize the 
    	--          sum||C(ui)-Qi||2 with a gradient method.



    generic class BSpGradient, BSpGradient_BFGS,  BSpParLeastSquare, BSpParFunction;
    	---Purpose: computes the approximation of a MultiLine by the
    	--          search for a new parameters to minimize the 
    	--          sum||C(ui)-Qi||2 with a gradient method.
    	--          The Result is a Bspline set.


    generic class Projection, ProLeastSquare, ProConstraint, ProFunction;
     	---Purpose: computes the approximation of a Multiline by
     	--          searching for a new parameter with a projection
     	--          method.
      
    deferred  class  SmoothCriterion;
    generic  class  LinearCriteria; 

    class  MyCriterion;
         ---Level: Internal
                 
    generic class Variational;
     	---Purpose: computes the approximation of a Multiline by
     	--          Variational optimization.



    --- instantiate classes:
    --  

    class Array1OfConstraintCouple instantiates Array1 from TCollection
            (ConstraintCouple);

    class HArray1OfConstraintCouple instantiates HArray1 from TCollection
    	    (ConstraintCouple,Array1OfConstraintCouple);



    class Array1OfMultiPoint instantiates Array1 from TCollection
    	    (MultiPoint);
	    
    class HArray1OfMultiPoint instantiates HArray1 from TCollection
    	     (MultiPoint,Array1OfMultiPoint);


    class Array1OfMultiCurve instantiates Array1 from TCollection
    	     (MultiCurve);

    class HArray1OfMultiCurve instantiates HArray1 from TCollection
    	     (MultiCurve, Array1OfMultiCurve);

    class SequenceOfMultiCurve instantiates Sequence from TCollection
    	     (MultiCurve);


    class Array1OfMultiBSpCurve instantiates Array1 from TCollection
    	     (MultiBSpCurve);

    class HArray1OfMultiBSpCurve instantiates HArray1 from TCollection
    	     (MultiBSpCurve, Array1OfMultiBSpCurve);

    class SequenceOfMultiBSpCurve instantiates Sequence from TCollection
    	     (MultiBSpCurve);
     
    
     BernsteinMatrix(NbPoles: in Integer    from Standard;
    	       	     U      : in Vector     from math;
                     A      : in out Matrix from math);
     

     Bernstein(NbPoles: in Integer    from Standard;
    	       U      : in Vector     from math;
               A      : in out Matrix from math; 
    	       DA     : in out Matrix from math);

    
     SecondDerivativeBernstein(U: Real; DDA: in out Vector from math);


     SplineFunction(NbPoles    : in     Integer        from Standard;
     	            Degree     : in     Integer        from Standard;
     	            Parameters : in     Vector         from math;
		    FlatKnots  : in     Vector         from math;
		    A          : in out Matrix         from math;
		    DA         : in out Matrix         from math;
                    Index      : in out IntegerVector  from math);
		    
end AppParCurves;