-- Created on: 1997-10-22
-- Created by: Philippe MANGIN
-- Copyright (c) 1997-1999 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 License 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.

class HermitJacobi from PLib  
     
inherits Base  from PLib 
  
--- Purpose: This class provides method  to work with Jacobi Polynomials
--  relativly to an order of constraint
--  q = myWorkDegree-2*(myNivConstr+1) 
--  Jk(t) for k=0,q compose the Jacobi Polynomial base relativly to the weigth W(t)
--  iorder is the integer  value for the constraints:
--   iorder = 0 <=> ConstraintOrder = GeomAbs_C0 
--   iorder = 1 <=> ConstraintOrder = GeomAbs_C1
--   iorder = 2 <=> ConstraintOrder = GeomAbs_C2
--   P(t) = H(t) + W(t) * Q(t) Where W(t) = (1-t**2)**(2*iordre+2)
--   the coefficients JacCoeff represents P(t) JacCoeff are stored as follow:
--       
--            c0(1)      c0(2) ....       c0(Dimension)
--            c1(1)      c1(2) ....       c1(Dimension)
--           
--         
--         
--            cDegree(1) cDegree(2) ....  cDegree(Dimension)
--         
--   The coefficients  
--           c0(1)                  c0(2) ....            c0(Dimension) 
--           c2*ordre+1(1)                ...          c2*ordre+1(dimension)
--          
--   represents the  part  of the polynomial in  the
--   Hermit's base: H(t) 
--   H(t) = c0H00(t) + c1H01(t) + ...c(iordre)H(0 ;iorder)+ c(iordre+1)H10(t)+...
--   The following coefficients represents the part of the
--   polynomial in the Jacobi base ie Q(t)
--   Q(t) = c2*iordre+2  J0(t) + ...+ cDegree JDegree-2*iordre-2

uses  
    Array2OfReal  from TColStd,
    Array1OfReal  from TColStd,
    Shape  from GeomAbs,
    Matrix from  math, 
    JacobiPolynomial from PLib 

raises
     ConstructionError from Standard

is

     Create ( WorkDegree      : Integer ; 
              ConstraintOrder : Shape from GeomAbs)
     returns HermitJacobi from PLib


---Purpose:
--   Initialize the polynomial class
--   Degree has to be <= 30
--   ConstraintOrder has to be GeomAbs_C0
--                             GeomAbs_C1
--                             GeomAbs_C2
                                                                                      
     raises ConstructionError from Standard;
--   if Degree or ConstraintOrder is non valid

      
--
--   Work in HermitJacobi base
    
     MaxError ( me ; Dimension : Integer ;
                HermJacCoeff : in  out  Real;
                NewDegree : Integer )
     returns Real;
    
---Purpose:
--   This  method computes the  maximum  error on the polynomial
--   W(t) Q(t) obtained by missing the coefficients of JacCoeff from
--   NewDegree +1 to Degree

     ReduceDegree ( me ; Dimension ,  MaxDegree  : Integer ;  Tol : Real ; 
                    HermJacCoeff :  in  out  Real;
                    NewDegree : out Integer ;
                    MaxError  : out Real);
                            
---Purpose:
--   Compute NewDegree <= MaxDegree so that MaxError is lower
--   than Tol. 
--   MaxError can be greater than Tol if it is not possible
--   to find a NewDegree <= MaxDegree.
--   In this case NewDegree = MaxDegree
-- 
     AverageError ( me ; Dimension : Integer ;
                    HermJacCoeff : in  out  Real;
                    NewDegree : Integer )
--   This method computes the average error on the polynomial W(t)Q(t)
--   obtained  by missing  the
--   coefficients JacCoeff  from  NewDegree +1 to Degree
     returns Real;


     ToCoefficients ( me ; Dimension,  Degree : Integer ;
                      HermJacCoeff : Array1OfReal from TColStd ;
                      Coefficients : out Array1OfReal from TColStd );
   
---Purpose:
--   Convert the polynomial P(t) = H(t) + W(t) Q(t) in the canonical base.
-- 

    D0123 (me : mutable; NDerive : Integer; U : Real;  
    	   BasisValue : out Array1OfReal from TColStd; 
	   BasisD1    : out Array1OfReal from TColStd; 
    	   BasisD2    : out Array1OfReal from TColStd; 
           BasisD3    : out Array1OfReal from TColStd)
---Purpose: Compute the values and the derivatives values of
--          the basis functions in u 
    is private;
 
    D0 (me : mutable; U : Real;  
    	BasisValue : out Array1OfReal from TColStd); 
---Purpose: Compute the values of the basis functions in u
--     
 
    D1 (me : mutable; U : Real;  
      	BasisValue : out Array1OfReal from TColStd; 
     	BasisD1    : out Array1OfReal from TColStd);
---Purpose: Compute the values and the derivatives values of
--          the basis functions in u
  
    D2 (me : mutable; U : Real;  
    	BasisValue : out Array1OfReal from TColStd; 
	BasisD1    : out Array1OfReal from TColStd; 
    	BasisD2    : out Array1OfReal from TColStd);
---Purpose: Compute the values and the derivatives values of
--          the basis functions in u

    D3 (me : mutable; U : Real;  
    	BasisValue : out Array1OfReal from TColStd; 
	BasisD1    : out Array1OfReal from TColStd; 
    	BasisD2    : out Array1OfReal from TColStd; 
        BasisD3    : out Array1OfReal from TColStd);
---Purpose: Compute the values and the derivatives values of
--          the basis functions in u

     WorkDegree (me)      
    --- Purpose: returns WorkDegree   
    ---C++: inline
    returns Integer;

     NivConstr (me)  
    ---Purpose: returns NivConstr 
    ---C++: inline
    returns Integer;
    
fields 
     myH       : Matrix from math; 
     myJacobi  : JacobiPolynomial from PLib; 
     myWCoeff  : Array1OfReal;  -- The cannonical Coefficients of W(t).

end HermitJacobi;