-- Created on: 1991-07-24
-- Created by: Michel CHAUVAT
-- 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.


-- Modified by skv - Thu Sep 30 15:19:59 2004 OCC593


private class FuncExtPS from Extrema

 inherits FunctionSetWithDerivatives from math
    ---Purpose: 
    --
    -- Functional for search of extremum of the distance between point P and 
    -- surface S, starting from approximate solution (u0, v0).
    --          
    -- The class inherits math_FunctionSetWithDerivatives and thus is intended
    -- for use in math_FunctionSetRoot algorithm .
    --          
    -- Denoting derivatives of the surface S(u,v) by u and v, respectively, as 
    -- Su and Sv, the two functions to be nullified are:
    --          
    -- F1(u,v) = (S - P) * Su
    -- F2(u,v) = (S - P) * Sv
    --          
    -- The derivatives of the functional are:
    --          
    -- Duf1(u,v) = Su^2    + (S-P) * Suu;
    -- Dvf1(u,v) = Su * Sv + (S-P) * Suv
    -- Duf2(u,v) = Sv * Su + (S-P) * Suv = Dvf1
    -- Dvf2(u,v) = Sv^2    + (S-P) * Svv
    --
    -- Here * denotes scalar product, and ^2 is square power. 

uses    POnSurf           from Extrema,
	SequenceOfPOnSurf from Extrema,
	SequenceOfReal    from TColStd,
	Pnt               from gp,
	Vector            from math,
	Matrix            from math,
	Surface           from Adaptor3d,
    	SurfacePtr        from Adaptor3d

raises  OutOfRange from Standard

is
    Create returns FuncExtPS;

    Create (P: Pnt; S: Surface from Adaptor3d) returns FuncExtPS;
    	---Purpose:

    Initialize(me: in out; S: Surface from Adaptor3d)
    	---Purpose: sets the field mysurf of the function.
    is static;
    
    SetPoint(me: in out; P: Pnt)
    	---Purpose: sets the field mysurf of the function.
    is static;

    ------------------------------------------------------------
    -- In all next methods, an exception is raised if the fields 
    -- were not initialized.

    NbVariables (me) returns Integer;

    NbEquations (me) returns Integer;

    Value (me: in out; UV: Vector; F: out Vector) returns Boolean;
    	---Purpose: Calculate Fi(U,V).

    Derivatives (me: in out; UV: Vector; DF: out Matrix)
    	returns Boolean;
    	---Purpose: Calculate Fi'(U,V).

    Values (me: in out; UV: Vector; F: out Vector; DF: out Matrix)
    	returns Boolean;
    	---Purpose: Calculate Fi(U,V) and Fi'(U,V).

    GetStateNumber (me: in out) returns Integer
    	---Purpose: Save the found extremum.
    	is redefined;

    NbExt (me) returns Integer;
    	---Purpose: Return the number of found extrema.

    SquareDistance (me; N: Integer) returns Real
    	---Purpose: Return the value of the Nth distance.
    	raises  OutOfRange;
	    	-- if N < 1 or N > NbExt(me).

    Point (me; N: Integer) returns POnSurf
    	---Purpose: Returns the Nth extremum.
    	raises  OutOfRange;
	    	-- if N < 1 or N > NbExt(me).

fields
    myP    : Pnt from gp;
    myS    : SurfacePtr from Adaptor3d;

    myU    : Real;          -- current value of U
    myV    : Real;          -- current value of V
    myPs   : Pnt from gp;   -- current point

    mySqDist: SequenceOfReal    from TColStd;
    myPoint: SequenceOfPOnSurf from Extrema;
    myPinit: Boolean;
    mySinit: Boolean;

end FuncExtPS;