-- File:	Geom_BezierSurface.cdl
-- Created:	Tue Mar  9 19:51:22 1993
-- Author:	JCV
--		<fid@phylox>
-- Copyright:	 Matra Datavision 1993
-- 
-- RBD : 15/10/98 ; Suppression de la methode privee coefficientsOK
-- 
-- 


class BezierSurface from Geom inherits BoundedSurface from Geom

    	---Purpose : Describes a rational or non-rational Bezier surface.
    	-- - A non-rational Bezier surface is defined by a table
    	--   of poles (also known as control points).
    	-- - A rational Bezier surface is defined by a table of
    	--   poles with varying associated weights.
    	-- This data is manipulated using two associative 2D arrays:
    	-- - the poles table, which is a 2D array of gp_Pnt, and
    	-- - the weights table, which is a 2D array of reals.
    	--  The bounds of these arrays are:
    	-- - 1 and NbUPoles for the row bounds, where
    	--   NbUPoles is the number of poles of the surface
    	--   in the u parametric direction, and
    	-- - 1 and NbVPoles for the column bounds, where
    	--   NbVPoles is the number of poles of the surface
    	--   in the v parametric direction.
    	--   The poles of the surface, the "control points", are the
    	-- points used to shape and reshape the surface. They
    	-- comprise a rectangular network of points:
    	-- - The points (1, 1), (NbUPoles, 1), (1,
    	--   NbVPoles) and (NbUPoles, NbVPoles)
    	--   are the four parametric "corners" of the surface.
    	-- - The first column of poles and the last column of
    	--   poles define two Bezier curves which delimit the
    	--   surface in the v parametric direction. These are
    	--   the v isoparametric curves corresponding to
    	--   values 0 and 1 of the v parameter.
    	-- - The first row of poles and the last row of poles
    	--   define two Bezier curves which delimit the surface
    	--   in the u parametric direction. These are the u
    	--   isoparametric curves corresponding to values 0
    	--   and 1 of the u parameter.
    	--  It is more difficult to define a geometrical significance
    	-- for the weights. However they are useful for
    	-- representing a quadric surface precisely. Moreover, if
    	-- the weights of all the poles are equal, the surface has
    	-- a polynomial equation, and hence is a "non-rational surface".
    	-- The non-rational surface is a special, but frequently
    	-- used, case, where all poles have identical weights.
    	-- The weights are defined and used only in the case of
    	-- a rational surface. This rational characteristic is
    	-- defined in each parametric direction. Hence, a
    	-- surface can be rational in the u parametric direction,
    	-- and non-rational in the v parametric direction.
    	-- Likewise, the degree of a surface is defined in each
    	-- parametric direction. The degree of a Bezier surface
    	-- in a given parametric direction is equal to the number
    	-- of poles of the surface in that parametric direction,
    	-- minus 1. This must be greater than or equal to 1.
    	-- However, the degree for a Geom_BezierSurface is
    	-- limited to a value of (25) which is defined and
    	-- controlled by the system. This value is returned by the
    	-- function MaxDegree.
    	-- The parameter range for a Bezier surface is [ 0, 1 ]
    	-- in the two parametric directions.
    	-- A Bezier surface can also be closed, or open, in each
    	-- parametric direction. If the first row of poles is
    	-- identical to the last row of poles, the surface is closed
    	-- in the u parametric direction. If the first column of
    	-- poles is identical to the last column of poles, the
    	-- surface is closed in the v parametric direction.
    	-- The continuity of a Bezier surface is infinite in the u
    	-- parametric direction and the in v parametric direction.
    	-- Note: It is not possible to build a Bezier surface with
    	-- negative weights. Any weight value that is less than,
    	-- or equal to, gp::Resolution() is considered
    	-- to be zero. Two weight values, W1 and W2, are
    	-- considered equal if: |W2-W1| <= gp::Resolution()
                

uses Array1OfReal      from TColStd,
     Array2OfReal      from TColStd,
     HArray2OfReal     from TColStd,
     Array1OfPnt       from TColgp,
     Array2OfPnt       from TColgp,
     Ax1               from gp, 
     Ax2               from gp,  
     HArray2OfPnt      from TColgp,
     Pnt               from gp,
     Trsf              from gp,
     Vec               from gp, 
     Curve             from Geom,
     Geometry          from Geom,
     Shape             from GeomAbs


raises ConstructionError from Standard,
       DimensionError    from Standard,
       RangeError        from Standard,
       OutOfRange        from Standard

is

 Create (SurfacePoles : Array2OfPnt from TColgp)
    returns mutable BezierSurface
        ---Purpose :
        --  Creates a non-rational Bezier surface with a set of poles.
        --  Control points representation :
        --     SPoles(Uorigin,Vorigin) ...................SPoles(Uorigin,Vend)
        --           .                                     .
        --           .                                     .
        --     SPoles(Uend, Vorigin) .....................SPoles(Uend, Vend)
        --  For the double array the row indice corresponds to the parametric
        --  U direction and the columns indice corresponds to the parametric
        --  V direction.
        --  The weights are defaulted to all being 1.
     raises ConstructionError;
        ---Purpose :
        --  Raised if the number of poles of the surface is lower than 2
        --  or greater than MaxDegree + 1 in one of the two directions 
        --  U or V.


  Create (SurfacePoles : Array2OfPnt  from TColgp;
    	  PoleWeights  : Array2OfReal from TColStd)
     returns mutable BezierSurface
        ---Purpose
        --  Creates a rational Bezier surface with a set of poles and a
        --  set of weights.
        --  For the double array the row indice corresponds to the parametric
        --  U direction and the columns indice corresponds to the parametric
        --  V direction.
        --  If all the weights are identical the surface is considered as 
        --  non-rational (the tolerance criterion is Resolution from package
        --  gp).
     raises ConstructionError;
        ---Purpose :
        --  Raised if SurfacePoles and PoleWeights have not the same
        --  Rowlength or have not the same ColLength.
        --  Raised if PoleWeights (i, j) <= Resolution from gp;
        --  Raised if the number of poles of the surface is lower than 2
        --  or greater than MaxDegree + 1 in one of the two directions U or V.


  ExchangeUV (me : mutable);
        ---Purpose : Exchanges the direction U and V on a Bezier surface
    	-- As a consequence:
    	-- - the poles and weights tables are transposed,
    	-- - degrees, rational characteristics and so on are
    	-- exchanged between the two parametric directions, and
    	-- - the orientation of the surface is reversed.

  Increase (me : mutable; UDeg, VDeg : Integer)
        ---Purpose : Increases the degree of this Bezier surface in the two parametric directions.
     raises ConstructionError;
        ---Purpose : 
        --  Raised if UDegree < UDegree <me>  or VDegree < VDegree <me> 
        --  Raised if the degree of the surface is greater than MaxDegree
        --  in one of the two directions U or V.


  InsertPoleColAfter (me : mutable; VIndex : Integer;
    	    	      CPoles : Array1OfPnt from TColgp)
        ---Purpose:
        --  Inserts a column of poles. If the surface is rational the weights
        --  values associated with CPoles are equal defaulted to 1.
     raises OutOfRange,
        ---Purpose:
        --  Raised if Vindex < 1 or VIndex > NbVPoles.
            ConstructionError;
        ---Purpose:
        --  raises if VDegree is greater than MaxDegree.
        --  raises if the Length of CPoles is not equal to NbUPoles


  InsertPoleColAfter (me : mutable; VIndex : Integer; 
                      CPoles : Array1OfPnt from TColgp;
    	    	      CPoleWeights : Array1OfReal from TColStd)
        ---Purpose :
        --  Inserts a column of poles and weights.
        --  If the surface was non-rational it can become rational.
     raises OutOfRange,
        ---Purpose:
        --  Raised if Vindex < 1 or VIndex > NbVPoles.
            ConstructionError;
        ---Purpose :  Raised if
        --  . VDegree is greater than MaxDegree.
        --  . the Length of CPoles is not equal to NbUPoles
        --  . a weight value is lower or equal to Resolution from 
        --    package gp


  InsertPoleColBefore (me : mutable; VIndex : Integer;
    	    	      CPoles : Array1OfPnt from TColgp)
        ---Purpose:
        --  Inserts a column of poles. If the surface is rational the weights
        --  values associated with CPoles are equal defaulted to 1.
     raises OutOfRange,
        ---Purpose:
        --  Raised if Vindex < 1 or VIndex > NbVPoles.
            ConstructionError;
        ---Purpose:
        --  Raised if VDegree is greater than MaxDegree.
        --  Raised if the Length of CPoles is not equal to NbUPoles



  InsertPoleColBefore (me : mutable; VIndex : Integer; 
                       CPoles : Array1OfPnt from TColgp;
    	    	       CPoleWeights : Array1OfReal from TColStd)
        ---Purpose :
        --  Inserts a column of poles and weights.
        --  If the surface was non-rational it can become rational.
     raises OutOfRange,
        ---Purpose:
        --  Raised if Vindex < 1 or VIndex > NbVPoles.
            ConstructionError;
        ---Purpose :  Raised if :
        --  . VDegree is greater than MaxDegree.
        --  . the Length of CPoles is not equal to NbUPoles
        --  . a weight value is lower or equal to Resolution from 
        --    package gp


  InsertPoleRowAfter (me : mutable; UIndex : Integer;
    	    	      CPoles : Array1OfPnt from TColgp)
        ---Purpose:
        --  Inserts a row of poles. If the surface is rational the weights
        --  values associated with CPoles are equal defaulted to 1.
     raises OutOfRange,
        ---Purpose:
        --  Raised if Uindex < 1 or UIndex > NbUPoles.
            ConstructionError;
        ---Purpose:
        --  Raised if UDegree is greater than MaxDegree.
        --  Raised if the Length of CPoles is not equal to NbVPoles


  InsertPoleRowAfter (me : mutable; UIndex : Integer; 
                      CPoles : Array1OfPnt from TColgp;
    	    	      CPoleWeights : Array1OfReal from TColStd)
        ---Purpose :
        --  Inserts a row of poles and weights.
        --  If the surface was non-rational it can become rational.
     raises OutOfRange,
        ---Purpose:
        --  Raised if Uindex < 1 or UIndex > NbUPoles.
            ConstructionError;
        ---Purpose :  Raised if :
        --  . UDegree is greater than MaxDegree.
        --  . the Length of CPoles is not equal to NbVPoles
        --  . a weight value is lower or equal to Resolution from 
        --    package gp


  InsertPoleRowBefore (me : mutable; UIndex : Integer;
    	    	       CPoles : Array1OfPnt from TColgp)
        ---Purpose:
        --  Inserts a row of poles. If the surface is rational the weights
        --  values associated with CPoles are equal defaulted to 1.
     raises OutOfRange,
        ---Purpose:
        --  Raised if Uindex < 1 or UIndex > NbUPoles.
            ConstructionError;
        ---Purpose:
        --  Raised if UDegree is greater than MaxDegree.
        --  Raised if the Length of CPoles is not equal to NbVPoles


  InsertPoleRowBefore (me : mutable; UIndex : Integer; 
                       CPoles : Array1OfPnt from TColgp;
    	    	       CPoleWeights : Array1OfReal from TColStd)
        ---Purpose :
        --  Inserts a row of poles and weights.
        --  If the surface was non-rational it can become rational.
     raises OutOfRange,
        ---Purpose:
        --  Raised if Uindex < 1 or UIndex > NbUPoles.
            ConstructionError;
        ---Purpose :  Raised if :
        --  . UDegree is greater than MaxDegree.
        --  . the Length of CPoles is not equal to NbVPoles
        --  . a weight value is lower or equal to Resolution from 
        --    pacakage gp


  RemovePoleCol (me : mutable; VIndex : Integer)
        ---Purpose : Removes a column of poles.
        --  If the surface was rational it can become non-rational.
     raises ConstructionError,
        ---Purpose :
        --  Raised if NbVPoles <= 2 after removing, a Bezier surface
        --  must have at least two columns of poles.
            OutOfRange;
        ---Purpose : Raised if Vindex < 1 or VIndex > NbVPoles


  RemovePoleRow (me : mutable; UIndex : Integer)
        ---Purpose : Removes a row of poles.
        --  If the surface was rational it can become non-rational.
     raises ConstructionError,
        ---Purpose :
        --  Raised if NbUPoles <= 2 after removing, a Bezier surface 
        --  must have at least two rows of poles.
            OutOfRange;
        ---Purpose : Raised if Uindex < 1 or UIndex > NbUPoles


  Segment (me : mutable; U1, U2, V1, V2 : Real);
    	---Purpose : Modifies this Bezier surface by segmenting it
    	-- between U1 and U2 in the u parametric direction,
    	-- and between V1 and V2 in the v parametric
    	-- direction. U1, U2, V1, and V2 can be outside the
    	-- bounds of this surface.
    	-- - U1 and U2 isoparametric Bezier curves,
    	-- segmented between V1 and V2, become the two
    	-- bounds of the surface in the v parametric
    	-- direction (0. and 1. u isoparametric curves).
    	-- - V1 and V2 isoparametric Bezier curves,
    	-- segmented between U1 and U2, become the two
    	-- bounds of the surface in the u parametric
    	-- direction (0. and 1. v isoparametric curves).
    	-- The poles and weights tables are modified, but the
    	-- degree of this surface in the u and v parametric
    	-- directions does not change.
    	-- U1 can be greater than U2, and V1 can be greater
    	-- than V2. In these cases, the corresponding
    	-- parametric direction is inverted. The orientation of
    	-- the surface is inverted if one (and only one)
    	-- parametric direction is inverted.
  

 SetPole (me : mutable; UIndex, VIndex : Integer; P : Pnt)
        ---Purpose : Modifies a pole value.
        --  If the surface is rational the weight of range (UIndex, VIndex)
        --  is not modified.
     raises OutOfRange;
        ---Purpose : 
        --  Raised if  UIndex < 1 or UIndex > NbUPoles  or  VIndex < 1
        --  or VIndex > NbVPoles.


 SetPole (me : mutable; UIndex, VIndex : Integer; P : Pnt; Weight : Real)
        ---Purpose :
        --  Substitutes the pole and the weight of range UIndex, VIndex.
        --  If the surface <me> is not rational it can become rational.
        --  if the surface was rational it can become non-rational.
     raises OutOfRange,
        ---Purpose : 
        --  raises if  UIndex < 1 or UIndex > NbUPoles  or  VIndex < 1
        --  or VIndex > NbVPoles.
           ConstructionError;
        ---Purpose : Raised if Weight <= Resolution from package gp.


  SetPoleCol (me : mutable; VIndex : Integer;
    	      CPoles : Array1OfPnt from TColgp)
        ---Purpose :  Modifies a column of poles.
        --  The length of CPoles can be lower but not greater than NbUPoles
        --  so you can modify just a part of the column.
     raises OutOfRange,
        ---Purpose :  Raised if VIndex < 1 or  VIndex > NbVPoles
            ConstructionError;
        ---Purpose : 
        --  Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles


  SetPoleCol (me : mutable; VIndex : Integer;
    	      CPoles : Array1OfPnt from TColgp;
              CPoleWeights : Array1OfReal from TColStd)
        ---Purpose :  Modifies a column of poles.
        --  If the surface was rational it can become non-rational
        --  If the surface was non-rational it can become rational.
        --  The length of CPoles can be lower but not greater than NbUPoles 
        --  so you can modify just a part of the column.
     raises OutOfRange,
        ---Purpose :  Raised if VIndex < 1 or  VIndex > NbVPoles
            ConstructionError;
        ---Purpose : 
        --  Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbUPoles
        --  Raised if CPoleWeights and CPoles have not the same bounds.
        --  Raised if one of the weight value CPoleWeights (i) is lower
        --  or equal to Resolution from package gp.


  SetPoleRow (me : mutable; UIndex : Integer;
    	      CPoles : Array1OfPnt from TColgp)
        ---Purpose :  Modifies a row of poles.
        --  The length of CPoles can be lower but not greater than NbVPoles
        --  so you can modify just a part of the row.
     raises OutOfRange,
        ---Purpose :  Raised if UIndex < 1 or  UIndex > NbUPoles
            ConstructionError;
        ---Purpose : 
        --  Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles



  SetPoleRow (me : mutable; UIndex : Integer;
    	      CPoles : Array1OfPnt from TColgp;
              CPoleWeights : Array1OfReal from TColStd)
        ---Purpose :  Modifies a row of poles and weights.
        --  If the surface was rational it can become non-rational.
        --  If the surface was non-rational it can become rational.
        --  The length of CPoles can be lower but not greater than NbVPoles 
        --  so you can modify just a part of the row.
     raises OutOfRange,
        ---Purpose :  Raised if UIndex < 1 or  UIndex > NbUPoles
            ConstructionError;
        ---Purpose : 
        --  Raised if CPoles.Lower() < 1 or CPoles.Upper() > NbVPoles
        --  Raised if CPoleWeights and CPoles have not the same bounds.
        --  Raised if one of the weight value CPoleWeights (i) is lower
        --  or equal to Resolution from gp.


  SetWeight (me : mutable; UIndex, VIndex : Integer; Weight : Real)
        ---Purpose :
        --  Modifies the weight of the pole of range UIndex, VIndex.
        --  If the surface was non-rational it can become rational.
        --  If the surface was rational it can become non-rational.
     raises OutOfRange,
        ---Purpose :
        --  Raised if UIndex < 1  or  UIndex > NbUPoles or VIndex < 1 or
        --  VIndex > NbVPoles.
            ConstructionError;
	---Purpose : Raised if Weight <= Resolution from package gp.


  SetWeightCol (me : mutable; VIndex : Integer;
    	        CPoleWeights : Array1OfReal from TColStd)
        ---Purpose :  Modifies a column of weights.
        --  If the surface was rational it can become non-rational.
        --  If the surface was non-rational it can become rational.
        --  The length of CPoleWeights can be lower but not greater than
        --  NbUPoles.
     raises OutOfRange,
        ---Purpose :  Raised if VIndex < 1 or  VIndex > NbVPoles
            ConstructionError;
        ---Purpose : 
        --  Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() >
        --  NbUPoles
        --  Raised if one of the weight value CPoleWeights (i) is lower
        --  or equal to Resolution from package gp.


  SetWeightRow (me : mutable; UIndex : Integer;
    	        CPoleWeights : Array1OfReal from TColStd)
        ---Purpose :  Modifies a row of weights.
        --  If the surface was rational it can become non-rational.
        --  If the surface was non-rational it can become rational.
        --  The length of CPoleWeights can be lower but not greater than
        --  NbVPoles.
     raises OutOfRange,
        ---Purpose :  Raised if UIndex < 1 or  UIndex > NbUPoles
            ConstructionError;
        ---Purpose : 
        --  Raised if CPoleWeights.Lower() < 1 or CPoleWeights.Upper() >
        --  NbVPoles
        --  Raised if one of the weight value CPoleWeights (i) is lower
        --  or equal to Resolution from package gp.


  UReverse (me : mutable);
        ---Purpose : Changes the orientation of this Bezier surface in the
    	-- u  parametric direction. The bounds of the
    	-- surface are not changed, but the given parametric
    	-- direction is reversed. Hence, the orientation of the surface is reversed.


  UReversedParameter (me; U : Real) returns Real;
	---Purpose: Computes the u (or v) parameter on the modified
    	-- surface, produced by reversing its u (or v) parametric
    	-- direction, for any point of u parameter U (or of v
    	-- parameter V) on this Bezier surface.
    	-- In the case of a Bezier surface, these functions return respectively:
    	-- - 1.-U, or 1.-V.


  VReverse (me : mutable);
        ---Purpose : Changes the orientation of this Bezier surface in the
    	-- v parametric direction. The bounds of the
    	-- surface are not changed, but the given parametric
    	-- direction is reversed. Hence, the orientation of the
    	-- surface is reversed.


  VReversedParameter (me; V : Real) returns Real;
	---Purpose: Computes the u (or v) parameter on the modified
    	-- surface, produced by reversing its u (or v) parametric
    	-- direction, for any point of u parameter U (or of v
    	-- parameter V) on this Bezier surface.
    	-- In the case of a Bezier surface, these functions return respectively:
    	-- - 1.-U, or 1.-V.
  

  Bounds (me; U1, U2, V1, V2 : out Real);
        ---Purpose : Returns the parametric bounds U1, U2, V1 and V2 of
    	-- this Bezier surface.
    	-- In the case of a Bezier surface, this function returns
    	--        U1 = 0, V1 = 0, U2 = 1, V2 = 1.


  Continuity (me)  returns Shape from GeomAbs;
        ---Purpose :
        --  Returns the continuity of the surface CN : the order of
        --  continuity is infinite.
       
  D0 (me; U, V : Real; P : out Pnt);

  D1 (me; U, V : Real; P : out Pnt; D1U, D1V : out Vec);

  D2 (me; U, V : Real; P : out Pnt; D1U, D1V, D2U, D2V, D2UV : out Vec);

  D3 (me; U, V : Real;  P : out Pnt;
      D1U, D1V, D2U, D2V, D2UV, D3U, D3V, D3UUV, D3UVV : out Vec);
    	---Purpose: Computes P, the point of parameters (U, V) of this Bezier surface, and
    	-- - one or more of the following sets of vectors:
    	-- - D1U and D1V, the first derivative vectors at this point,
    	--   - D2U, D2V and D2UV, the second derivative
    	--    vectors at this point,
    	--   - D3U, D3V, D3UUV and D3UVV, the third
    	--    derivative vectors at this point.
    	-- Note: The parameters U and V can be outside the bounds of the surface.
        
  DN (me; U, V : Real; Nu, Nv : Integer)  returns Vec
        ---Purpose : Computes the derivative of order Nu in the u
    	--  parametric direction, and Nv in the v parametric
    	-- direction, at the point of parameters (U, V) of this Bezier surface.
    	-- Note: The parameters U and V can be outside the bounds of the surface.
    	-- Exceptions
    	-- Standard_RangeError if:
    	-- - Nu + Nv is less than 1, or Nu or Nv is negative.
     raises RangeError;

  NbUPoles (me)  returns Integer;
        ---Purpose : Returns the number of poles in the U direction.

  NbVPoles (me)  returns Integer;
        ---Purpose : Returns the number of poles in the V direction.


  Pole (me; UIndex, VIndex : Integer)  returns Pnt
        ---Purpose : Returns the pole of range UIndex, VIndex
     raises OutOfRange;
        ---Purpose : Raised if UIndex < 1 or UIndex > NbUPoles, or
        --  VIndex < 1 or VIndex > NbVPoles.

 
  Poles (me; P : out Array2OfPnt from TColgp)
        ---Purpose : Returns the poles of the Bezier surface.
     raises DimensionError;
        ---Purpose :
        --  Raised if the length of P in the U an V direction is not equal to
        --  NbUPoles and NbVPoles.


  UDegree (me)   returns Integer;
        ---Purpose : 
        --  Returns the degree of the surface in the U direction it is 
        --  NbUPoles - 1


  UIso (me; U : Real)  returns mutable Curve;
        ---Purpose :
        --  Computes the U isoparametric curve. For a Bezier surface the
        --  UIso curve is a Bezier curve.


  VDegree (me)  returns Integer;
        ---Purpose : 
        --  Returns the degree of the surface in the V direction it is 
        --  NbVPoles - 1


  VIso (me; V : Real)  returns mutable Curve;
        ---Purpose :
        --  Computes the V isoparametric curve. For a Bezier surface the
        --  VIso  curve is a Bezier curve.


  Weight (me; UIndex, VIndex : Integer)   returns Real
        ---Purpose : Returns the weight of range UIndex, VIndex
     raises OutOfRange;
        ---Purpose : 
        --  Raised if UIndex < 1 or UIndex > NbUPoles, or
        --            VIndex < 1 or VIndex > NbVPoles.


  Weights (me; W : out Array2OfReal from TColStd)
        ---Purpose : Returns the weights of the Bezier surface.
     raises DimensionError;
        ---Purpose :
        --  Raised if the length of W in the U an V direction is not
        --  equal to NbUPoles and NbVPoles.

  
  IsUClosed (me)  returns Boolean;
        ---Purpose :
        --  Returns True if the first control points row and the 
        --  last control points row are identical. The tolerance
        --  criterion is Resolution from package gp.


  IsVClosed (me)  returns Boolean;
        ---Purpose :
        --  Returns True if the first control points column
        --  and the last control points column are identical.
        --  The tolerance criterion is Resolution from package gp.


  IsCNu (me; N : Integer) returns Boolean;
        ---Purpose : Returns True, a Bezier surface is always  CN


  IsCNv (me; N : Integer)  returns Boolean;
        ---Purpose : Returns True, a BezierSurface is always  CN


  IsUPeriodic (me)  returns Boolean;
        ---Purpose : Returns False.


  IsVPeriodic (me)  returns Boolean;
        ---Purpose : Returns False.


  IsURational (me)  returns Boolean;
        ---Purpose :
        --  Returns False if the weights are identical in the U direction,
        --  The tolerance criterion is Resolution from package gp.
        --- Example :
        --                 |1.0, 1.0, 1.0|
        --   if Weights =  |0.5, 0.5, 0.5|   returns False
        --                 |2.0, 2.0, 2.0|


  IsVRational (me)  returns Boolean;
        ---Purpose :
        --  Returns False if the weights are identical in the V direction,
        --  The tolerance criterion is Resolution from package gp.
        --- Example :
        --                 |1.0, 2.0, 0.5|
        --   if Weights =  |1.0, 2.0, 0.5|   returns False
        --                 |1.0, 2.0, 0.5|


  Transform (me : mutable; T : Trsf);
---Purpose: Applies the transformation T to this Bezier surface.

  MaxDegree (myclass)   returns Integer;
        ---Purpose:
        --  Returns the value of the maximum polynomial degree of a 
        --  Bezier surface. This value is 25.


  Create (SurfacePoles, SurfaceCoefficients : HArray2OfPnt  from TColgp;
          PoleWeights, CoefficientWeights   : HArray2OfReal from TColStd;
	  IsURational, IsVRational          : Boolean)
     returns mutable BezierSurface
     is private;


  Resolution(me          : mutable; 
             Tolerance3D :     Real ;
    	     UTolerance  : out Real ;
	     VTolerance  : out Real) ;
    	---Purpose: Computes two tolerance values for this Bezier
    	-- surface, based on the given tolerance in 3D space
    	-- Tolerance3D. The tolerances computed are:
    	-- - UTolerance in the u parametric direction, and
    	-- - VTolerance in the v parametric direction.
    	-- If f(u,v) is the equation of this Bezier surface,
    	-- UTolerance and VTolerance guarantee that:
      	--          | u1 - u0 | < UTolerance and 
      	--          | v1 - v0 | < VTolerance 
      	--          ====> |f (u1,v1) - f (u0,v0)| < Tolerance3D

  
  Copy (me)  returns mutable like me;
    	---Purpose: Creates a new object which is a copy of this Bezier surface.

  Init (me : mutable; Poles   :  HArray2OfPnt  from TColgp;
    	              Weights :  HArray2OfReal from TColStd) 
  
        ---Purpose : Set  poles  to  Poles,  weights to  Weights  (not
        --         copied). 
        --         Create the arrays of coefficients.  Poles
        --         and    Weights  are   assumed   to  have the  first
        --         coefficient 1.
        --         
  raises ConstructionError -- if nbpoles < 2 or nbpoles > MaDegree

  is static private;

  
  UpdateCoefficients(me : mutable; 
    	    	     U  : Real from Standard = 0.0;
    	    	     V  : Real from Standard = 0.0)
    	---Purpose: Recompute the coeficients.
  is static private;



fields

    urational : Boolean;
    vrational : Boolean;
    poles     : HArray2OfPnt  from TColgp;
    weights   : HArray2OfReal from TColStd;

    coeffs    : HArray2OfPnt  from TColgp;
    wcoeffs   : HArray2OfReal from TColStd;

    ucacheparameter : Real ;
    vcacheparameter : Real ;
  -- Parameters at which the Taylor expension is stored in 
  -- the cache  
    ucachespanlenght : Real ;
    vcachespanlenght : Real ;
  -- Always 1. for the moment.
    ucachespanindex : Integer ;
    vcachespanindex : Integer ;
  -- the span for which the cache is valid if 
  -- validcache is 1 
    validcache : Integer ;

  -- usefull to evaluate the parametric resolutions
    umaxderivinv  : Real from Standard;
    vmaxderivinv  : Real from Standard;
    maxderivinvok : Boolean from Standard;

end;