path: root/src/Geom/Geom_BezierCurve.cdl

-- File:	Geom_BezierCurve.cdl
-- Created:	Tue Mar  9 19:49:01 1993
-- Author:	Philippe DAUTRY
--		<fid@phylox>
-- Copyright:	 Matra Datavision 1993


class BezierCurve from Geom inherits BoundedCurve from Geom

        ---Purpose : Describes a rational or non-rational Bezier curve
    	-- - a non-rational Bezier curve is defined by a table of
    	--   poles (also called control points),
    	-- - a rational Bezier curve is defined by a table of
    	--   poles with varying weights.
    	--  These data are manipulated by two parallel arrays:
    	-- - the poles table, which is an array of gp_Pnt points, and
    	-- - the weights table, which is an array of reals.
    	-- The bounds of these arrays are 1 and "the number of "poles" of the curve.
    	-- The poles of the curve are "control points" used to deform the curve.
    	-- The first pole is the start point of the curve, and the
    	-- last pole is the end point of the curve. The segment
    	-- that joins the first pole to the second pole is the
    	-- tangent to the curve at its start point, and the
    	-- segment that joins the last pole to the
    	-- second-from-last pole is the tangent to the curve at its end point.
    	-- It is more difficult to give a geometric signification to
    	-- the weights but they are useful for providing the exact
    	-- representations of arcs of a circle or ellipse.
    	-- Moreover, if the weights of all poles are equal, the
    	-- curve is polynomial; it is therefore a non-rational
    	-- curve. The non-rational curve is a special and
    	-- frequently used case. The weights are defined and
    	-- used only in the case of a rational curve.
    	-- The degree of a Bezier curve is equal to the number
    	-- of poles, minus 1. It must be greater than or equal to
    	-- 1. However, the degree of a Geom_BezierCurve
    	-- curve is limited to a value (25) which is defined and
    	-- controlled by the system. This value is returned by the function MaxDegree.
    	-- The parameter range for a Bezier curve is [ 0, 1 ].
    	-- If the first and last control points of the Bezier curve
    	-- are the same point then the curve is closed. For
    	-- example, to create a closed Bezier curve with four
    	-- control points, you have to give the set of control
    	-- points P1, P2, P3 and P1.
    	-- The continuity of a Bezier curve is infinite.
    	-- It is not possible to build a Bezier curve with negative
    	-- weights. We consider that a weight value is zero if it
    	-- is less than or equal to gp::Resolution(). We
    	-- also consider that two weight values W1 and W2 are equal if:
    	-- |W2 - W1| <= gp::Resolution().
    	--   Warning
    	-- - When considering the continuity of a closed Bezier
    	--   curve at the junction point, remember that a curve
    	--   of this type is never periodic. This means that the
    	--   derivatives for the parameter u = 0 have no
    	--   reason to be the same as the derivatives for the
    	--   parameter u = 1 even if the curve is closed.
    	-- - The length of a Bezier curve can be null.
       


uses  Array1OfReal      from TColStd,
      HArray1OfReal     from TColStd,
      Array1OfPnt       from TColgp,
      Ax1               from gp, 
      Ax2               from gp,
      Pnt               from gp, 
      HArray1OfPnt      from TColgp, 
      Vec               from gp, 
      Trsf              from gp,
      Geometry          from Geom,
      Shape             from GeomAbs


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


is 

  Create (CurvePoles : Array1OfPnt from TColgp)
    returns mutable BezierCurve
        ---Purpose :  Creates a non rational Bezier curve with a set of poles 
        --         CurvePoles.  The weights are defaulted to all being 1.
    	--         Raises ConstructionError if the number of poles is greater than MaxDegree + 1
        --         or lower than 2.
     raises ConstructionError;
      


  Create (CurvePoles : Array1OfPnt from TColgp;
    	  PoleWeights : Array1OfReal from TColStd) 
     returns mutable BezierCurve
        ---Purpose :  Creates a rational Bezier curve with the set of poles
        --  CurvePoles and the set of weights  PoleWeights .
        --  If all the weights are identical the curve is considered 
        --  as non rational. Raises ConstructionError if 
        --  the number of poles is greater than  MaxDegree + 1 or lower
        --  than 2 or CurvePoles and CurveWeights have not the same length
        --  or one weight value is lower or equal to Resolution from package gp.
     raises ConstructionError;
       



  Increase (me : mutable; Degree : Integer)
        ---Purpose :  Increases the degree of a bezier curve. Degree is the new 
        --  degree of <me>. Raises ConstructionError 
    	--    if Degree is greater than MaxDegree or lower than 2 
        --  or lower than the initial degree of <me>.
     raises ConstructionError;
      

  InsertPoleAfter (me : mutable; Index : Integer; P : Pnt)
        ---Purpose :  Inserts a pole P after the pole of range Index.
        --  If the curve <me> is rational the weight value for the new 
        --  pole of range Index is 1.0.
     raises OutOfRange,
        ---Purpose : raised if Index is not in the range [1, NbPoles]
            ConstructionError;
        ---Purpose : 
        --  raised if the resulting number of poles is greater than 
        --  MaxDegree + 1.


  InsertPoleAfter (me : mutable; Index : Integer; P : Pnt; Weight : Real)
        ---Purpose :
        --  Inserts a pole with its weight in the set of poles after the
        --  pole of range Index. If the curve was non rational it can
        --  become rational if all the weights are not identical.
     raises OutOfRange,
        ---Purpose : Raised if Index is not in the range [1, NbPoles]
            ConstructionError;
        ---Purpose : 
        --  Raised if the resulting number of poles is greater than 
        --  MaxDegree + 1.
        --  Raised if Weight is lower or equal to Resolution from package gp.


  InsertPoleBefore (me : mutable; Index : Integer; P : Pnt)
        ---Purpose :  Inserts a pole P before the pole of range Index.
        --  If the curve <me> is rational the weight value for the new
        --  pole of range Index is 1.0.
     raises OutOfRange,
        ---Purpose : Raised if Index is not in the range [1, NbPoles]
            ConstructionError;
        ---Purpose : 
        --  Raised if the resulting number of poles is greater than 
        --  MaxDegree + 1.



  InsertPoleBefore (me : mutable; Index : Integer; P : Pnt; Weight : Real)
        ---Purpose :
        --  Inserts a pole with its weight in the set of poles after 
        --  the pole of range Index. If the curve was non rational it
        --  can become rational if all the weights are not identical.
     raises OutOfRange,
        ---Purpose : Raised if Index is not in the range [1, NbPoles]
            ConstructionError;
        ---Purpose : 
        --  Raised if the resulting number of poles is greater than 
        --  MaxDegree + 1.
        --  Raised if Weight is lower or equal to Resolution from 
        --  package gp.

  RemovePole (me : mutable; Index : Integer)
        ---Purpose : Removes the pole of range Index.
        --  If the curve was rational it can become non rational.
     raises OutOfRange,
        ---Purpose : Raised if Index is not in the range [1, NbPoles]
            ConstructionError;
        --- Purpose : Raised if Degree is lower than 2.


  Reverse (me : mutable);
        ---Purpose :
        --  Reverses the direction of parametrization of <me>
        --  Value (NewU) =  Value (1 - OldU)


  ReversedParameter(me; U : Real) returns Real;
	---Purpose: Returns the  parameter on the  reversed  curve for
	--          the point of parameter U on <me>.
	--          
	--          returns 1-U


  Segment (me : mutable; U1, U2 : Real);
        ---Purpose :
        --  Segments the curve between U1 and U2 which can be out
        --  of the bounds of the curve. The curve is oriented from U1
        --  to U2.
        --  The control points are modified, the first and the last point
        --  are not the same but the parametrization range is [0, 1] 
        --  else it could not be a Bezier curve.
        --  Warnings :
        --  Even if <me> is not closed it can become closed after the 
        --  segmentation for example if U1 or U2 are out of the bounds 
        --  of the curve <me> or if the curve makes loop.
        --  After the segmentation the length of a curve can be null.


  SetPole (me : mutable; Index : Integer; P : Pnt)
        ---Purpose :
        --  Substitutes the pole of range index with P.
        --  If the curve <me> is rational the weight of range Index 
        --  is not modified.
     raises OutOfRange;
        ---Purpose : raiseD if Index is not in the range [1, NbPoles]


  SetPole (me : mutable; Index : Integer; P : Pnt; Weight : Real)
        ---Purpose :
        --  Substitutes the pole and the weights of range Index.
        --  If the curve <me> is not rational it can become rational 
        --  if all the weights are not identical.
        --  If the curve was rational it can become non rational if
        --  all the weights are identical.
     raises OutOfRange,
        ---Purpose : Raised if Index is not in the range [1, NbPoles]
            ConstructionError;
        ---Purpose : Raised if Weight <= Resolution from package gp


  SetWeight (me : mutable; Index : Integer; Weight : Real)
        ---Purpose :
        --  Changes the weight of the pole of range Index.
        --  If the curve <me> is not rational it can become rational 
        --  if all the weights are not identical.
        --  If the curve was rational it can become non rational if
        --  all the weights are identical.
     raises OutOfRange,
        ---Purpose : Raised if Index is not in the range [1, NbPoles]
            ConstructionError;
        ---Purpose : Raised if Weight <= Resolution from package gp



  IsClosed (me)   returns Boolean;
        ---Purpose :
        --  Returns True if the distance between the first point 
        --  and the last point of the curve is lower or equal to
        --  the Resolution from package gp.


  IsCN (me; N : Integer)   returns Boolean;
        ---Purpose : Continuity of the curve, returns True. 


  IsPeriodic (me)   returns Boolean;
        ---Purpose : 
        --  Returns True if the parametrization of a curve is periodic.
        --  (P(u) = P(u + T) T = constante)


  IsRational (me)   returns Boolean;
        ---Purpose :
        --  Returns false if all the weights are identical. The tolerance
        --  criterion is Resolution from package gp.


  Continuity (me)   returns Shape from GeomAbs;
        ---Purpose :  a Bezier curve is CN


  Degree (me)   returns Integer;
        ---Purpose : Returns the polynomial degree of the curve.
        --  it is the number of poles - 1




        ---Purpose : point P and derivatives (V1, V2, V3) computation
        --  The Bezier Curve has a Polynomial representation so the 
        --  parameter U can be out of the bounds of the curve.


  D0 (me; U : Real; P : out Pnt);

  D1 (me; U : Real; P : out Pnt; V1 : out Vec);

  D2 (me; U : Real; P : out Pnt; V1, V2 : out Vec);

  D3 (me; U : Real; P : out Pnt; V1, V2, V3 : out Vec);
    	---Purpose: For this Bezier curve, computes
    	-- - the point P of parameter U, or
    	-- - the point P and one or more of the following values:
    	--   - V1, the first derivative vector,
    	--   - V2, the second derivative vector,
    	--   - V3, the third derivative vector.
    	-- Note: the parameter U can be outside the bounds of the curve.
        
  DN (me; U : Real; N : Integer)  returns Vec
        ---Purpose : For the point of parameter U of this Bezier curve,
    	-- computes the vector corresponding to the Nth derivative.
    	-- Note: the parameter U can be outside the bounds of the curve.
    	-- Exceptions Standard_RangeError if N is less than 1.
     raises RangeError;


  StartPoint (me)  returns Pnt;
        ---Purpose: Returns Value (U=0.), it is the first control point of the curve.


  EndPoint (me) returns Pnt;
        ---Purpose: Returns Value (U=1.), it is the last control point of the Bezier curve.


  FirstParameter (me) returns Real;
        ---Purpose : Returns the value of the first  parameter of this
    	-- Bezier curve. This is 0.0, which gives the start point of this Bezier curve


  LastParameter (me) returns Real;
        ---Purpose : Returns the value of the last parameter of this
    	-- Bezier curve. This is  1.0, which gives the end point of this Bezier curve.


  NbPoles (me)  returns Integer;
    	---Purpose: Returns the number of poles of this Bezier curve.

  Pole (me; Index : Integer) returns Pnt
        ---Purpose : Returns the pole of range Index.
     raises OutOfRange;
        ---Purpose : Raised if Index is not in the range [1, NbPoles]


  Poles (me; P : out Array1OfPnt from TColgp)
        ---Purpose : Returns all the poles of the curve.
     raises DimensionError;
        ---Purpose : 
        --  Raised if the length of P is not equal to the number of poles.


  Weight (me; Index : Integer)   returns Real  
        ---Purpose : Returns the weight of range Index.
     raises OutOfRange;
        ---Purpose : Raised if Index is not in the range [1, NbPoles]


  Weights (me; W : out Array1OfReal from TColStd)
        ---Purpose : Returns all the weights of the curve.
     raises DimensionError;
        ---Purpose : 
        --  Raised if the length of W is not equal to the number of poles.
        



  Transform (me : mutable; T : Trsf);

    	---Purpose: Applies the transformation T to this Bezier curve.
	     

  MaxDegree (myclass)   returns Integer;
        ---Purpose :
        --  Returns the value of the maximum polynomial degree
    	-- of any Geom_BezierCurve curve. This value is 25.


  Resolution(me          : mutable; 
             Tolerance3D : Real;
             UTolerance  : out Real);
	---Purpose:  Computes for this Bezier curve the parametric
    	-- tolerance UTolerance for a given 3D tolerance Tolerance3D.
    	-- If f(t) is the equation of this Bezier curve,
    	-- UTolerance ensures that:
    	-- |t1-t0| < UTolerance ===> |f(t1)-f(t0)| < Tolerance3D

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

  Init (me : mutable; Poles   :  HArray1OfPnt  from TColgp;
    	              Weights :  HArray1OfReal from TColStd) 
  
        ---Purpose : Set  poles  to  Poles,  weights to  Weights  (not
        --         copied). If Weights is   null  the  curve is    non
        --         rational. Create the arrays of coefficients.  Poles
        --         and    Weights  are   assumed   to  have the  first
        --         coefficient 1.
        --         Update rational and closed.
        --         
  raises ConstructionError -- if nbpoles < 2 or nbboles > MaDegree + 1

  is static private;

  CoefficientsOK(me; U : Real) returns Boolean
  
        ---Purpose : returns true if the coefficients have been
        --           computed with the right value of cacheparameter
        --           for the given U value.
        -- 
        is static private;
  
  UpdateCoefficients(me : mutable; U : Real from Standard = 0.0)
    	---Purpose: Recompute the coeficients.
  is static private;



fields

   rational : Boolean;
   closed   : Boolean;
   poles    : HArray1OfPnt  from TColgp;
   weights  : HArray1OfReal from TColStd;

   coeffs   : HArray1OfPnt  from TColgp;
   wcoeffs  : HArray1OfReal from TColStd;
   -- computed at parametercache. 

   validcache      : Integer;
   -- = 1 the cache is valid 
   -- = 0 the cache is invalid
   parametercache    : Real;
   -- Parameter at which the Taylor expension is stored in 
   -- the cache, often 0., sometimes 1..
   spanlenghtcache   : Real;
   -- always 1. for the moment.

   -- usefull to evaluate the parametric resolution
   maxderivinv   : Real from Standard;
   maxderivinvok : Boolean from Standard;

end;