Describes a rational or non-rational Bezier surface. More...

#include <Geom_BezierSurface.hxx>

Inheritance diagram for Geom_BezierSurface:

[legend]

Public Member Functions
	Geom_BezierSurface (const TColgp_Array2OfPnt &SurfacePoles)
	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. More...

	Geom_BezierSurface (const TColgp_Array2OfPnt &SurfacePoles, const TColStd_Array2OfReal &PoleWeights)
	—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). More...

void	ExchangeUV ()
	Exchanges the direction U and V on a Bezier surface As a consequence: More...

void	Increase (const Standard_Integer UDeg, const Standard_Integer VDeg)
	Increases the degree of this Bezier surface in the two parametric directions. More...

void	InsertPoleColAfter (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles)
	Inserts a column of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1. More...

void	InsertPoleColAfter (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights)
	Inserts a column of poles and weights. If the surface was non-rational it can become rational. More...

void	InsertPoleColBefore (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles)
	Inserts a column of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1. More...

void	InsertPoleColBefore (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights)
	Inserts a column of poles and weights. If the surface was non-rational it can become rational. More...

void	InsertPoleRowAfter (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles)
	Inserts a row of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1. More...

void	InsertPoleRowAfter (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights)
	Inserts a row of poles and weights. If the surface was non-rational it can become rational. More...

void	InsertPoleRowBefore (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles)
	Inserts a row of poles. If the surface is rational the weights values associated with CPoles are equal defaulted to 1. More...

void	InsertPoleRowBefore (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights)
	Inserts a row of poles and weights. If the surface was non-rational it can become rational. More...

void	RemovePoleCol (const Standard_Integer VIndex)
	Removes a column of poles. If the surface was rational it can become non-rational. More...

void	RemovePoleRow (const Standard_Integer UIndex)
	Removes a row of poles. If the surface was rational it can become non-rational. More...

void	Segment (const Standard_Real U1, const Standard_Real U2, const Standard_Real V1, const Standard_Real V2)
	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. More...

void	SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt &P)
	Modifies a pole value. If the surface is rational the weight of range (UIndex, VIndex) is not modified. More...

void	SetPole (const Standard_Integer UIndex, const Standard_Integer VIndex, const gp_Pnt &P, const Standard_Real Weight)
	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. More...

void	SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles)
	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. Raised if VIndex < 1 or VIndex > NbVPoles. More...

void	SetPoleCol (const Standard_Integer VIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights)
	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. Raised if VIndex < 1 or VIndex > NbVPoles. More...

void	SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles)
	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. Raised if UIndex < 1 or UIndex > NbUPoles. More...

void	SetPoleRow (const Standard_Integer UIndex, const TColgp_Array1OfPnt &CPoles, const TColStd_Array1OfReal &CPoleWeights)
	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. Raised if UIndex < 1 or UIndex > NbUPoles. More...

void	SetWeight (const Standard_Integer UIndex, const Standard_Integer VIndex, const Standard_Real Weight)
	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. More...

void	SetWeightCol (const Standard_Integer VIndex, const TColStd_Array1OfReal &CPoleWeights)
	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. Raised if VIndex < 1 or VIndex > NbVPoles. More...

void	SetWeightRow (const Standard_Integer UIndex, const TColStd_Array1OfReal &CPoleWeights)
	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. Raised if UIndex < 1 or UIndex > NbUPoles. More...

void	UReverse ()
	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. More...

Standard_Real	UReversedParameter (const Standard_Real U) const
	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: More...

void	VReverse ()
	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. More...

Standard_Real	VReversedParameter (const Standard_Real V) const
	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: More...

void	Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const
	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. More...

GeomAbs_Shape	Continuity () const
	Returns the continuity of the surface CN : the order of continuity is infinite. More...

void	D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const
	Computes the point of parameter U,V on the surface. More...

void	D1 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const
	Computes the point P and the first derivatives in the directions U and V at this point. Raised if the continuity of the surface is not C1. More...

void	D2 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV) const
	Computes the point P, the first and the second derivatives in the directions U and V at this point. Raised if the continuity of the surface is not C2. More...

void	D3 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V, gp_Vec &D2U, gp_Vec &D2V, gp_Vec &D2UV, gp_Vec &D3U, gp_Vec &D3V, gp_Vec &D3UUV, gp_Vec &D3UVV) const
	Computes P, the point of parameters (U, V) of this Bezier surface, and. More...

gp_Vec	DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const
	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: More...

Standard_Integer	NbUPoles () const
	Returns the number of poles in the U direction. More...

Standard_Integer	NbVPoles () const
	Returns the number of poles in the V direction. More...

gp_Pnt	Pole (const Standard_Integer UIndex, const Standard_Integer VIndex) const
	Returns the pole of range UIndex, VIndex Raised if UIndex < 1 or UIndex > NbUPoles, or VIndex < 1 or VIndex > NbVPoles. More...

void	Poles (TColgp_Array2OfPnt &P) const
	Returns the poles of the Bezier surface. More...

Standard_Integer	UDegree () const
	Returns the degree of the surface in the U direction it is NbUPoles - 1. More...

Handle< Geom_Curve >	UIso (const Standard_Real U) const
	Computes the U isoparametric curve. For a Bezier surface the UIso curve is a Bezier curve. More...

Standard_Integer	VDegree () const
	Returns the degree of the surface in the V direction it is NbVPoles - 1. More...

Handle< Geom_Curve >	VIso (const Standard_Real V) const
	Computes the V isoparametric curve. For a Bezier surface the VIso curve is a Bezier curve. More...

Standard_Real	Weight (const Standard_Integer UIndex, const Standard_Integer VIndex) const
	Returns the weight of range UIndex, VIndex. More...

void	Weights (TColStd_Array2OfReal &W) const
	Returns the weights of the Bezier surface. More...

Standard_Boolean	IsUClosed () const
	Returns True if the first control points row and the last control points row are identical. The tolerance criterion is Resolution from package gp. More...

Standard_Boolean	IsVClosed () const
	Returns True if the first control points column and the last control points column are identical. The tolerance criterion is Resolution from package gp. More...

Standard_Boolean	IsCNu (const Standard_Integer N) const
	Returns True, a Bezier surface is always CN. More...

Standard_Boolean	IsCNv (const Standard_Integer N) const
	Returns True, a BezierSurface is always CN. More...

Standard_Boolean	IsUPeriodic () const
	Returns False. More...

Standard_Boolean	IsVPeriodic () const
	Returns False. More...

Standard_Boolean	IsURational () const
	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\|. More...

Standard_Boolean	IsVRational () const
	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\|. More...

void	Transform (const gp_Trsf &T)
	Applies the transformation T to this Bezier surface. More...

void	Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance, Standard_Real &VTolerance)
	Computes two tolerance values for this Bezier surface, based on the given tolerance in 3D space Tolerance3D. The tolerances computed are: More...

Handle< Geom_Geometry >	Copy () const
	Creates a new object which is a copy of this Bezier surface. More...

Public Member Functions inherited from Geom_Surface
Handle< Geom_Surface >	UReversed () const
	Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned. More...

Handle< Geom_Surface >	VReversed () const
	Reverses the V direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned. More...

virtual void	TransformParameters (Standard_Real &U, Standard_Real &V, const gp_Trsf &T) const
	Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>. More...

virtual gp_GTrsf2d	ParametricTransformation (const gp_Trsf &T) const
	Returns a 2d transformation used to find the new parameters of a point on the transformed surface. More...

virtual Standard_Real	UPeriod () const
	Returns the period of this surface in the u parametric direction. raises if the surface is not uperiodic. More...

virtual Standard_Real	VPeriod () const
	Returns the period of this surface in the v parametric direction. raises if the surface is not vperiodic. More...

gp_Pnt	Value (const Standard_Real U, const Standard_Real V) const
	Computes the point of parameter U on the surface. More...

Public Member Functions inherited from Geom_Geometry
void	Mirror (const gp_Pnt &P)
	Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry. More...

void	Mirror (const gp_Ax1 &A1)
	Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More...

void	Mirror (const gp_Ax2 &A2)
	Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection). More...

void	Rotate (const gp_Ax1 &A1, const Standard_Real Ang)
	Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians. More...

void	Scale (const gp_Pnt &P, const Standard_Real S)
	Scales a Geometry. S is the scaling value. More...

void	Translate (const gp_Vec &V)
	Translates a Geometry. V is the vector of the tanslation. More...

void	Translate (const gp_Pnt &P1, const gp_Pnt &P2)
	Translates a Geometry from the point P1 to the point P2. More...

Handle< Geom_Geometry >	Mirrored (const gp_Pnt &P) const

Handle< Geom_Geometry >	Mirrored (const gp_Ax1 &A1) const

Handle< Geom_Geometry >	Mirrored (const gp_Ax2 &A2) const

Handle< Geom_Geometry >	Rotated (const gp_Ax1 &A1, const Standard_Real Ang) const

Handle< Geom_Geometry >	Scaled (const gp_Pnt &P, const Standard_Real S) const

Handle< Geom_Geometry >	Transformed (const gp_Trsf &T) const

Handle< Geom_Geometry >	Translated (const gp_Vec &V) const

Handle< Geom_Geometry >	Translated (const gp_Pnt &P1, const gp_Pnt &P2) const

Public Member Functions inherited from MMgt_TShared
virtual void	Delete () const
	Memory deallocator for transient classes. More...

Public Member Functions inherited from Standard_Transient
	Standard_Transient ()
	Empty constructor. More...

	Standard_Transient (const Standard_Transient &)
	Copy constructor – does nothing. More...

Standard_Transient &	operator= (const Standard_Transient &)
	Assignment operator, needed to avoid copying reference counter. More...

virtual	~Standard_Transient ()
	Destructor must be virtual. More...

virtual const Handle_Standard_Type &	DynamicType () const
	Returns a type information object about this object. More...

Standard_Boolean	IsInstance (const Handle_Standard_Type &theType) const
	Returns a true value if this is an instance of Type. More...

Standard_Boolean	IsInstance (const Standard_CString theTypeName) const
	Returns a true value if this is an instance of TypeName. More...

Standard_Boolean	IsKind (const Handle_Standard_Type &theType) const
	Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...

Standard_Boolean	IsKind (const Standard_CString theTypeName) const
	Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More...

virtual Handle_Standard_Transient	This () const
	Returns a Handle which references this object. Must never be called to objects created in stack. More...

Standard_Integer	GetRefCount () const
	Get the reference counter of this object. More...

Static Public Member Functions
static Standard_Integer	MaxDegree ()
	Returns the value of the maximum polynomial degree of a Bezier surface. This value is 25. More...

Detailed Description

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()

Constructor & Destructor Documentation

Geom_BezierSurface::Geom_BezierSurface ( const TColgp_Array2OfPnt & SurfacePoles )

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.

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.

Geom_BezierSurface::Geom_BezierSurface	(	const TColgp_Array2OfPnt &	SurfacePoles,
		const TColStd_Array2OfReal &	PoleWeights
	)

—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).

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.

Member Function Documentation

void Geom_BezierSurface::Bounds	(	Standard_Real &	U1,
		Standard_Real &	U2,
		Standard_Real &	V1,
		Standard_Real &	V2
	)		const

virtual

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.

void Geom_BezierSurface::Increase	(	const Standard_Integer	UDeg,
		const Standard_Integer	VDeg
	)

void Geom_BezierSurface::InsertPoleColAfter	(	const Standard_Integer	VIndex,
		const TColgp_Array1OfPnt &	CPoles
	)

void Geom_BezierSurface::InsertPoleColBefore	(	const Standard_Integer	VIndex,
		const TColgp_Array1OfPnt &	CPoles
	)

void Geom_BezierSurface::InsertPoleRowAfter	(	const Standard_Integer	UIndex,
		const TColgp_Array1OfPnt &	CPoles
	)

void Geom_BezierSurface::InsertPoleRowBefore	(	const Standard_Integer	UIndex,
		const TColgp_Array1OfPnt &	CPoles
	)

gp_Pnt Geom_BezierSurface::Pole	(	const Standard_Integer	UIndex,
		const Standard_Integer	VIndex
	)		const

void Geom_BezierSurface::Resolution	(	const Standard_Real	Tolerance3D,
		Standard_Real &	UTolerance,
		Standard_Real &	VTolerance
	)

void Geom_BezierSurface::Segment	(	const Standard_Real	U1,
		const Standard_Real	U2,
		const Standard_Real	V1,
		const Standard_Real	V2
	)

void Geom_BezierSurface::SetPole	(	const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const gp_Pnt &	P
	)

void Geom_BezierSurface::SetPoleCol	(	const Standard_Integer	VIndex,
		const TColgp_Array1OfPnt &	CPoles
	)

void Geom_BezierSurface::SetPoleRow	(	const Standard_Integer	UIndex,
		const TColgp_Array1OfPnt &	CPoles
	)

void Geom_BezierSurface::SetWeight	(	const Standard_Integer	UIndex,
		const Standard_Integer	VIndex,
		const Standard_Real	Weight
	)

void Geom_BezierSurface::SetWeightCol	(	const Standard_Integer	VIndex,
		const TColStd_Array1OfReal &	CPoleWeights
	)

void Geom_BezierSurface::SetWeightRow	(	const Standard_Integer	UIndex,
		const TColStd_Array1OfReal &	CPoleWeights
	)

Standard_Real Geom_BezierSurface::Weight	(	const Standard_Integer	UIndex,
		const Standard_Integer	VIndex
	)		const

Geom_BezierSurface Class Reference

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation