Open CASCADE Technology
7.2.0

Describes an offset surface in 3D space. An offset surface is defined by: More...
#include <Geom_OffsetSurface.hxx>
Public Member Functions  
Geom_OffsetSurface (const Handle< Geom_Surface > &S, const Standard_Real Offset, const Standard_Boolean isNotCheckC0=Standard_False)  
Constructs a surface offset from the basis surface S, where Offset is the distance between the offset surface and the basis surface at any point. A point on the offset surface is built by measuring the offset value along a normal vector at a point on S. This normal vector is given by the cross product D1u^D1v, where D1u and D1v are the vectors tangential to the basis surface in the u and v parametric directions at this point. The side of S on which the offset value is measured is indicated by this normal vector if Offset is positive, or is the inverse sense if Offset is negative. If isNotCheckC0 = TRUE checking if basis surface has C0continuity is not made. Warnings : More...  
void  SetBasisSurface (const Handle< Geom_Surface > &S, const Standard_Boolean isNotCheckC0=Standard_False) 
Raised if S is not at least C1. Warnings : No check is done to verify that a unique normal direction is defined at any point of the basis surface S. If isNotCheckC0 = TRUE checking if basis surface has C0continuity is not made. Exceptions Standard_ConstructionError if the surface S is not at least "C1" continuous. More...  
void  SetOffsetValue (const Standard_Real D) 
Changes this offset surface by assigning D as the offset value. More...  
Standard_Real  Offset () const 
Returns the offset value of this offset surface. More...  
const Handle< Geom_Surface > &  BasisSurface () const 
Returns the basis surface of this offset surface. Note: The basis surface can be an offset surface. More...  
const Handle< Geom_OsculatingSurface > &  OsculatingSurface () const 
Returns osculating surface if base surface is Bspline or Bezier. More...  
void  UReverse () override 
Changes the orientation of this offset surface in the u parametric direction. The bounds of the surface are not changed but the given parametric direction is reversed. More...  
Standard_Real  UReversedParameter (const Standard_Real U) const override 
Computes the u parameter on the modified surface, produced by reversing the u parametric direction of this offset surface, for any point of u parameter U on this offset surface. More...  
void  VReverse () override 
Changes the orientation of this offset surface in the v parametric direction. The bounds of the surface are not changed but the given parametric direction is reversed. More...  
Standard_Real  VReversedParameter (const Standard_Real V) const override 
Computes the v parameter on the modified surface, produced by reversing the or v parametric direction of this offset surface, for any point of v parameter V on this offset surface. More...  
void  Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const override 
Returns the parametric bounds U1, U2, V1 and V2 of this offset surface. If the surface is infinite, this function can return: More...  
GeomAbs_Shape  Continuity () const override 
This method returns the continuity of the basis surface  1. Continuity of the Offset surface : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Surface, C2 : continuity of the second derivative all along the Surface, C3 : continuity of the third derivative all along the Surface, CN : the order of continuity is infinite. Example : If the basis surface is C2 in the V direction and C3 in the U direction Shape = C1. Warnings : If the basis surface has a unique normal direction defined at any point this method gives the continuity of the offset surface otherwise the effective continuity can be lower than the continuity of the basis surface  1. More...  
Standard_Boolean  IsCNu (const Standard_Integer N) const override 
This method answer True if the continuity of the basis surface is N + 1 in the U parametric direction. We suppose in this class that a unique normal is defined at any point on the basis surface. Raised if N <0. More...  
Standard_Boolean  IsCNv (const Standard_Integer N) const override 
This method answer True if the continuity of the basis surface is N + 1 in the V parametric direction. We suppose in this class that a unique normal is defined at any point on the basis surface. Raised if N <0. More...  
Standard_Boolean  IsUClosed () const override 
Checks whether this offset surface is closed in the u parametric direction. Returns true if, taking uFirst and uLast as the parametric bounds in the u parametric direction, the distance between the points P(uFirst,v) and P(uLast,v) is less than or equal to gp::Resolution() for each value of the parameter v. More...  
Standard_Boolean  IsVClosed () const override 
Checks whether this offset surface is closed in the u or v parametric direction. Returns true if taking vFirst and vLast as the parametric bounds in the v parametric direction, the distance between the points P(u,vFirst) and P(u,vLast) is less than or equal to gp::Resolution() for each value of the parameter u. More...  
Standard_Boolean  IsUPeriodic () const override 
Returns true if this offset surface is periodic in the u parametric direction, i.e. if the basis surface of this offset surface is periodic in this direction. More...  
virtual Standard_Real  UPeriod () const override 
Returns the period of this offset surface in the u parametric direction respectively, i.e. the period of the basis surface of this offset surface in this parametric direction. raises if the surface is not uperiodic. More...  
Standard_Boolean  IsVPeriodic () const override 
Returns true if this offset surface is periodic in the v parametric direction, i.e. if the basis surface of this offset surface is periodic in this direction. More...  
virtual Standard_Real  VPeriod () const override 
Returns the period of this offset surface in the v parametric direction respectively, i.e. the period of the basis surface of this offset surface in this parametric direction. raises if the surface is not vperiodic. More...  
Handle< Geom_Curve >  UIso (const Standard_Real U) const override 
Computes the U isoparametric curve. More...  
Handle< Geom_Curve >  VIso (const Standard_Real V) const override 
Computes the V isoparametric curve. More...  
void  D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const override 
P (U, V) = Pbasis + Offset * Ndir where Ndir = D1Ubasis ^ D1Vbasis / D1Ubasis ^ D1Vbasis is the normal direction of the basis surface. Pbasis, D1Ubasis, D1Vbasis are the point and the first derivatives on the basis surface. If Ndir is undefined this method computes an approched normal direction using the following limited development : Ndir = N0 + DNdir/DU + DNdir/DV + Eps with Eps>0 which requires to compute the second derivatives on the basis surface. If the normal direction cannot be approximate for this order of derivation the exception UndefinedValue is raised. More...  
void  D1 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const override 
Raised if the continuity of the basis surface is not C2. 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 override 
—Purpose ; Raised if the continuity of the basis surface is not C3. 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 override 
Raised if the continuity of the basis surface is not C4. More...  
gp_Vec  DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const override 
Computes the derivative of order Nu in the direction u and Nv in the direction v. —Purpose ; Raised if the continuity of the basis surface is not CNu + 1 in the U direction and CNv + 1 in the V direction. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0. More...  
void  Transform (const gp_Trsf &T) override 
Applies the transformation T to this offset surface. Note: the basis surface is also modified. More...  
virtual void  TransformParameters (Standard_Real &U, Standard_Real &V, const gp_Trsf &T) const override 
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 override 
Returns a 2d transformation used to find the new parameters of a point on the transformed surface. More...  
Handle< Geom_Geometry >  Copy () const override 
Creates a new object which is a copy of this offset surface. More...  
Handle< Geom_Surface >  Surface () const 
returns an equivalent surface of the offset surface when the basis surface is a canonic surface or a rectangular limited surface on canonic surface or if the offset is null. More...  
Standard_Boolean  UOsculatingSurface (const Standard_Real U, const Standard_Real V, Standard_Boolean &IsOpposite, Handle< Geom_BSplineSurface > &UOsculSurf) const 
if Standard_True, L is the local osculating surface along U at the point U,V. It means that DL/DU is collinear to DS/DU . If IsOpposite == Standard_True these vectors have opposite direction. More...  
Standard_Boolean  VOsculatingSurface (const Standard_Real U, const Standard_Real V, Standard_Boolean &IsOpposite, Handle< Geom_BSplineSurface > &VOsculSurf) const 
if Standard_True, L is the local osculating surface along V at the point U,V. It means that DL/DV is collinear to DS/DV . If IsOpposite == Standard_True these vectors have opposite direction. More...  
GeomAbs_Shape  GetBasisSurfContinuity () const 
Returns continuity of the basis 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...  
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 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 void  Delete () const 
Memory deallocator for transient classes. More...  
virtual const opencascade::handle< Standard_Type > &  DynamicType () const 
Returns a type descriptor about this object. More...  
Standard_Boolean  IsInstance (const opencascade::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 opencascade::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...  
Standard_Transient *  This () const 
Returns nonconst pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero. More...  
Standard_Integer  GetRefCount () const 
Get the reference counter of this object. More...  
void  IncrementRefCounter () const 
Increments the reference counter of this object. More...  
Standard_Integer  DecrementRefCounter () const 
Decrements the reference counter of this object; returns the decremented value. More...  
Additional Inherited Members  
Public Types inherited from Standard_Transient  
typedef void  base_type 
Returns a type descriptor about this object. More...  
Static Public Member Functions inherited from Standard_Transient  
static const char *  get_type_name () 
Returns a type descriptor about this object. More...  
static const opencascade::handle< Standard_Type > &  get_type_descriptor () 
Returns type descriptor of Standard_Transient class. More...  
Describes an offset surface in 3D space. An offset surface is defined by:
Geom_OffsetSurface::Geom_OffsetSurface  (  const Handle< Geom_Surface > &  S, 
const Standard_Real  Offset,  
const Standard_Boolean  isNotCheckC0 = Standard_False 

) 
Constructs a surface offset from the basis surface S, where Offset is the distance between the offset surface and the basis surface at any point. A point on the offset surface is built by measuring the offset value along a normal vector at a point on S. This normal vector is given by the cross product D1u^D1v, where D1u and D1v are the vectors tangential to the basis surface in the u and v parametric directions at this point. The side of S on which the offset value is measured is indicated by this normal vector if Offset is positive, or is the inverse sense if Offset is negative. If isNotCheckC0 = TRUE checking if basis surface has C0continuity is not made. Warnings :

inline 
Returns the basis surface of this offset surface. Note: The basis surface can be an offset surface.

overridevirtual 
Returns the parametric bounds U1, U2, V1 and V2 of this offset surface. If the surface is infinite, this function can return:
Implements Geom_Surface.

overridevirtual 
This method returns the continuity of the basis surface  1. Continuity of the Offset surface : C0 : only geometric continuity, C1 : continuity of the first derivative all along the Surface, C2 : continuity of the second derivative all along the Surface, C3 : continuity of the third derivative all along the Surface, CN : the order of continuity is infinite. Example : If the basis surface is C2 in the V direction and C3 in the U direction Shape = C1. Warnings : If the basis surface has a unique normal direction defined at any point this method gives the continuity of the offset surface otherwise the effective continuity can be lower than the continuity of the basis surface  1.
Implements Geom_Surface.

overridevirtual 
Creates a new object which is a copy of this offset surface.
Implements Geom_Geometry.

overridevirtual 
P (U, V) = Pbasis + Offset * Ndir where Ndir = D1Ubasis ^ D1Vbasis / D1Ubasis ^ D1Vbasis is the normal direction of the basis surface. Pbasis, D1Ubasis, D1Vbasis are the point and the first derivatives on the basis surface. If Ndir is undefined this method computes an approched normal direction using the following limited development : Ndir = N0 + DNdir/DU + DNdir/DV + Eps with Eps>0 which requires to compute the second derivatives on the basis surface. If the normal direction cannot be approximate for this order of derivation the exception UndefinedValue is raised.
Raised if the continuity of the basis surface is not C1. Raised if the order of derivation required to compute the normal direction is greater than the second order.
Implements Geom_Surface.

overridevirtual 
Raised if the continuity of the basis surface is not C2.
Implements Geom_Surface.

overridevirtual 
—Purpose ; Raised if the continuity of the basis surface is not C3.
Implements Geom_Surface.

overridevirtual 
Raised if the continuity of the basis surface is not C4.
Implements Geom_Surface.

overridevirtual 
Computes the derivative of order Nu in the direction u and Nv in the direction v. —Purpose ; Raised if the continuity of the basis surface is not CNu + 1 in the U direction and CNv + 1 in the V direction. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
The following methods compute the value and derivatives on the offset surface and returns the derivatives on the basis surface too. The computation of the value and derivatives on the basis surface are used to evaluate the offset surface.
Warnings : The exception UndefinedValue or UndefinedDerivative is raised if it is not possible to compute a unique offset direction.
Implements Geom_Surface.

inline 
Returns continuity of the basis surface.

overridevirtual 
This method answer True if the continuity of the basis surface is N + 1 in the U parametric direction. We suppose in this class that a unique normal is defined at any point on the basis surface. Raised if N <0.
Implements Geom_Surface.

overridevirtual 
This method answer True if the continuity of the basis surface is N + 1 in the V parametric direction. We suppose in this class that a unique normal is defined at any point on the basis surface. Raised if N <0.
Implements Geom_Surface.

overridevirtual 
Checks whether this offset surface is closed in the u parametric direction. Returns true if, taking uFirst and uLast as the parametric bounds in the u parametric direction, the distance between the points P(uFirst,v) and P(uLast,v) is less than or equal to gp::Resolution() for each value of the parameter v.
Implements Geom_Surface.

overridevirtual 
Returns true if this offset surface is periodic in the u parametric direction, i.e. if the basis surface of this offset surface is periodic in this direction.
Implements Geom_Surface.

overridevirtual 
Checks whether this offset surface is closed in the u or v parametric direction. Returns true if taking vFirst and vLast as the parametric bounds in the v parametric direction, the distance between the points P(u,vFirst) and P(u,vLast) is less than or equal to gp::Resolution() for each value of the parameter u.
Implements Geom_Surface.

overridevirtual 
Returns true if this offset surface is periodic in the v parametric direction, i.e. if the basis surface of this offset surface is periodic in this direction.
Implements Geom_Surface.

inline 
Returns the offset value of this offset surface.

inline 
Returns osculating surface if base surface is Bspline or Bezier.

overridevirtual 
Returns a 2d transformation used to find the new parameters of a point on the transformed surface.
me>Transformed(T)>Value(U',V')
is the same point as
me>Value(U,V).Transformed(T)
Where U',V' are obtained by transforming U,V with th 2d transformation returned by
me>ParametricTransformation(T)
This methods calls the basis surface method.
Reimplemented from Geom_Surface.
void Geom_OffsetSurface::SetBasisSurface  (  const Handle< Geom_Surface > &  S, 
const Standard_Boolean  isNotCheckC0 = Standard_False 

) 
Raised if S is not at least C1. Warnings : No check is done to verify that a unique normal direction is defined at any point of the basis surface S. If isNotCheckC0 = TRUE checking if basis surface has C0continuity is not made. Exceptions Standard_ConstructionError if the surface S is not at least "C1" continuous.
void Geom_OffsetSurface::SetOffsetValue  (  const Standard_Real  D  ) 
Changes this offset surface by assigning D as the offset value.
Handle< Geom_Surface > Geom_OffsetSurface::Surface  (  )  const 
returns an equivalent surface of the offset surface when the basis surface is a canonic surface or a rectangular limited surface on canonic surface or if the offset is null.

overridevirtual 
Applies the transformation T to this offset surface. Note: the basis surface is also modified.
Implements Geom_Geometry.

overridevirtual 
Computes the parameters on the transformed surface for the transform of the point of parameters U,V on <me>.
me>Transformed(T)>Value(U',V')
is the same point as
me>Value(U,V).Transformed(T)
Where U',V' are the new values of U,V after calling
me>TranformParameters(U,V,T) This methods calls the basis surface method.
Reimplemented from Geom_Surface.

overridevirtual 
Computes the U isoparametric curve.
Implements Geom_Surface.
Standard_Boolean Geom_OffsetSurface::UOsculatingSurface  (  const Standard_Real  U, 
const Standard_Real  V,  
Standard_Boolean &  IsOpposite,  
Handle< Geom_BSplineSurface > &  UOsculSurf  
)  const 
if Standard_True, L is the local osculating surface along U at the point U,V. It means that DL/DU is collinear to DS/DU . If IsOpposite == Standard_True these vectors have opposite direction.

overridevirtual 
Returns the period of this offset surface in the u parametric direction respectively, i.e. the period of the basis surface of this offset surface in this parametric direction. raises if the surface is not uperiodic.
Reimplemented from Geom_Surface.

overridevirtual 
Changes the orientation of this offset surface in the u parametric direction. The bounds of the surface are not changed but the given parametric direction is reversed.
Implements Geom_Surface.

overridevirtual 
Computes the u parameter on the modified surface, produced by reversing the u parametric direction of this offset surface, for any point of u parameter U on this offset surface.
Implements Geom_Surface.

overridevirtual 
Computes the V isoparametric curve.
Te followings methods compute value and derivatives.
Warnings An exception is raised if a unique normal vector is not defined on the basis surface for the parametric value (U,V). No check is done at the creation time and we suppose in this package that the offset surface can be defined at any point.
Implements Geom_Surface.
Standard_Boolean Geom_OffsetSurface::VOsculatingSurface  (  const Standard_Real  U, 
const Standard_Real  V,  
Standard_Boolean &  IsOpposite,  
Handle< Geom_BSplineSurface > &  VOsculSurf  
)  const 
if Standard_True, L is the local osculating surface along V at the point U,V. It means that DL/DV is collinear to DS/DV . If IsOpposite == Standard_True these vectors have opposite direction.

overridevirtual 
Returns the period of this offset surface in the v parametric direction respectively, i.e. the period of the basis surface of this offset surface in this parametric direction. raises if the surface is not vperiodic.
Reimplemented from Geom_Surface.

overridevirtual 
Changes the orientation of this offset surface in the v parametric direction. The bounds of the surface are not changed but the given parametric direction is reversed.
Implements Geom_Surface.

overridevirtual 
Computes the v parameter on the modified surface, produced by reversing the or v parametric direction of this offset surface, for any point of v parameter V on this offset surface.
Implements Geom_Surface.