Open CASCADE Technology  6.9.0
Public Member Functions

Geom_Surface Class Referenceabstract

Describes the common behavior of surfaces in 3D space. The Geom package provides many implementations of concrete derived surfaces, such as planes, cylinders, cones, spheres and tori, surfaces of linear extrusion, surfaces of revolution, Bezier and BSpline surfaces, and so on. The key characteristic of these surfaces is that they are parameterized. Geom_Surface demonstrates: More...

#include <Geom_Surface.hxx>

Inheritance diagram for Geom_Surface:
Inheritance graph
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Public Member Functions

virtual void UReverse ()=0
 Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified. More...
 
Handle< Geom_SurfaceUReversed () const
 Reverses the U direction of parametrization of <me>. The bounds of the surface are not modified. A copy of <me> is returned. More...
 
virtual Standard_Real UReversedParameter (const Standard_Real U) const =0
 Returns the parameter on the Ureversed surface for the point of parameter U on <me>. More...
 
virtual void VReverse ()=0
 Reverses the V direction of parametrization of <me>. The bounds of the surface are not modified. More...
 
Handle< Geom_SurfaceVReversed () 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 Standard_Real VReversedParameter (const Standard_Real V) const =0
 Returns the parameter on the Vreversed surface for the point of parameter V on <me>. 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 void Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const =0
 Returns the parametric bounds U1, U2, V1 and V2 of this surface. If the surface is infinite, this function can return a value equal to Precision::Infinite: instead of Standard_Real::LastReal. More...
 
virtual Standard_Boolean IsUClosed () const =0
 Checks whether this surface is closed in the u parametric direction. Returns true if, in the u parametric direction: taking uFirst and uLast as the parametric bounds in the u parametric direction, for each parameter v, the distance between the points P(uFirst, v) and P(uLast, v) is less than or equal to gp::Resolution(). More...
 
virtual Standard_Boolean IsVClosed () const =0
 Checks whether this surface is closed in the u parametric direction. Returns true if, in the v parametric direction: taking vFirst and vLast as the parametric bounds in the v parametric direction, for each parameter u, the distance between the points P(u, vFirst) and P(u, vLast) is less than or equal to gp::Resolution(). More...
 
virtual Standard_Boolean IsUPeriodic () const =0
 Checks if this surface is periodic in the u parametric direction. Returns true if: 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_Boolean IsVPeriodic () const =0
 Checks if this surface is periodic in the v parametric direction. Returns true if: 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...
 
virtual Handle< Geom_CurveUIso (const Standard_Real U) const =0
 Computes the U isoparametric curve. More...
 
virtual Handle< Geom_CurveVIso (const Standard_Real V) const =0
 Computes the V isoparametric curve. More...
 
virtual GeomAbs_Shape Continuity () const =0
 Returns the Global Continuity of the surface in direction U and V : 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, G1 : tangency continuity all along the surface, G2 : curvature continuity all along the surface, CN : the order of continuity is infinite. Example : If the surface is C1 in the V parametric direction and C2 in the U parametric direction Shape = C1. More...
 
virtual Standard_Boolean IsCNu (const Standard_Integer N) const =0
 Returns the order of continuity of the surface in the U parametric direction. Raised if N < 0. More...
 
virtual Standard_Boolean IsCNv (const Standard_Integer N) const =0
 Returns the order of continuity of the surface in the V parametric direction. Raised if N < 0. More...
 
virtual void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const =0
 Computes the point of parameter U,V on the surface. More...
 
virtual void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const =0
 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...
 
virtual 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 =0
 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...
 
virtual 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 =0
 Computes the point P, the first,the second and the third derivatives in the directions U and V at this point. Raised if the continuity of the surface is not C2. More...
 
virtual gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const =0
 —Purpose ; Computes the derivative of order Nu in the direction U and Nv in the direction V at the point P(U, V). 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...
 
virtual void Transform (const gp_Trsf &T)=0
 Transformation of a geometric object. This tansformation can be a translation, a rotation, a symmetry, a scaling or a complex transformation obtained by combination of the previous elementaries transformations. (see class Transformation of the package Geom). More...
 
Handle< Geom_GeometryMirrored (const gp_Pnt &P) const
 
Handle< Geom_GeometryMirrored (const gp_Ax1 &A1) const
 
Handle< Geom_GeometryMirrored (const gp_Ax2 &A2) const
 
Handle< Geom_GeometryRotated (const gp_Ax1 &A1, const Standard_Real Ang) const
 
Handle< Geom_GeometryScaled (const gp_Pnt &P, const Standard_Real S) const
 
Handle< Geom_GeometryTransformed (const gp_Trsf &T) const
 
Handle< Geom_GeometryTranslated (const gp_Vec &V) const
 
Handle< Geom_GeometryTranslated (const gp_Pnt &P1, const gp_Pnt &P2) const
 
virtual Handle< Geom_GeometryCopy () const =0
 Creates a new object which is a copy of this geometric object. More...
 
- 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_Transientoperator= (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...
 

Detailed Description

Describes the common behavior of surfaces in 3D space. The Geom package provides many implementations of concrete derived surfaces, such as planes, cylinders, cones, spheres and tori, surfaces of linear extrusion, surfaces of revolution, Bezier and BSpline surfaces, and so on. The key characteristic of these surfaces is that they are parameterized. Geom_Surface demonstrates:

Member Function Documentation

virtual void Geom_Surface::Bounds ( Standard_Real U1,
Standard_Real U2,
Standard_Real V1,
Standard_Real V2 
) const
pure virtual

Returns the parametric bounds U1, U2, V1 and V2 of this surface. If the surface is infinite, this function can return a value equal to Precision::Infinite: instead of Standard_Real::LastReal.

Implemented in Geom_BSplineSurface, Geom_BezierSurface, ShapeExtend_CompositeSurface, Geom_SurfaceOfRevolution, Geom_ConicalSurface, Geom_RectangularTrimmedSurface, Geom_Plane, Geom_ToroidalSurface, Geom_OffsetSurface, Geom_CylindricalSurface, Geom_SurfaceOfLinearExtrusion, Geom_SphericalSurface, and GeomPlate_Surface.

virtual GeomAbs_Shape Geom_Surface::Continuity ( ) const
pure virtual

Returns the Global Continuity of the surface in direction U and V : 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, G1 : tangency continuity all along the surface, G2 : curvature continuity all along the surface, CN : the order of continuity is infinite. Example : If the surface is C1 in the V parametric direction and C2 in the U parametric direction Shape = C1.

Implemented in Geom_BSplineSurface, Geom_BezierSurface, ShapeExtend_CompositeSurface, GeomPlate_Surface, Geom_RectangularTrimmedSurface, Geom_OffsetSurface, Geom_ElementarySurface, and Geom_SweptSurface.

virtual void Geom_Surface::D0 ( const Standard_Real  U,
const Standard_Real  V,
gp_Pnt P 
) const
pure virtual

Computes the point of parameter U,V on the surface.

Raised only for an "OffsetSurface" if it is not possible to compute the current point.

Implemented in Geom_BSplineSurface, Geom_BezierSurface, ShapeExtend_CompositeSurface, Geom_SurfaceOfRevolution, Geom_OffsetSurface, Geom_ConicalSurface, Geom_RectangularTrimmedSurface, GeomPlate_Surface, Geom_ToroidalSurface, Geom_SphericalSurface, Geom_Plane, Geom_CylindricalSurface, and Geom_SurfaceOfLinearExtrusion.

virtual void Geom_Surface::D1 ( const Standard_Real  U,
const Standard_Real  V,
gp_Pnt P,
gp_Vec D1U,
gp_Vec D1V 
) const
pure virtual

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.

Implemented in Geom_BSplineSurface, Geom_BezierSurface, Geom_SurfaceOfRevolution, ShapeExtend_CompositeSurface, Geom_OffsetSurface, Geom_ConicalSurface, Geom_RectangularTrimmedSurface, GeomPlate_Surface, Geom_ToroidalSurface, Geom_SphericalSurface, Geom_Plane, Geom_CylindricalSurface, and Geom_SurfaceOfLinearExtrusion.

virtual void Geom_Surface::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
pure virtual

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.

Implemented in Geom_BSplineSurface, Geom_BezierSurface, Geom_SurfaceOfRevolution, ShapeExtend_CompositeSurface, Geom_OffsetSurface, Geom_ConicalSurface, Geom_RectangularTrimmedSurface, GeomPlate_Surface, Geom_ToroidalSurface, Geom_SphericalSurface, Geom_Plane, Geom_CylindricalSurface, and Geom_SurfaceOfLinearExtrusion.

virtual void Geom_Surface::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
pure virtual

Computes the point P, the first,the second and the third derivatives in the directions U and V at this point. Raised if the continuity of the surface is not C2.

Implemented in Geom_BSplineSurface, Geom_BezierSurface, Geom_SurfaceOfRevolution, ShapeExtend_CompositeSurface, Geom_OffsetSurface, Geom_ConicalSurface, Geom_RectangularTrimmedSurface, GeomPlate_Surface, Geom_ToroidalSurface, Geom_SphericalSurface, Geom_Plane, Geom_CylindricalSurface, and Geom_SurfaceOfLinearExtrusion.

virtual gp_Vec Geom_Surface::DN ( const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  Nu,
const Standard_Integer  Nv 
) const
pure virtual

—Purpose ; Computes the derivative of order Nu in the direction U and Nv in the direction V at the point P(U, V).

Raised if the continuity of the surface is not CNu in the U direction or not CNv in the V direction. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.

Implemented in Geom_BSplineSurface, Geom_BezierSurface, Geom_SurfaceOfRevolution, Geom_OffsetSurface, ShapeExtend_CompositeSurface, Geom_ConicalSurface, Geom_RectangularTrimmedSurface, GeomPlate_Surface, Geom_ToroidalSurface, Geom_SphericalSurface, Geom_Plane, Geom_CylindricalSurface, and Geom_SurfaceOfLinearExtrusion.

virtual Standard_Boolean Geom_Surface::IsCNu ( const Standard_Integer  N) const
pure virtual
virtual Standard_Boolean Geom_Surface::IsCNv ( const Standard_Integer  N) const
pure virtual
virtual Standard_Boolean Geom_Surface::IsUClosed ( ) const
pure virtual

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

Implemented in Geom_BSplineSurface, Geom_BezierSurface, ShapeExtend_CompositeSurface, Geom_SurfaceOfRevolution, Geom_ConicalSurface, Geom_OffsetSurface, Geom_RectangularTrimmedSurface, Geom_ToroidalSurface, Geom_Plane, Geom_CylindricalSurface, Geom_SphericalSurface, Geom_SurfaceOfLinearExtrusion, and GeomPlate_Surface.

virtual Standard_Boolean Geom_Surface::IsUPeriodic ( ) const
pure virtual

Checks if this surface is periodic in the u parametric direction. Returns true if:

  • this surface is closed in the u parametric direction, and
  • there is a constant T such that the distance between the points P (u, v) and P (u + T, v) (or the points P (u, v) and P (u, v + T)) is less than or equal to gp::Resolution(). Note: T is the parametric period in the u parametric direction.

Implemented in Geom_BSplineSurface, Geom_BezierSurface, Geom_SurfaceOfRevolution, ShapeExtend_CompositeSurface, Geom_ConicalSurface, Geom_RectangularTrimmedSurface, Geom_OffsetSurface, Geom_ToroidalSurface, Geom_Plane, Geom_CylindricalSurface, Geom_SphericalSurface, GeomPlate_Surface, and Geom_SurfaceOfLinearExtrusion.

virtual Standard_Boolean Geom_Surface::IsVClosed ( ) const
pure virtual

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

Implemented in Geom_BSplineSurface, Geom_BezierSurface, ShapeExtend_CompositeSurface, Geom_SurfaceOfRevolution, Geom_ConicalSurface, Geom_OffsetSurface, Geom_RectangularTrimmedSurface, Geom_ToroidalSurface, Geom_Plane, Geom_CylindricalSurface, Geom_SphericalSurface, GeomPlate_Surface, and Geom_SurfaceOfLinearExtrusion.

virtual Standard_Boolean Geom_Surface::IsVPeriodic ( ) const
pure virtual

Checks if this surface is periodic in the v parametric direction. Returns true if:

  • this surface is closed in the v parametric direction, and
  • there is a constant T such that the distance between the points P (u, v) and P (u + T, v) (or the points P (u, v) and P (u, v + T)) is less than or equal to gp::Resolution(). Note: T is the parametric period in the v parametric direction.

Implemented in Geom_BSplineSurface, Geom_BezierSurface, Geom_SurfaceOfRevolution, ShapeExtend_CompositeSurface, Geom_ConicalSurface, Geom_RectangularTrimmedSurface, Geom_OffsetSurface, Geom_ToroidalSurface, GeomPlate_Surface, Geom_Plane, Geom_CylindricalSurface, Geom_SphericalSurface, and Geom_SurfaceOfLinearExtrusion.

virtual gp_GTrsf2d Geom_Surface::ParametricTransformation ( const gp_Trsf T) const
virtual

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 returns an identity transformation

It can be redefined. For example on the Plane, Cylinder, Cone, Revolved and Extruded surfaces.

Reimplemented in Geom_OffsetSurface, Geom_RectangularTrimmedSurface, Geom_SurfaceOfLinearExtrusion, Geom_SurfaceOfRevolution, Geom_ConicalSurface, Geom_Plane, Geom_CylindricalSurface, and GeomPlate_Surface.

virtual void Geom_Surface::TransformParameters ( Standard_Real U,
Standard_Real V,
const gp_Trsf T 
) const
virtual

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 does not change <U> and <V>

It can be redefined. For example on the Plane, Cylinder, Cone, Revolved and Extruded surfaces.

Reimplemented in Geom_OffsetSurface, Geom_RectangularTrimmedSurface, Geom_SurfaceOfLinearExtrusion, Geom_SurfaceOfRevolution, Geom_ConicalSurface, Geom_Plane, Geom_CylindricalSurface, and GeomPlate_Surface.

virtual Handle< Geom_Curve > Geom_Surface::UIso ( const Standard_Real  U) const
pure virtual
virtual Standard_Real Geom_Surface::UPeriod ( ) const
virtual

Returns the period of this surface in the u parametric direction. raises if the surface is not uperiodic.

Reimplemented in Geom_RectangularTrimmedSurface, Geom_OffsetSurface, and GeomPlate_Surface.

virtual void Geom_Surface::UReverse ( )
pure virtual
Handle< Geom_Surface > 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.

virtual Standard_Real Geom_Surface::UReversedParameter ( const Standard_Real  U) const
pure virtual

Returns the parameter on the Ureversed surface for the point of parameter U on <me>.

me->UReversed()->Value(me->UReversedParameter(U),V)

is the same point as

me->Value(U,V)

Implemented in Geom_BezierSurface, Geom_BSplineSurface, ShapeExtend_CompositeSurface, Geom_SurfaceOfRevolution, Geom_RectangularTrimmedSurface, Geom_ToroidalSurface, Geom_OffsetSurface, Geom_ConicalSurface, Geom_SphericalSurface, Geom_ElementarySurface, Geom_Plane, Geom_SurfaceOfLinearExtrusion, Geom_CylindricalSurface, and GeomPlate_Surface.

gp_Pnt Geom_Surface::Value ( const Standard_Real  U,
const Standard_Real  V 
) const

Computes the point of parameter U on the surface.

It is implemented with D0

Raised only for an "OffsetSurface" if it is not possible to compute the current point.

virtual Handle< Geom_Curve > Geom_Surface::VIso ( const Standard_Real  V) const
pure virtual
virtual Standard_Real Geom_Surface::VPeriod ( ) const
virtual

Returns the period of this surface in the v parametric direction. raises if the surface is not vperiodic.

Reimplemented in Geom_RectangularTrimmedSurface, Geom_OffsetSurface, and GeomPlate_Surface.

virtual void Geom_Surface::VReverse ( )
pure virtual
Handle< Geom_Surface > 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.

virtual Standard_Real Geom_Surface::VReversedParameter ( const Standard_Real  V) const
pure virtual

Returns the parameter on the Vreversed surface for the point of parameter V on <me>.

me->VReversed()->Value(U,me->VReversedParameter(V))

is the same point as

me->Value(U,V)

Implemented in Geom_BezierSurface, Geom_BSplineSurface, ShapeExtend_CompositeSurface, Geom_SurfaceOfRevolution, Geom_RectangularTrimmedSurface, Geom_ToroidalSurface, Geom_OffsetSurface, Geom_ConicalSurface, Geom_SurfaceOfLinearExtrusion, Geom_ElementarySurface, Geom_Plane, Geom_SphericalSurface, Geom_CylindricalSurface, and GeomPlate_Surface.


The documentation for this class was generated from the following file: