Open CASCADE Technology
6.9.0
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Describes a torus. A torus is defined by its major and minor radii, and positioned in space with a coordinate system (a gp_Ax3 object) as follows: More...
#include <Geom_ToroidalSurface.hxx>
Public Member Functions | |
Geom_ToroidalSurface (const gp_Ax3 &A3, const Standard_Real MajorRadius, const Standard_Real MinorRadius) | |
A3 is the local coordinate system of the surface. The orientation of increasing V parametric value is defined by the rotation around the main axis (ZAxis) in the trigonometric sense. The parametrization of the surface in the U direction is defined such as the normal Vector (N = D1U ^ D1V) is oriented towards the "outside region" of the surface. Warnings : It is not forbidden to create a toroidal surface with MajorRadius = MinorRadius = 0.0. More... | |
Geom_ToroidalSurface (const gp_Torus &T) | |
Creates a ToroidalSurface from a non transient Torus from package gp. More... | |
void | SetMajorRadius (const Standard_Real MajorRadius) |
Modifies this torus by changing its major radius. Exceptions Standard_ConstructionError if: More... | |
void | SetMinorRadius (const Standard_Real MinorRadius) |
Modifies this torus by changing its minor radius. Exceptions Standard_ConstructionError if: More... | |
void | SetTorus (const gp_Torus &T) |
Converts the gp_Torus torus T into this torus. More... | |
gp_Torus | Torus () const |
Returns the non transient torus with the same geometric properties as <me>. More... | |
Standard_Real | UReversedParameter (const Standard_Real U) const |
Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U. More... | |
Standard_Real | VReversedParameter (const Standard_Real U) const |
Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U. More... | |
Standard_Real | Area () const |
Computes the aera of the surface. 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 torus. For a torus: U1 = V1 = 0 and V1 = V2 = 2*PI . More... | |
void | Coefficients (TColStd_Array1OfReal &Coef) const |
Returns the coefficients of the implicit equation of the surface in the absolute cartesian coordinate system : Coef(1) * X**4 + Coef(2) * Y**4 + Coef(3) * Z**4 + Coef(4) * X**3 * Y + Coef(5) * X**3 * Z + Coef(6) * Y**3 * X + Coef(7) * Y**3 * Z + Coef(8) * Z**3 * X + Coef(9) * Z**3 * Y + Coef(10) * X**2 * Y**2 + Coef(11) * X**2 * Z**2 + Coef(12) * Y**2 * Z**2 + Coef(13) * X**3 + Coef(14) * Y**3 + Coef(15) * Z**3 + Coef(16) * X**2 * Y + Coef(17) * X**2 * Z + Coef(18) * Y**2 * X + Coef(19) * Y**2 * Z + Coef(20) * Z**2 * X + Coef(21) * Z**2 * Y + Coef(22) * X**2 + Coef(23) * Y**2 + Coef(24) * Z**2 + Coef(25) * X * Y + Coef(26) * X * Z + Coef(27) * Y * Z + Coef(28) * X + Coef(29) * Y + Coef(30) * Z + Coef(31) = 0.0 Raised if the length of Coef is lower than 31. More... | |
Standard_Real | MajorRadius () const |
Returns the major radius, or the minor radius, of this torus. More... | |
Standard_Real | MinorRadius () const |
Returns the major radius, or the minor radius, of this torus. More... | |
Standard_Real | Volume () const |
Computes the volume. More... | |
Standard_Boolean | IsUClosed () const |
Returns True. More... | |
Standard_Boolean | IsVClosed () const |
Returns True. More... | |
Standard_Boolean | IsUPeriodic () const |
Returns True. More... | |
Standard_Boolean | IsVPeriodic () const |
Returns True. More... | |
Handle< Geom_Curve > | UIso (const Standard_Real U) const |
Computes the U isoparametric curve. More... | |
Handle< Geom_Curve > | VIso (const Standard_Real V) const |
Computes the V isoparametric curve. More... | |
void | D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const |
Computes the point P (U, V) on the surface. P (U, V) = Loc + MinorRadius * Sin (V) * Zdir + (MajorRadius + MinorRadius * Cos(V)) * (cos (U) * XDir + sin (U) * YDir) where Loc is the origin of the placement plane (XAxis, YAxis) XDir is the direction of the XAxis and YDir the direction of the YAxis and ZDir the direction of the ZAxis. More... | |
void | D1 (const Standard_Real U, const Standard_Real V, gp_Pnt &P, gp_Vec &D1U, gp_Vec &D1V) const |
Computes the current point and the first derivatives in the directions U and V. 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 current point, the first and the second derivatives in the directions U and V. 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 the current point, the first,the second and the third derivatives in the directions U and V. 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 direction u and Nv in the direction v. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0. More... | |
void | Transform (const gp_Trsf &T) |
Applies the transformation T to this torus. More... | |
Handle< Geom_Geometry > | Copy () const |
Creates a new object which is a copy of this torus. More... | |
Public Member Functions inherited from Geom_ElementarySurface | |
void | SetAxis (const gp_Ax1 &A1) |
Changes the main axis (ZAxis) of the elementary surface. More... | |
void | SetLocation (const gp_Pnt &Loc) |
Changes the location of the local coordinates system of the surface. More... | |
void | SetPosition (const gp_Ax3 &A3) |
Changes the local coordinates system of the surface. More... | |
gp_Ax1 | Axis () const |
Returns the main axis of the surface (ZAxis). More... | |
gp_Pnt | Location () const |
Returns the location point of the local coordinate system of the surface. More... | |
const gp_Ax3 & | Position () const |
Returns the local coordinates system of the surface. More... | |
virtual void | UReverse () |
Reverses the U parametric direction of the surface. More... | |
virtual void | VReverse () |
Reverses the V parametric direction of the surface. More... | |
GeomAbs_Shape | Continuity () const |
Returns GeomAbs_CN, the global continuity of any elementary surface. More... | |
Standard_Boolean | IsCNu (const Standard_Integer N) const |
Returns True. More... | |
Standard_Boolean | IsCNv (const Standard_Integer N) const |
Returns True. 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... | |
Additional Inherited Members | |
Protected Attributes inherited from Geom_ElementarySurface | |
gp_Ax3 | pos |
Describes a torus. A torus is defined by its major and minor radii, and positioned in space with a coordinate system (a gp_Ax3 object) as follows:
Geom_ToroidalSurface::Geom_ToroidalSurface | ( | const gp_Ax3 & | A3, |
const Standard_Real | MajorRadius, | ||
const Standard_Real | MinorRadius | ||
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A3 is the local coordinate system of the surface. The orientation of increasing V parametric value is defined by the rotation around the main axis (ZAxis) in the trigonometric sense. The parametrization of the surface in the U direction is defined such as the normal Vector (N = D1U ^ D1V) is oriented towards the "outside region" of the surface. Warnings : It is not forbidden to create a toroidal surface with MajorRadius = MinorRadius = 0.0.
Raised if MinorRadius < 0.0 or if MajorRadius < 0.0
Geom_ToroidalSurface::Geom_ToroidalSurface | ( | const gp_Torus & | T | ) |
Creates a ToroidalSurface from a non transient Torus from package gp.
Standard_Real Geom_ToroidalSurface::Area | ( | ) | const |
Computes the aera of the surface.
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Returns the parametric bounds U1, U2, V1 and V2 of this torus. For a torus: U1 = V1 = 0 and V1 = V2 = 2*PI .
Implements Geom_Surface.
void Geom_ToroidalSurface::Coefficients | ( | TColStd_Array1OfReal & | Coef | ) | const |
Returns the coefficients of the implicit equation of the surface in the absolute cartesian coordinate system : Coef(1) * X**4 + Coef(2) * Y**4 + Coef(3) * Z**4 + Coef(4) * X**3 * Y + Coef(5) * X**3 * Z + Coef(6) * Y**3 * X + Coef(7) * Y**3 * Z + Coef(8) * Z**3 * X + Coef(9) * Z**3 * Y + Coef(10) * X**2 * Y**2 + Coef(11) * X**2 * Z**2 + Coef(12) * Y**2 * Z**2 + Coef(13) * X**3 + Coef(14) * Y**3 + Coef(15) * Z**3 + Coef(16) * X**2 * Y + Coef(17) * X**2 * Z + Coef(18) * Y**2 * X + Coef(19) * Y**2 * Z + Coef(20) * Z**2 * X + Coef(21) * Z**2 * Y + Coef(22) * X**2 + Coef(23) * Y**2 + Coef(24) * Z**2 + Coef(25) * X * Y + Coef(26) * X * Z + Coef(27) * Y * Z + Coef(28) * X + Coef(29) * Y + Coef(30) * Z + Coef(31) = 0.0 Raised if the length of Coef is lower than 31.
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Creates a new object which is a copy of this torus.
Implements Geom_Geometry.
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Computes the point P (U, V) on the surface. P (U, V) = Loc + MinorRadius * Sin (V) * Zdir + (MajorRadius + MinorRadius * Cos(V)) * (cos (U) * XDir + sin (U) * YDir) where Loc is the origin of the placement plane (XAxis, YAxis) XDir is the direction of the XAxis and YDir the direction of the YAxis and ZDir the direction of the ZAxis.
Implements Geom_Surface.
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Computes the current point and the first derivatives in the directions U and V.
Implements Geom_Surface.
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Computes the current point, the first and the second derivatives in the directions U and V.
Implements Geom_Surface.
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Computes the current point, the first,the second and the third derivatives in the directions U and V.
Implements Geom_Surface.
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Computes the derivative of order Nu in the direction u and Nv in the direction v. Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
Implements Geom_Surface.
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Returns True.
Implements Geom_Surface.
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Returns True.
Implements Geom_Surface.
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Returns True.
Implements Geom_Surface.
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Returns True.
Implements Geom_Surface.
Standard_Real Geom_ToroidalSurface::MajorRadius | ( | ) | const |
Returns the major radius, or the minor radius, of this torus.
Standard_Real Geom_ToroidalSurface::MinorRadius | ( | ) | const |
Returns the major radius, or the minor radius, of this torus.
void Geom_ToroidalSurface::SetMajorRadius | ( | const Standard_Real | MajorRadius | ) |
Modifies this torus by changing its major radius. Exceptions Standard_ConstructionError if:
void Geom_ToroidalSurface::SetMinorRadius | ( | const Standard_Real | MinorRadius | ) |
Modifies this torus by changing its minor radius. Exceptions Standard_ConstructionError if:
void Geom_ToroidalSurface::SetTorus | ( | const gp_Torus & | T | ) |
Converts the gp_Torus torus T into this torus.
gp_Torus Geom_ToroidalSurface::Torus | ( | ) | const |
Returns the non transient torus with the same geometric properties as <me>.
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Applies the transformation T to this torus.
Implements Geom_Geometry.
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Computes the U isoparametric curve.
For a toroidal surface the UIso curve is a circle. The center of the Uiso circle is at the distance MajorRadius from the location point of the toroidal surface. Warnings : The radius of the circle can be zero if for the surface MinorRadius = 0.0
Implements Geom_Surface.
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Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U.
Implements Geom_ElementarySurface.
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Computes the V isoparametric curve.
For a ToroidalSurface the VIso curve is a circle. The axis of the circle is the main axis (ZAxis) of the toroidal surface. Warnings : The radius of the circle can be zero if for the surface MajorRadius = MinorRadius
Implements Geom_Surface.
Standard_Real Geom_ToroidalSurface::Volume | ( | ) | const |
Computes the volume.
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Return the parameter on the Ureversed surface for the point of parameter U on <me>. Return 2.PI - U.
Implements Geom_ElementarySurface.