Describes a sphere. A sphere is defined by its radius, and is positioned in space by a coordinate system (a gp_Ax3 object), the origin of which is the center of the sphere. This coordinate system is the "local coordinate system" of the sphere. The following apply: More...
#include <Geom_SphericalSurface.hxx>
Public Member Functions | |
| Geom_SphericalSurface (const gp_Ax3 &A3, const Standard_Real Radius) | |
| A3 is the local coordinate system of the surface. At the creation the parametrization of the surface is defined such as the normal Vector (N = D1U ^ D1V) is directed away from the center of the sphere. The direction of increasing parametric value V is defined by the rotation around the "YDirection" of A2 in the trigonometric sense and the orientation of increasing parametric value U is defined by the rotation around the main direction of A2 in the trigonometric sense. Warnings : It is not forbidden to create a spherical surface with Radius = 0.0 Raised if Radius < 0.0. More... | |
| Geom_SphericalSurface (const gp_Sphere &S) | |
| Creates a SphericalSurface from a non persistent Sphere from package gp. More... | |
| void | SetRadius (const Standard_Real R) |
| Assigns the value R to the radius of this sphere. Exceptions Standard_ConstructionError if R is less than 0.0. More... | |
| void | SetSphere (const gp_Sphere &S) |
| Converts the gp_Sphere S into this sphere. More... | |
| gp_Sphere | Sphere () const |
| Returns a non persistent sphere with the same geometric properties as <me>. More... | |
| Standard_Real | UReversedParameter (const Standard_Real U) const override |
| Computes the u parameter on the modified surface, when reversing its u parametric direction, for any point of u parameter U on this sphere. In the case of a sphere, these functions returns 2.PI - U. More... | |
| Standard_Real | VReversedParameter (const Standard_Real V) const override |
| Computes the v parameter on the modified surface, when reversing its v parametric direction, for any point of v parameter V on this sphere. In the case of a sphere, these functions returns -U. More... | |
| Standard_Real | Area () const |
| Computes the aera of the spherical 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 sphere. For a sphere: U1 = 0, U2 = 2*PI, V1 = -PI/2, V2 = PI/2. More... | |
| void | Coefficients (Standard_Real &A1, Standard_Real &A2, Standard_Real &A3, Standard_Real &B1, Standard_Real &B2, Standard_Real &B3, Standard_Real &C1, Standard_Real &C2, Standard_Real &C3, Standard_Real &D) const |
| Returns the coefficients of the implicit equation of the quadric in the absolute cartesian coordinates system : These coefficients are normalized. A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + 2.(C1.X + C2.Y + C3.Z) + D = 0.0. More... | |
| Standard_Real | Radius () const |
| Computes the coefficients of the implicit equation of this quadric in the absolute Cartesian coordinate system: A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + 2.(C1.X + C2.Y + C3.Z) + D = 0.0 An implicit normalization is applied (i.e. A1 = A2 = 1. in the local coordinate system of this sphere). More... | |
| Standard_Real | Volume () const |
| Computes the volume of the spherical surface. More... | |
| Standard_Boolean | IsUClosed () const override |
| Returns True. More... | |
| Standard_Boolean | IsVClosed () const override |
| Returns False. More... | |
| Standard_Boolean | IsUPeriodic () const override |
| Returns True. More... | |
| Standard_Boolean | IsVPeriodic () const override |
| Returns False. More... | |
| Handle< Geom_Curve > | UIso (const Standard_Real U) const override |
| Computes the U isoparametric curve. The U isoparametric curves of the surface are defined by the section of the spherical surface with plane obtained by rotation of the plane (Location, XAxis, ZAxis) around ZAxis. This plane defines the origin of parametrization u. For a SphericalSurface the UIso curve is a Circle. Warnings : The radius of this circle can be zero. More... | |
| Handle< Geom_Curve > | VIso (const Standard_Real V) const override |
| Computes the V isoparametric curve. The V isoparametric curves of the surface are defined by the section of the spherical surface with plane parallel to the plane (Location, XAxis, YAxis). This plane defines the origin of parametrization V. Be careful if V is close to PI/2 or 3*PI/2 the radius of the circle becomes tiny. It is not forbidden in this toolkit to create circle with radius = 0.0 For a SphericalSurface the VIso curve is a Circle. Warnings : The radius of this circle can be zero. More... | |
| void | D0 (const Standard_Real U, const Standard_Real V, gp_Pnt &P) const override |
| Computes the point P (U, V) on the surface. P (U, V) = Loc + Radius * Sin (V) * Zdir + Radius * 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 override |
| 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 override |
| 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 override |
| 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 override |
| 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) override |
| Applies the transformation T to this sphere. More... | |
| Handle< Geom_Geometry > | Copy () const override |
| Creates a new object which is a copy of this sphere. 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 () override |
| Reverses the U parametric direction of the surface. More... | |
| virtual void | VReverse () override |
| Reverses the V parametric direction of the surface. More... | |
| GeomAbs_Shape | Continuity () const override |
| Returns GeomAbs_CN, the global continuity of any elementary surface. More... | |
| Standard_Boolean | IsCNu (const Standard_Integer N) const override |
| Returns True. More... | |
| Standard_Boolean | IsCNv (const Standard_Integer N) const override |
| 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 override |
| 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 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 non-const 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... | |
| Protected Attributes inherited from Geom_ElementarySurface | |
| gp_Ax3 | pos |
Detailed Description
Describes a sphere. A sphere is defined by its radius, and is positioned in space by a coordinate system (a gp_Ax3 object), the origin of which is the center of the sphere. This coordinate system is the "local coordinate system" of the sphere. The following apply:
- Rotation around its "main Axis", in the trigonometric sense given by the "X Direction" and the "Y Direction", defines the u parametric direction.
- Its "X Axis" gives the origin for the u parameter.
- The "reference meridian" of the sphere is a half-circle, of radius equal to the radius of the sphere. It is located in the plane defined by the origin, "X Direction" and "main Direction", centered on the origin, and positioned on the positive side of the "X Axis".
- Rotation around the "Y Axis" gives the v parameter on the reference meridian.
- The "X Axis" gives the origin of the v parameter on the reference meridian.
- The v parametric direction is oriented by the "main Direction", i.e. when v increases, the Z coordinate increases. (This implies that the "Y Direction" orients the reference meridian only when the local coordinate system is indirect.)
- The u isoparametric curve is a half-circle obtained by rotating the reference meridian of the sphere through an angle u around the "main Axis", in the trigonometric sense defined by the "X Direction" and the "Y Direction". The parametric equation of the sphere is: P(u,v) = O + R*cos(v)*(cos(u)*XDir + sin(u)*YDir)+R*sin(v)*ZDir where:
- O, XDir, YDir and ZDir are respectively the origin, the "X Direction", the "Y Direction" and the "Z Direction" of its local coordinate system, and
- R is the radius of the sphere. The parametric range of the two parameters is:
- [ 0, 2.*Pi ] for u, and
- [ - Pi/2., + Pi/2. ] for v.
Constructor & Destructor Documentation
| Geom_SphericalSurface::Geom_SphericalSurface | ( | const gp_Ax3 & | A3, |
| const Standard_Real | Radius | ||
| ) |
A3 is the local coordinate system of the surface. At the creation the parametrization of the surface is defined such as the normal Vector (N = D1U ^ D1V) is directed away from the center of the sphere. The direction of increasing parametric value V is defined by the rotation around the "YDirection" of A2 in the trigonometric sense and the orientation of increasing parametric value U is defined by the rotation around the main direction of A2 in the trigonometric sense. Warnings : It is not forbidden to create a spherical surface with Radius = 0.0 Raised if Radius < 0.0.
| Geom_SphericalSurface::Geom_SphericalSurface | ( | const gp_Sphere & | S | ) |
Creates a SphericalSurface from a non persistent Sphere from package gp.
Member Function Documentation
| Standard_Real Geom_SphericalSurface::Area | ( | ) | const |
Computes the aera of the spherical surface.
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overridevirtual |
Returns the parametric bounds U1, U2, V1 and V2 of this sphere. For a sphere: U1 = 0, U2 = 2*PI, V1 = -PI/2, V2 = PI/2.
Implements Geom_Surface.
| void Geom_SphericalSurface::Coefficients | ( | Standard_Real & | A1, |
| Standard_Real & | A2, | ||
| Standard_Real & | A3, | ||
| Standard_Real & | B1, | ||
| Standard_Real & | B2, | ||
| Standard_Real & | B3, | ||
| Standard_Real & | C1, | ||
| Standard_Real & | C2, | ||
| Standard_Real & | C3, | ||
| Standard_Real & | D | ||
| ) | const |
Returns the coefficients of the implicit equation of the quadric in the absolute cartesian coordinates system : These coefficients are normalized. A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + 2.(C1.X + C2.Y + C3.Z) + D = 0.0.
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overridevirtual |
Creates a new object which is a copy of this sphere.
Implements Geom_Geometry.
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overridevirtual |
Computes the point P (U, V) on the surface. P (U, V) = Loc + Radius * Sin (V) * Zdir + Radius * 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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overridevirtual |
Computes the current point and the first derivatives in the directions U and V.
Implements Geom_Surface.
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overridevirtual |
Computes the current point, the first and the second derivatives in the directions U and V.
Implements Geom_Surface.
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overridevirtual |
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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overridevirtual |
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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overridevirtual |
Returns True.
Implements Geom_Surface.
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overridevirtual |
Returns True.
Implements Geom_Surface.
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overridevirtual |
Returns False.
Implements Geom_Surface.
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overridevirtual |
Returns False.
Implements Geom_Surface.
| Standard_Real Geom_SphericalSurface::Radius | ( | ) | const |
Computes the coefficients of the implicit equation of this quadric in the absolute Cartesian coordinate system: A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) + 2.(C1.X + C2.Y + C3.Z) + D = 0.0 An implicit normalization is applied (i.e. A1 = A2 = 1. in the local coordinate system of this sphere).
| void Geom_SphericalSurface::SetRadius | ( | const Standard_Real | R | ) |
Assigns the value R to the radius of this sphere. Exceptions Standard_ConstructionError if R is less than 0.0.
| void Geom_SphericalSurface::SetSphere | ( | const gp_Sphere & | S | ) |
Converts the gp_Sphere S into this sphere.
| gp_Sphere Geom_SphericalSurface::Sphere | ( | ) | const |
Returns a non persistent sphere with the same geometric properties as <me>.
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overridevirtual |
Applies the transformation T to this sphere.
Implements Geom_Geometry.
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overridevirtual |
Computes the U isoparametric curve. The U isoparametric curves of the surface are defined by the section of the spherical surface with plane obtained by rotation of the plane (Location, XAxis, ZAxis) around ZAxis. This plane defines the origin of parametrization u. For a SphericalSurface the UIso curve is a Circle. Warnings : The radius of this circle can be zero.
Implements Geom_Surface.
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overridevirtual |
Computes the u parameter on the modified surface, when reversing its u parametric direction, for any point of u parameter U on this sphere. In the case of a sphere, these functions returns 2.PI - U.
Implements Geom_ElementarySurface.
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overridevirtual |
Computes the V isoparametric curve. The V isoparametric curves of the surface are defined by the section of the spherical surface with plane parallel to the plane (Location, XAxis, YAxis). This plane defines the origin of parametrization V. Be careful if V is close to PI/2 or 3*PI/2 the radius of the circle becomes tiny. It is not forbidden in this toolkit to create circle with radius = 0.0 For a SphericalSurface the VIso curve is a Circle. Warnings : The radius of this circle can be zero.
Implements Geom_Surface.
| Standard_Real Geom_SphericalSurface::Volume | ( | ) | const |
Computes the volume of the spherical surface.
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overridevirtual |
Computes the v parameter on the modified surface, when reversing its v parametric direction, for any point of v parameter V on this sphere. In the case of a sphere, these functions returns -U.
Implements Geom_ElementarySurface.
The documentation for this class was generated from the following file:
