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Geom


Geom_ConicalSurface Class Reference

Describes a cone.
A cone is defined by the half-angle at its apex, and
is positioned in space by a coordinate system (a
gp_Ax3 object) and a reference radius as follows:
- The "main Axis" of the coordinate system is the
axis of revolution of the cone.
- The plane defined by the origin, the "X Direction"
and the "Y Direction" of the coordinate system is
the reference plane of the cone. The intersection
of the cone with this reference plane is a circle of
radius equal to the reference radius.
- The apex of the cone is on the negative side of
the "main Axis" of the coordinate system if the
half-angle is positive, and on the positive side if
the half-angle is negative.
This coordinate system is the "local coordinate <br> system" of the cone. 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.
- Its "main Direction" is the v parametric direction of the cone.
- Its origin is the origin of the v parameter.
The parametric range of the two parameters is:
- [ 0, 2.*Pi ] for u, and - ] -infinity, +infinity [ for v
The parametric equation of the cone is: P(u, v) =
O + (R + v*tan(Ang)) * (cos(u)*XDir + sin(u)*YDir) + v*ZDir where:
- O, XDir, YDir and ZDir are respectively
the origin, the "X Direction", the "Y Direction" and
the "Z Direction" of the cone's local coordinate system,
- Ang is the half-angle at the apex of the cone, and
- R is the reference radius.
.

#include <Geom_ConicalSurface.hxx>

Inheritance diagram for Geom_ConicalSurface:

Inheritance graph
[legend]

Public Member Functions

Standard_EXPORT Geom_ConicalSurface (const gp_Ax3 &A3, const Standard_Real Ang, const Standard_Real Radius)
 A3 defines the local coordinate system of the conical surface.
Ang is the conical surface semi-angle ]0, PI/2[.
Radius is the radius of the circle Viso in the placement plane
of the conical surface defined with "XAxis" and "YAxis".
The "ZDirection" of A3 defines the direction of the surface's
axis of symmetry.
If the location point of A3 is the apex of the surface
Radius = 0 .
At the creation the parametrization of the surface is defined
such that the normal Vector (N = D1U ^ D1V) is oriented towards
the "outside region" of the surface.
Raised if Radius < 0.0 or Ang < Resolution from gp or
Ang >= PI/ - Resolution
.
Standard_EXPORT Geom_ConicalSurface (const gp_Cone &C)
 Creates a ConicalSurface from a non transient Cone from
package gp.
.
Standard_EXPORT void SetCone (const gp_Cone &C)
 Set <me> so that <me> has the same geometric properties as C.
.
Standard_EXPORT void SetRadius (const Standard_Real R)
 Changes the radius of the conical surface in the placement
plane (Z = 0, V = 0). The local coordinate system is not
modified.
//! Raised if R < 0.0
.
Standard_EXPORT void SetSemiAngle (const Standard_Real Ang)
 Changes the semi angle of the conical surface.
Raised if Ang < Resolution or Ang >= PI/2 - Resolution
.
Standard_EXPORT gp_Cone Cone () const
 returns a non transient cone with the same geometric properties
as <me>.

Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const
 return 2.PI - U.

Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const
 Computes the u (or v) parameter on the modified
surface, when reversing its u (or v) parametric
direction, for any point of u parameter U (or of v
parameter V) on this cone.
In the case of a cone, these functions return respectively:
- 2.*Pi - U, -V.
.
virtual Standard_EXPORT void VReverse ()
 Changes the orientation of this cone in the v
parametric direction. The bounds of the surface are
not changed but the v parametric direction is reversed.
As a consequence, for a cone:
- the "main Direction" of the local coordinate system
is reversed, and
- the half-angle at the apex is inverted.
.
virtual Standard_EXPORT 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>.

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 multiplies V by T.ScaleFactor()
.
virtual Standard_EXPORT 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.

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 a scale centered on the
U axis with T.ScaleFactor
.
Standard_EXPORT gp_Pnt Apex () const
 Computes the apex of this cone. It is on the negative
side of the axis of revolution of this cone if the
half-angle at the apex is positive, and on the positive
side of the "main Axis" if the half-angle is negative.
.
Standard_EXPORT void Bounds (Standard_Real &U1, Standard_Real &U2, Standard_Real &V1, Standard_Real &V2) const
 The conical surface is infinite in the V direction so
V1 = Realfirst from Standard and V2 = RealLast.
U1 = 0 and U2 = 2*PI.
.
Standard_EXPORT 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 coordinate 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
.
Standard_EXPORT Standard_Real RefRadius () const
 Returns the reference radius of this cone.
The reference radius is the radius of the circle formed
by the intersection of this cone and its reference
plane (i.e. the plane defined by the origin, "X <br> Direction" and "Y Direction" of the local coordinate
system of this cone).
If the apex of this cone is on the origin of the local
coordinate system of this cone, the returned value is 0.
.
Standard_EXPORT Standard_Real SemiAngle () const
 returns the semi-angle of the conical surface ]0.0, PI/[.

Standard_EXPORT Standard_Boolean IsUClosed () const
 returns True.

Standard_EXPORT Standard_Boolean IsVClosed () const
 returns False.

Standard_EXPORT Standard_Boolean IsUPeriodic () const
 Returns True.
.
Standard_EXPORT Standard_Boolean IsVPeriodic () const
 Returns False.
.
Standard_EXPORT Handle_Geom_Curve UIso (const Standard_Real U) const
 Builds the U isoparametric line of this cone. The
origin of this line is on the reference plane of this
cone (i.e. the plane defined by the origin, "X Direction"
and "Y Direction" of the local coordinate system of this cone).
.
Standard_EXPORT Handle_Geom_Curve VIso (const Standard_Real V) const
 Builds the V isoparametric circle of this cone. It is the
circle on this cone, located in the plane of Z
coordinate V in the local coordinate system of this
cone. The "Axis" of this circle is the axis of revolution
of this cone. Its starting point is defined by the "X <br> Direction" of this cone.
Warning
If the V isoparametric circle is close to the apex of
this cone, the radius of the circle becomes very small.
It is possible to have a circle with radius equal to 0.0.
.
Standard_EXPORT 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 + (RefRadius + V * tan (Semi-Angle)) *
(cos (U) * XDir + sin (U) * YDir) + V * ZDir
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.
.
Standard_EXPORT 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.
.
Standard_EXPORT 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.
.
Standard_EXPORT 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.
.
Standard_EXPORT 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 cone.
Exceptions
Standard_RangeError if:
- Nu + Nv is less than 1,
- Nu or Nv is negative.
.
Standard_EXPORT void Transform (const gp_Trsf &T)
 Applies the transformation T to this cone.
.
Standard_EXPORT Handle_Geom_Geometry Copy () const
 Creates a new object which is a copy of this cone.
.
Standard_EXPORT const Handle (Standard_Type)&DynamicType() const

Private Attributes

Standard_Real radius
Standard_Real semiAngle

Constructor & Destructor Documentation

Standard_EXPORT Geom_ConicalSurface::Geom_ConicalSurface const gp_Ax3 &  A3,
const Standard_Real  Ang,
const Standard_Real  Radius
 

Standard_EXPORT Geom_ConicalSurface::Geom_ConicalSurface const gp_Cone &  C  ) 
 


Member Function Documentation

Standard_EXPORT gp_Pnt Geom_ConicalSurface::Apex  )  const
 

Standard_EXPORT void Geom_ConicalSurface::Bounds Standard_Real &  U1,
Standard_Real &  U2,
Standard_Real &  V1,
Standard_Real &  V2
const [virtual]
 

Implements Geom_Surface.

Standard_EXPORT void Geom_ConicalSurface::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
 

Standard_EXPORT gp_Cone Geom_ConicalSurface::Cone  )  const
 

Standard_EXPORT Handle_Geom_Geometry Geom_ConicalSurface::Copy  )  const [virtual]
 

Implements Geom_Geometry.

Standard_EXPORT void Geom_ConicalSurface::D0 const Standard_Real  U,
const Standard_Real  V,
gp_Pnt &  P
const [virtual]
 

Implements Geom_Surface.

Standard_EXPORT void Geom_ConicalSurface::D1 const Standard_Real  U,
const Standard_Real  V,
gp_Pnt &  P,
gp_Vec &  D1U,
gp_Vec &  D1V
const [virtual]
 

Implements Geom_Surface.

Standard_EXPORT void Geom_ConicalSurface::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 [virtual]
 

Implements Geom_Surface.

Standard_EXPORT void Geom_ConicalSurface::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 [virtual]
 

Implements Geom_Surface.

Standard_EXPORT gp_Vec Geom_ConicalSurface::DN const Standard_Real  U,
const Standard_Real  V,
const Standard_Integer  Nu,
const Standard_Integer  Nv
const [virtual]
 

Implements Geom_Surface.

Standard_EXPORT const Geom_ConicalSurface::Handle Standard_Type   )  const
 

Reimplemented from Geom_ElementarySurface.

Standard_EXPORT Standard_Boolean Geom_ConicalSurface::IsUClosed  )  const [virtual]
 

Implements Geom_Surface.

Standard_EXPORT Standard_Boolean Geom_ConicalSurface::IsUPeriodic  )  const [virtual]
 

Implements Geom_Surface.

Standard_EXPORT Standard_Boolean Geom_ConicalSurface::IsVClosed  )  const [virtual]
 

Implements Geom_Surface.

Standard_EXPORT Standard_Boolean Geom_ConicalSurface::IsVPeriodic  )  const [virtual]
 

Implements Geom_Surface.

virtual Standard_EXPORT gp_GTrsf2d Geom_ConicalSurface::ParametricTransformation const gp_Trsf &  T  )  const [virtual]
 

Reimplemented from Geom_Surface.

Standard_EXPORT Standard_Real Geom_ConicalSurface::RefRadius  )  const
 

Standard_EXPORT Standard_Real Geom_ConicalSurface::SemiAngle  )  const
 

Standard_EXPORT void Geom_ConicalSurface::SetCone const gp_Cone &  C  ) 
 

Standard_EXPORT void Geom_ConicalSurface::SetRadius const Standard_Real  R  ) 
 

Standard_EXPORT void Geom_ConicalSurface::SetSemiAngle const Standard_Real  Ang  ) 
 

Standard_EXPORT void Geom_ConicalSurface::Transform const gp_Trsf &  T  )  [virtual]
 

Implements Geom_Geometry.

virtual Standard_EXPORT void Geom_ConicalSurface::TransformParameters Standard_Real &  U,
Standard_Real &  V,
const gp_Trsf &  T
const [virtual]
 

Reimplemented from Geom_Surface.

Standard_EXPORT Handle_Geom_Curve Geom_ConicalSurface::UIso const Standard_Real  U  )  const [virtual]
 

Implements Geom_Surface.

Standard_EXPORT Standard_Real Geom_ConicalSurface::UReversedParameter const Standard_Real  U  )  const [virtual]
 

Implements Geom_ElementarySurface.

Standard_EXPORT Handle_Geom_Curve Geom_ConicalSurface::VIso const Standard_Real  V  )  const [virtual]
 

Implements Geom_Surface.

virtual Standard_EXPORT void Geom_ConicalSurface::VReverse  )  [virtual]
 

Reimplemented from Geom_ElementarySurface.

Standard_EXPORT Standard_Real Geom_ConicalSurface::VReversedParameter const Standard_Real  V  )  const [virtual]
 

Implements Geom_ElementarySurface.


Field Documentation

Standard_Real Geom_ConicalSurface::radius [private]
 

Standard_Real Geom_ConicalSurface::semiAngle [private]
 


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