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Geom


Geom_Curve Class Reference

The abstract class Curve describes the common
behavior of curves in 3D space. The Geom package
provides numerous concrete classes of derived
curves, including lines, circles, conics, Bezier or
BSpline curves, etc.
The main characteristic of these curves is that they
are parameterized. The Geom_Curve class shows:
- how to work with the parametric equation of a curve
in order to calculate the point of parameter u,
together with the vector tangent and the derivative
vectors of order 2, 3,..., N at this point;
- how to obtain general information about the curve
(for example, level of continuity, closed
characteristics, periodicity, bounds of the parameter field);
- how the parameter changes when a geometric
transformation is applied to the curve or when the
orientation of the curve is inverted.
All curves must have a geometric continuity: a curve is
at least "C0". Generally, this property is checked at
the time of construction or when the curve is edited.
Where this is not the case, the documentation states so explicitly.
Warning
The Geom package does not prevent the
construction of curves with null length or curves which
self-intersect.
.

#include <Geom_Curve.hxx>

Inheritance diagram for Geom_Curve:

Inheritance graph
[legend]

Public Member Functions

virtual Standard_EXPORT void Reverse ()=0
 Changes the direction of parametrization of <me>.
The "FirstParameter" and the "LastParameter" are not changed
but the orientation of the curve is modified. If the curve
is bounded the StartPoint of the initial curve becomes the
EndPoint of the reversed curve and the EndPoint of the initial
curve becomes the StartPoint of the reversed curve.
.
virtual Standard_EXPORT Standard_Real ReversedParameter (const Standard_Real U) const =0
 Returns the parameter on the reversed curve for
the point of parameter U on <me>.

me->Reversed()->Value(me->ReversedParameter(U))

is the same point as

me->Value(U)
.
virtual Standard_EXPORT Standard_Real TransformedParameter (const Standard_Real U, const gp_Trsf &T) const
 Returns the parameter on the transformed curve for
the transform of the point of parameter U on <me>.

me->Transformed(T)->Value(me->TransformedParameter(U,T))

is the same point as

me->Value(U).Transformed(T)

This methods returns <u>

It can be redefined. For example on the Line.
.
virtual Standard_EXPORT Standard_Real ParametricTransformation (const gp_Trsf &T) const
 Returns a coefficient to compute the parameter on
the transformed curve for the transform of the
point on <me>.

Transformed(T)->Value(U * ParametricTransformation(T))

is the same point as

Value(U).Transformed(T)

This methods returns 1.

It can be redefined. For example on the Line.
.
Standard_EXPORT Handle_Geom_Curve Reversed () const
 Returns a copy of <me> reversed.
.
virtual Standard_EXPORT Standard_Real FirstParameter () const =0
 Returns the value of the first parameter.
Warnings :
It can be RealFirst from package Standard
if the curve is infinite
.
virtual Standard_EXPORT Standard_Real LastParameter () const =0
 Returns the value of the last parameter.
Warnings :
It can be RealLast from package Standard
if the curve is infinite
.
virtual Standard_EXPORT Standard_Boolean IsClosed () const =0
 Returns true if the curve is closed.
Some curves such as circle are always closed, others such as line
are never closed (by definition).
Some Curves such as OffsetCurve can be closed or not. These curves
are considered as closed if the distance between the first point
and the last point of the curve is lower or equal to the Resolution
from package gp wich is a fixed criterion independant of the
application.
.
virtual Standard_EXPORT Standard_Boolean IsPeriodic () const =0
 Is the parametrization of the curve periodic ?
It is possible only if the curve is closed and if the
following relation is satisfied :
for each parametric value U the distance between the point
P(u) and the point P (u + T) is lower or equal to Resolution
from package gp, T is the period and must be a constant.
There are three possibilities :
. the curve is never periodic by definition (SegmentLine)
. the curve is always periodic by definition (Circle)
. the curve can be defined as periodic (BSpline). In this case
a function SetPeriodic allows you to give the shape of the
curve. The general rule for this case is : if a curve can be
periodic or not the default periodicity set is non periodic
and you have to turn (explicitly) the curve into a periodic
curve if you want the curve to be periodic.
.
virtual Standard_EXPORT Standard_Real Period () const
 Returns the period of this curve.
Exceptions Standard_NoSuchObject if this curve is not periodic.
.
virtual Standard_EXPORT GeomAbs_Shape Continuity () const =0
 It is the global continuity of the curve
C0 : only geometric continuity,
C1 : continuity of the first derivative all along the Curve,
C2 : continuity of the second derivative all along the Curve,
C3 : continuity of the third derivative all along the Curve,
G1 : tangency continuity all along the Curve,
G2 : curvature continuity all along the Curve,
CN : the order of continuity is infinite.
.
virtual Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const =0
 Returns true if the degree of continuity of this curve is at least N.
Exceptions - Standard_RangeError if N is less than 0.
.
virtual Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt &P) const =0
 Returns in P the point of parameter U.
If the curve is periodic then the returned point is P(U) with
U = Ustart + (U - Uend) where Ustart and Uend are the
parametric bounds of the curve.
Raised only for the "OffsetCurve" if it is not possible to
compute the current point. For example when the first
derivative on the basis curve and the offset direction
are parallel.
.
virtual Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const =0
 Returns the point P of parameter U and the first derivative V1.
//! Raised if the continuity of the curve is not C1.
.
virtual Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const =0
 Returns the point P of parameter U, the first and second
derivatives V1 and V2.
//! Raised if the continuity of the curve is not C2.
.
virtual Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const =0
 Returns the point P of parameter U, the first, the second
and the third derivative.
//! Raised if the continuity of the curve is not C3.
.
virtual Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Integer N) const =0
 The returned vector gives the value of the derivative for the
order of derivation N.
//! Raised if the continuity of the curve is not CN.

//! Raised if the derivative cannot be computed
easily. e.g. rational bspline and n > 3.
//! Raised if N < 1.
.
Standard_EXPORT gp_Pnt Value (const Standard_Real U) const
 Computes the point of parameter U on <me>.
If the curve is periodic then the returned point is P(U) with
U = Ustart + (U - Uend) where Ustart and Uend are the
parametric bounds of the curve.
it is implemented with D0.
Raised only for the "OffsetCurve" if it is not possible to
compute the current point. For example when the first
derivative on the basis curve and the offset direction are parallel.
.
Standard_EXPORT const Handle (Standard_Type)&DynamicType() const

Member Function Documentation

virtual Standard_EXPORT GeomAbs_Shape Geom_Curve::Continuity  )  const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Conic, Geom_Line, Geom_OffsetCurve, and Geom_TrimmedCurve.

virtual Standard_EXPORT void Geom_Curve::D0 const Standard_Real  U,
gp_Pnt &  P
const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT void Geom_Curve::D1 const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1
const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT void Geom_Curve::D2 const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1,
gp_Vec &  V2
const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT void Geom_Curve::D3 const Standard_Real  U,
gp_Pnt &  P,
gp_Vec &  V1,
gp_Vec &  V2,
gp_Vec &  V3
const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT gp_Vec Geom_Curve::DN const Standard_Real  U,
const Standard_Integer  N
const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT Standard_Real Geom_Curve::FirstParameter  )  const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

Standard_EXPORT const Geom_Curve::Handle Standard_Type   )  const
 

Reimplemented from Geom_Geometry.

Reimplemented in Geom_BezierCurve, Geom_BoundedCurve, Geom_BSplineCurve, Geom_Circle, Geom_Conic, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT Standard_Boolean Geom_Curve::IsClosed  )  const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT Standard_Boolean Geom_Curve::IsCN const Standard_Integer  N  )  const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Conic, Geom_Line, Geom_OffsetCurve, and Geom_TrimmedCurve.

virtual Standard_EXPORT Standard_Boolean Geom_Curve::IsPeriodic  )  const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT Standard_Real Geom_Curve::LastParameter  )  const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT Standard_Real Geom_Curve::ParametricTransformation const gp_Trsf &  T  )  const [virtual]
 

Reimplemented in Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT Standard_Real Geom_Curve::Period  )  const [virtual]
 

Reimplemented in Geom_OffsetCurve, and Geom_TrimmedCurve.

virtual Standard_EXPORT void Geom_Curve::Reverse  )  [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Conic, Geom_Line, Geom_OffsetCurve, and Geom_TrimmedCurve.

Standard_EXPORT Handle_Geom_Curve Geom_Curve::Reversed  )  const
 

virtual Standard_EXPORT Standard_Real Geom_Curve::ReversedParameter const Standard_Real  U  )  const [pure virtual]
 

Implemented in Geom_BezierCurve, Geom_BSplineCurve, Geom_Circle, Geom_Conic, Geom_Ellipse, Geom_Hyperbola, Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

virtual Standard_EXPORT Standard_Real Geom_Curve::TransformedParameter const Standard_Real  U,
const gp_Trsf &  T
const [virtual]
 

Reimplemented in Geom_Line, Geom_OffsetCurve, Geom_Parabola, and Geom_TrimmedCurve.

Standard_EXPORT gp_Pnt Geom_Curve::Value const Standard_Real  U  )  const
 


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