Open CASCADE Technology 6.6.0
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This class implements the basis services for an offset curve
in 3D space. The Offset curve in this package can be a self
intersecting curve even if the basis curve does not
self-intersect. The self intersecting portions are not deleted
at the construction time.
An offset curve is a curve at constant distance (Offset) from
a basis curve in a reference direction V. The offset curve
takes its parametrization from the basis curve.
The Offset curve is in the direction of of the normal N
defined with the cross product V^T where the vector T
is given by the first derivative on the basis curve with
non zero length.
The distance offset may be positive or negative to indicate the
preferred side of the curve :
. distance offset >0 => the curve is in the direction of N
. distance offset >0 => the curve is in the direction of - N
On the Offset curve :
Value (U) = BasisCurve.Value(U) + (Offset * (T ^ V)) / ||T ^ V||
At any point the Offset direction V must not be parallel to the
vector T and the vector T must not have null length else the
offset curve is not defined. So the offset curve has not the
same continuity as the basis curve.
Warnings :
In this package we suppose that the continuity of the offset
curve is one degree less than the continuity of the basis
curve and we don't check that at any point ||T^V|| != 0.0
So to evaluate the curve it is better to check that the offset
curve is well defined at any point because an exception could
be raised. The check is not done in this package at the creation
of the offset curve because the control needs the use of an
algorithm which cannot be implemented in this package.
The OffsetCurve is closed if the first point and the last point
are the same (The distance between these two points is lower or
equal to the Resolution sea package gp) . The OffsetCurve can be
closed even if the basis curve is not closed.
#include <Geom_OffsetCurve.hxx>
Public Member Functions | |
Geom_OffsetCurve (const Handle< Geom_Curve > &C, const Standard_Real Offset, const gp_Dir &V) | |
C is the basis curve, Offset is the distance between <me> and the basis curve at any point. V defines the fixed reference direction (offset direction). If P is a point on the basis curve and T the first derivative with non zero length at this point, the corresponding point on the offset curve is in the direction of the vector-product N = V ^ T where N is a unitary vector. Warnings : In this package the entities are not shared. The OffsetCurve is built with a copy of the curve C. So when C is modified the OffsetCurve is not modified Raised if the basis curve C is not at least C1. Warnings : No check is done to know if ||V^T|| != 0.0 at any point. | |
void | Reverse () |
Changes the orientation of this offset curve. As a result: | |
Standard_Real | ReversedParameter (const Standard_Real U) const |
Computes the parameter on the reversed curve for the point of parameter U on this offset curve. | |
void | SetBasisCurve (const Handle< Geom_Curve > &C) |
Changes this offset curve by assigning C as the basis curve from which it is built. Exceptions Standard_ConstructionError if the curve C is not at least "C1" continuous. | |
void | SetDirection (const gp_Dir &V) |
Changes this offset curve by assigning V as the reference vector used to compute the offset direction. | |
void | SetOffsetValue (const Standard_Real D) |
Changes this offset curve by assigning D as the offset value. | |
Handle_Geom_Curve | BasisCurve () const |
Returns the basis curve of this offset curve. Note: The basis curve can be an offset curve. | |
GeomAbs_Shape | Continuity () const |
Returns the global continuity of this offset curve as a value of the GeomAbs_Shape enumeration. The degree of continuity of this offset curve is equal to the degree of continuity of the basis curve minus 1. Continuity of the Offset 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. Warnings : Returns the continuity of the basis curve - 1. The offset curve must have a unique offset direction defined at any point. | |
const gp_Dir & | Direction () const |
Returns the reference vector of this offset curve. //! Value and derivatives Warnings : The exception UndefinedValue or UndefinedDerivative is raised if it is not possible to compute a unique offset direction. If T is the first derivative with not null length and V the offset direction the relation ||T(U) ^ V|| != 0 must be satisfied to evaluate the offset curve. No check is done at the creation time and we suppose in this package that the offset curve is well defined. | |
void | D0 (const Standard_Real U, gp_Pnt &P) const |
Warning! this should not be called if the basis curve is not at least C1. Nevertheless if used on portion where the curve is C1, it is OK | |
void | D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const |
Warning! this should not be called if the continuity of the basis curve is not C2. Nevertheless, it's OK to use it on portion where the curve is C2 | |
void | D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const |
Warning! this should not be called if the continuity of the basis curve is not C3. Nevertheless, it's OK to use it on portion where the curve is C3 | |
void | D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const |
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. | |
gp_Vec | DN (const Standard_Real U, const Standard_Integer N) const |
The returned vector gives the value of the derivative for the order of derivation N. The following functions compute the value and derivatives on the offset curve and returns the derivatives on the basis curve too. The computation of the value and derivatives on the basis curve are used to evaluate the offset curve Warning: The exception UndefinedValue or UndefinedDerivative is raised if it is not possible to compute a unique offset direction. //! Raised if N < 1. | |
void | Value (const Standard_Real U, gp_Pnt &P, gp_Pnt &Pbasis, gp_Vec &V1basis) const |
Warning! this should not be called if the basis curve is not at least C1. Nevertheless if used on portion where the curve is C1, it is OK | |
void | D0 (const Standard_Real U, gp_Pnt &P, gp_Pnt &Pbasis, gp_Vec &V1basis) const |
Warning! this should not be called if the continuity of the basis curve is not C1. Nevertheless, it's OK to use it on portion where the curve is C1 | |
void | D1 (const Standard_Real U, gp_Pnt &P, gp_Pnt &Pbasis, gp_Vec &V1, gp_Vec &V1basis, gp_Vec &V2basis) const |
Warning! this should not be called if the continuity of the basis curve is not C1. Nevertheless, it's OK to use it on portion where the curve is C1 | |
void | D2 (const Standard_Real U, gp_Pnt &P, gp_Pnt &Pbasis, gp_Vec &V1, gp_Vec &V2, gp_Vec &V1basis, gp_Vec &V2basis, gp_Vec &V3basis) const |
Warning! this should not be called if the continuity of the basis curve is not C3. Nevertheless, it's OK to use it on portion where the curve is C3 | |
Standard_Real | FirstParameter () const |
Returns the value of the first parameter. Warnings : It can be RealFirst from package Standard if the curve is infinite | |
Standard_Real | LastParameter () const |
Returns the value of the first or last parameter of this offset curve. The first parameter corresponds to the start point of the curve. The last parameter corresponds to the end point. Note: the first and last parameters of this offset curve are also the ones of its basis curve. | |
Standard_Real | Offset () const |
Returns the offset value of this offset curve. | |
Standard_Boolean | IsClosed () const |
Returns True if the distance between the start point and the end point of the curve is lower or equal to Resolution from package gp. | |
Standard_Boolean | IsCN (const Standard_Integer N) const |
Returns true if the degree of continuity of the basis curve of this offset curve is at least N + 1. This method answer True if the continuity of the basis curve is N + 1. We suppose in this class that a normal direction to the basis curve (used to compute the offset curve) is defined at any point on the basis curve. //! Raised if N < 0. | |
Standard_Boolean | IsPeriodic () const |
Returns true if this offset curve is periodic, i.e. if the basis curve of this offset curve is periodic. | |
virtual Standard_Real | Period () const |
Returns the period of this offset curve, i.e. the period of the basis curve of this offset curve. Exceptions Standard_NoSuchObject if the basis curve is not periodic. | |
void | Transform (const gp_Trsf &T) |
Applies the transformation T to this offset curve. Note: the basis curve is also modified. | |
virtual 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 calls the basis curve method. | |
virtual 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 calls the basis curve method. | |
Handle_Geom_Geometry | Copy () const |
Creates a new object which is a copy of this offset curve. |
Geom_OffsetCurve::Geom_OffsetCurve | ( | const Handle< Geom_Curve > & | C, |
const Standard_Real | Offset, | ||
const gp_Dir & | V | ||
) |
Handle_Geom_Curve Geom_OffsetCurve::BasisCurve | ( | ) | const |
GeomAbs_Shape Geom_OffsetCurve::Continuity | ( | ) | const [virtual] |
Implements Geom_Curve.
Handle_Geom_Geometry Geom_OffsetCurve::Copy | ( | ) | const [virtual] |
Implements Geom_Geometry.
void Geom_OffsetCurve::D0 | ( | const Standard_Real | U, |
gp_Pnt & | P | ||
) | const [virtual] |
Implements Geom_Curve.
void Geom_OffsetCurve::D0 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Pnt & | Pbasis, | ||
gp_Vec & | V1basis | ||
) | const |
void Geom_OffsetCurve::D1 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Pnt & | Pbasis, | ||
gp_Vec & | V1, | ||
gp_Vec & | V1basis, | ||
gp_Vec & | V2basis | ||
) | const |
void Geom_OffsetCurve::D1 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Vec & | V1 | ||
) | const [virtual] |
Implements Geom_Curve.
void Geom_OffsetCurve::D2 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Pnt & | Pbasis, | ||
gp_Vec & | V1, | ||
gp_Vec & | V2, | ||
gp_Vec & | V1basis, | ||
gp_Vec & | V2basis, | ||
gp_Vec & | V3basis | ||
) | const |
void Geom_OffsetCurve::D2 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Vec & | V1, | ||
gp_Vec & | V2 | ||
) | const [virtual] |
Implements Geom_Curve.
void Geom_OffsetCurve::D3 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Vec & | V1, | ||
gp_Vec & | V2, | ||
gp_Vec & | V3 | ||
) | const [virtual] |
Implements Geom_Curve.
const gp_Dir& Geom_OffsetCurve::Direction | ( | ) | const |
gp_Vec Geom_OffsetCurve::DN | ( | const Standard_Real | U, |
const Standard_Integer | N | ||
) | const [virtual] |
Implements Geom_Curve.
Standard_Real Geom_OffsetCurve::FirstParameter | ( | ) | const [virtual] |
Implements Geom_Curve.
Standard_Boolean Geom_OffsetCurve::IsClosed | ( | ) | const [virtual] |
Implements Geom_Curve.
Standard_Boolean Geom_OffsetCurve::IsCN | ( | const Standard_Integer | N | ) | const [virtual] |
Implements Geom_Curve.
Standard_Boolean Geom_OffsetCurve::IsPeriodic | ( | ) | const [virtual] |
Implements Geom_Curve.
Standard_Real Geom_OffsetCurve::LastParameter | ( | ) | const [virtual] |
Implements Geom_Curve.
Standard_Real Geom_OffsetCurve::Offset | ( | ) | const |
virtual Standard_Real Geom_OffsetCurve::ParametricTransformation | ( | const gp_Trsf & | T | ) | const [virtual] |
Reimplemented from Geom_Curve.
virtual Standard_Real Geom_OffsetCurve::Period | ( | ) | const [virtual] |
Reimplemented from Geom_Curve.
void Geom_OffsetCurve::Reverse | ( | ) | [virtual] |
Implements Geom_Curve.
Standard_Real Geom_OffsetCurve::ReversedParameter | ( | const Standard_Real | U | ) | const [virtual] |
Implements Geom_Curve.
void Geom_OffsetCurve::SetBasisCurve | ( | const Handle< Geom_Curve > & | C | ) |
void Geom_OffsetCurve::SetDirection | ( | const gp_Dir & | V | ) |
void Geom_OffsetCurve::SetOffsetValue | ( | const Standard_Real | D | ) |
void Geom_OffsetCurve::Transform | ( | const gp_Trsf & | T | ) | [virtual] |
Implements Geom_Geometry.
virtual Standard_Real Geom_OffsetCurve::TransformedParameter | ( | const Standard_Real | U, |
const gp_Trsf & | T | ||
) | const [virtual] |
Reimplemented from Geom_Curve.
void Geom_OffsetCurve::Value | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Pnt & | Pbasis, | ||
gp_Vec & | V1basis | ||
) | const |