This class implements the basis services for the creation, edition, modification and evaluation of planar offset curve. The offset curve is obtained by offsetting by distance along the normal to a basis curve defined in 2D 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 and the offset curve takes its parametrization from the basis curve. The Offset curve is in the direction of the normal to the basis curve N. 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 ^ Z)) / ||T ^ Z|| where T is the tangent vector to the basis curve and Z the direction of the normal vector to the plane of the curve, N = T ^ Z defines the offset direction and should not have null length. More...
#include <Geom2d_OffsetCurve.hxx>
Public Member Functions | |
| Geom2d_OffsetCurve (const Handle< Geom2d_Curve > &C, const Standard_Real Offset, const Standard_Boolean isNotCheckC0=Standard_False) | |
| Constructs a curve offset from the basis curve C, where Offset is the distance between the offset curve and the basis curve at any point. A point on the offset curve is built by measuring the offset value along a normal vector at a point on C. This normal vector is obtained by rotating the vector tangential to C at 90 degrees in the anti-trigonometric sense. The side of C on which the offset value is measured is indicated by this normal vector if Offset is positive, or in the inverse sense if Offset is negative. If isNotCheckC0 = TRUE checking if basis curve has C0-continuity is not made. 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 Warning! if isNotCheckC0 = false, ConstructionError raised if the basis curve C is not at least C1. No check is done to know if ||V^Z|| != 0.0 at any point. More... | |
| void | Reverse () |
| Changes the direction of parametrization of <me>. As a result: More... | |
| 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. More... | |
| void | SetBasisCurve (const Handle< Geom2d_Curve > &C, const Standard_Boolean isNotCheckC0=Standard_False) |
| Changes this offset curve by assigning C as the basis curve from which it is built. If isNotCheckC0 = TRUE checking if basis curve has C0-continuity is not made. Exceptions if isNotCheckC0 = false, Standard_ConstructionError if the curve C is not at least "C1" continuous. More... | |
| void | SetOffsetValue (const Standard_Real D) |
| Changes this offset curve by assigning D as the offset value. More... | |
| Handle< Geom2d_Curve > | BasisCurve () const |
| Returns the basis curve of this offset curve. The basis curve can be an offset curve. More... | |
| GeomAbs_Shape | Continuity () const |
| 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 normal direction defined at any point. Value and derivatives. More... | |
| void | D0 (const Standard_Real U, gp_Pnt2d &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. More... | |
| void | D1 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &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. More... | |
| void | D2 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &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. More... | |
| void | D3 (const Standard_Real U, gp_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const |
| Warning! This should not be called if the continuity of the basis curve is not C4. Nevertheless, it's OK to use it on portion where the curve is C4. More... | |
| gp_Vec2d | 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. Warning! this should not be called raises UndefunedDerivative if the continuity of the basis curve is not CN+1. Nevertheless, it's OK to use it on portion where the curve is CN+1 raises RangeError if N < 1. raises NotImplemented if N > 3. 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 Warnings : The exception UndefinedValue or UndefinedDerivative is raised if it is not possible to compute a unique offset direction. More... | |
| void | Value (const Standard_Real U, gp_Pnt2d &P, gp_Pnt2d &Pbasis, gp_Vec2d &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. More... | |
| void | D1 (const Standard_Real U, gp_Pnt2d &P, gp_Pnt2d &Pbasis, gp_Vec2d &V1, gp_Vec2d &V1basis, gp_Vec2d &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. More... | |
| void | D2 (const Standard_Real U, gp_Pnt2d &P, gp_Pnt2d &Pbasis, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V1basis, gp_Vec2d &V2basis, gp_Vec2d &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. More... | |
| Standard_Real | FirstParameter () const |
| Returns the value of the first parameter. Warnings : It can be RealFirst or RealLast from package Standard if the curve is infinite. More... | |
| 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. More... | |
| Standard_Real | Offset () const |
| Returns the offset value of this offset curve. More... | |
| 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. More... | |
| Standard_Boolean | IsCN (const Standard_Integer N) const |
| Is the order of continuity of the curve N ? Warnings : 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. More... | |
| Standard_Boolean | IsPeriodic () const |
| Is the parametrization of a curve is periodic ? If the basis curve is a circle or an ellipse the corresponding OffsetCurve is periodic. If the basis curve can't be periodic (for example BezierCurve) the OffsetCurve can't be periodic. More... | |
| 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. More... | |
| void | Transform (const gp_Trsf2d &T) |
| Applies the transformation T to this offset curve. Note: the basis curve is also modified. More... | |
| virtual Standard_Real | TransformedParameter (const Standard_Real U, const gp_Trsf2d &T) const |
| Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>. More... | |
| virtual Standard_Real | ParametricTransformation (const gp_Trsf2d &T) const |
| Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>. More... | |
| Handle< Geom2d_Geometry > | Copy () const |
| Creates a new object, which is a copy of this offset curve. More... | |
| GeomAbs_Shape | GetBasisCurveContinuity () const |
| Returns continuity of the basis curve. More... | |
 Public Member Functions inherited from Geom2d_Curve | |
| Handle< Geom2d_Curve > | Reversed () const |
| Creates a reversed duplicate Changes the orientation of this curve. The first and last parameters are not changed, but the parametric direction of the curve is reversed. If the curve is bounded: More... | |
| gp_Pnt2d | 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. More... | |
| Public Member Functions inherited from Geom2d_Geometry | |
| void | Mirror (const gp_Pnt2d &P) |
| Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry and assigns the result to this geometric object. More... | |
| void | Mirror (const gp_Ax2d &A) |
| Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More... | |
| void | Rotate (const gp_Pnt2d &P, const Standard_Real Ang) |
| Rotates a Geometry. P is the center of the rotation. Ang is the angular value of the rotation in radians. More... | |
| void | Scale (const gp_Pnt2d &P, const Standard_Real S) |
| Scales a Geometry. S is the scaling value. More... | |
| void | Translate (const gp_Vec2d &V) |
| Translates a Geometry. V is the vector of the tanslation. More... | |
| void | Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2) |
| Translates a Geometry from the point P1 to the point P2. More... | |
| Handle< Geom2d_Geometry > | Mirrored (const gp_Pnt2d &P) const |
| Handle< Geom2d_Geometry > | Mirrored (const gp_Ax2d &A) const |
| Handle< Geom2d_Geometry > | Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const |
| Handle< Geom2d_Geometry > | Scaled (const gp_Pnt2d &P, const Standard_Real S) const |
| Handle< Geom2d_Geometry > | Transformed (const gp_Trsf2d &T) const |
| Handle< Geom2d_Geometry > | Translated (const gp_Vec2d &V) const |
| Handle< Geom2d_Geometry > | Translated (const gp_Pnt2d &P1, const gp_Pnt2d &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... | |
Detailed Description
This class implements the basis services for the creation, edition, modification and evaluation of planar offset curve. The offset curve is obtained by offsetting by distance along the normal to a basis curve defined in 2D 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 and the offset curve takes its parametrization from the basis curve. The Offset curve is in the direction of the normal to the basis curve N. 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 ^ Z)) / ||T ^ Z|| where T is the tangent vector to the basis curve and Z the direction of the normal vector to the plane of the curve, N = T ^ Z defines the offset direction and should not have null length.
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^Z|| != 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.
Constructor & Destructor Documentation
| Geom2d_OffsetCurve::Geom2d_OffsetCurve | ( | const Handle< Geom2d_Curve > & | C, |
| const Standard_Real | Offset, | ||
| const Standard_Boolean | isNotCheckC0 = Standard_False |
||
| ) |
Constructs a curve offset from the basis curve C, where Offset is the distance between the offset curve and the basis curve at any point. A point on the offset curve is built by measuring the offset value along a normal vector at a point on C. This normal vector is obtained by rotating the vector tangential to C at 90 degrees in the anti-trigonometric sense. The side of C on which the offset value is measured is indicated by this normal vector if Offset is positive, or in the inverse sense if Offset is negative. If isNotCheckC0 = TRUE checking if basis curve has C0-continuity is not made. 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 Warning! if isNotCheckC0 = false, ConstructionError raised if the basis curve C is not at least C1. No check is done to know if ||V^Z|| != 0.0 at any point.
Member Function Documentation
| Handle< Geom2d_Curve > Geom2d_OffsetCurve::BasisCurve | ( | ) | const |
Returns the basis curve of this offset curve. The basis curve can be an offset curve.
|
virtual |
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 normal direction defined at any point. 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 Z the direction normal to the plane of the curve, the relation ||T(U) ^ Z|| != 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.
Implements Geom2d_Curve.
|
virtual |
Creates a new object, which is a copy of this offset curve.
Implements Geom2d_Geometry.
|
virtual |
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.
Implements Geom2d_Curve.
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virtual |
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.
Implements Geom2d_Curve.
| void Geom2d_OffsetCurve::D1 | ( | const Standard_Real | U, |
| gp_Pnt2d & | P, | ||
| gp_Pnt2d & | Pbasis, | ||
| gp_Vec2d & | V1, | ||
| gp_Vec2d & | V1basis, | ||
| gp_Vec2d & | 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.
|
virtual |
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.
Implements Geom2d_Curve.
| void Geom2d_OffsetCurve::D2 | ( | const Standard_Real | U, |
| gp_Pnt2d & | P, | ||
| gp_Pnt2d & | Pbasis, | ||
| gp_Vec2d & | V1, | ||
| gp_Vec2d & | V2, | ||
| gp_Vec2d & | V1basis, | ||
| gp_Vec2d & | V2basis, | ||
| gp_Vec2d & | 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.
|
virtual |
Warning! This should not be called if the continuity of the basis curve is not C4. Nevertheless, it's OK to use it on portion where the curve is C4.
Implements Geom2d_Curve.
|
virtual |
The returned vector gives the value of the derivative for the order of derivation N. Warning! this should not be called raises UndefunedDerivative if the continuity of the basis curve is not CN+1. Nevertheless, it's OK to use it on portion where the curve is CN+1 raises RangeError if N < 1. raises NotImplemented if N > 3. 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 Warnings : The exception UndefinedValue or UndefinedDerivative is raised if it is not possible to compute a unique offset direction.
Implements Geom2d_Curve.
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virtual |
Returns the value of the first parameter. Warnings : It can be RealFirst or RealLast from package Standard if the curve is infinite.
Implements Geom2d_Curve.
| GeomAbs_Shape Geom2d_OffsetCurve::GetBasisCurveContinuity | ( | ) | const |
Returns continuity of the basis curve.
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virtual |
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.
Implements Geom2d_Curve.
|
virtual |
Is the order of continuity of the curve N ? Warnings : 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.
Implements Geom2d_Curve.
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virtual |
Is the parametrization of a curve is periodic ? If the basis curve is a circle or an ellipse the corresponding OffsetCurve is periodic. If the basis curve can't be periodic (for example BezierCurve) the OffsetCurve can't be periodic.
Implements Geom2d_Curve.
|
virtual |
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.
Implements Geom2d_Curve.
| Standard_Real Geom2d_OffsetCurve::Offset | ( | ) | const |
Returns the offset value of this offset curve.
|
virtual |
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.
Reimplemented from Geom2d_Curve.
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virtual |
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.
Reimplemented from Geom2d_Curve.
|
virtual |
Changes the direction of parametrization of <me>. As a result:
- the basis curve is reversed,
- the start point of the initial curve becomes the end point of the reversed curve,
- the end point of the initial curve becomes the start point of the reversed curve, and
- the first and last parameters are recomputed.
Implements Geom2d_Curve.
|
virtual |
Computes the parameter on the reversed curve for the point of parameter U on this offset curve.
Implements Geom2d_Curve.
| void Geom2d_OffsetCurve::SetBasisCurve | ( | const Handle< Geom2d_Curve > & | C, |
| const Standard_Boolean | isNotCheckC0 = Standard_False |
||
| ) |
Changes this offset curve by assigning C as the basis curve from which it is built. If isNotCheckC0 = TRUE checking if basis curve has C0-continuity is not made. Exceptions if isNotCheckC0 = false, Standard_ConstructionError if the curve C is not at least "C1" continuous.
| void Geom2d_OffsetCurve::SetOffsetValue | ( | const Standard_Real | D | ) |
Changes this offset curve by assigning D as the offset value.
|
virtual |
Applies the transformation T to this offset curve. Note: the basis curve is also modified.
Implements Geom2d_Geometry.
|
virtual |
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.
Reimplemented from Geom2d_Curve.
| void Geom2d_OffsetCurve::Value | ( | const Standard_Real | U, |
| gp_Pnt2d & | P, | ||
| gp_Pnt2d & | Pbasis, | ||
| gp_Vec2d & | 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.
The documentation for this class was generated from the following file:
