Line in two-dimensional space. More...

#include <cur_line.h>

Inheritance diagram for MbLine:

Collaboration diagram for MbLine:

Public Member Functions
Line initialization functions.
void	Init (const MbLine &other)

void	Init (const MbCartPoint &pnt, double angle)

void	Init (const MbCartPoint &pnt, const MbDirection &dir)

void	Init (const MbCartPoint &pnt, const MbVector &dir)

void	Init (const MbCartPoint &p1, const MbCartPoint &p2)

void	Init (double a, double b, double c)

Common functions of geometric object.
MbePlaneType	IsA () const override
	Get the object type.

bool	IsSimilar (const MbPlaneItem &) const override
	Determine whether the objects are similar. More...

bool	SetEqual (const MbPlaneItem &) override
	Make the objects equal. More...

bool	IsSame (const MbPlaneItem &other, double accuracy=LENGTH_EPSILON) const override
	Determine whether objects are equal. More...

void	Transform (const MbMatrix &, MbRegTransform ireg=nullptr, const MbSurface newSurface=nullptr) override
	Transform according to the matrix. More...

void	Move (const MbVector &, MbRegTransform =nullptr, const MbSurface newSurface=nullptr) override
	Translate along a vector. More...

void	Rotate (const MbCartPoint &pnt, const MbDirection &angle, MbRegTransform =nullptr, const MbSurface newSurface=nullptr) override
	Rotate about a point. More...

MbPlaneItem &	Duplicate (MbRegDuplicate *=nullptr) const override
	Create a copy. More...

void	AddYourGabaritTo (MbRect &) const override
	Extend the given bounding rectangle so that it encloses this object.

void	AddYourGabaritMtr (MbRect &, const MbMatrix &) const override
	Add a bounding box to rectangle. More...

void	CalculateGabarit (MbRect &) const override
	Detect the bounding box of a curve. More...

void	CalculateLocalGabarit (const MbMatrix &into, MbRect &local) const override
	Calculate bounding box in the local coordinate system. More...

bool	IsVisibleInRect (const MbRect &, bool exact=false) const override
	Determine visibility of an object in rectangle. More...

double	DistanceToPoint (const MbCartPoint &) const override
	Calculate the distance to a point.

bool	DistanceToPointIfLess (const MbCartPoint &toP, double &d) const override
	Calculate the distance to a point. More...

bool	IsVisibleInRect (const MbRect &rect, bool exact=false) const override
	Determine visibility of an object in rectangle. More...

Functions describing the domain of a curve.
double	GetTMin () const override
	Get the minimum value of parameter.

double	GetTMax () const override
	Get the maximum value of parameter.

Functions for working in the domain of a curve.
Functions: PointOn, FirstDer, SecondDer, ThirdDer,... correct the parameter when it is outside domain.
void	PointOn (double &t, MbCartPoint &p) const override
	Calculate a point on the curve. More...

void	FirstDer (double &t, MbVector &fd) const override
	Calculate first derivative.

void	SecondDer (double &t, MbVector &sd) const override
	Calculate second derivative.

void	ThirdDer (double &t, MbVector &td) const override
	Calculate third derivative.

Function for working inside and outside of the curve domain.
Function _PointOn, _FirstDer, _SecondDer, _ThirdDer,... do not correct a parameter when it is outside domain. If non-closed curve is outside of the domain in the general case it continues along a tangent, which it has at the respective end.
void	_PointOn (double t, MbCartPoint &p) const override
	Calculate point at curve and its extension. More...

void	_FirstDer (double t, MbVector &v) const override
	Calculate first derivative at curve and its extension.

void	_SecondDer (double t, MbVector &v) const override
	Calculate second derivative at curve and its extension.

void	_ThirdDer (double t, MbVector &v) const override
	Calculate third derivative at curve and its extension.

Functions for get of the group of data inside and outside the curve's domain of parameter.
void	Explore (double &t, bool ext, MbCartPoint &pnt, MbVector &fir, MbVector sec, MbVector thir) const override
	Calculate point and derivatives of object for given parameter. More...

Common functions of curve
MbCurve *	Offset (double rad) const override
	Construct the equidistant curve which is shifted by the given value.

MbeState	DeletePart (double t1, double t2, MbCurve *&part2) override
	Delete the piece of a curve. More...

MbeState	TrimmPart (double t1, double t2, MbCurve *&part2) override
	Keep the piece of a curve. More...

MbCurve *	Trimmed (double t1, double t2, int sense, const MbDimAccuracy &xyEps, bool saveParamLenAndLaw) const override
	Construct a trimmed curve with the given two-dimensional accuracy. More...

bool	HasLength (double &) const override
	Calculate the metric length of a curve. More...

double	GetMetricLength () const override
	Calculate the metric length of a curve. More...

virtual double	LengthBetween2Points (MbCartPoint &p1, MbCartPoint &p2, MbCartPoint *pc=nullptr) const override
	Calculate minimal length of a curve between two points on it. More...

bool	DistanceAlong (double &t, double len, int curveDir, double eps=Math::LengthEps, VERSION version=Math::DefaultMathVersion()) const override
	Translate parameter along the curve. More...

double	Step (double t, double sag) const override
	Calculate parameter step. More...

double	DeviationStep (double t, double angle) const override
	Calculate parameter step. More...

double	DistanceToPointSign (const MbCartPoint &to) const

MbeItemLocation	PointRelative (const MbCartPoint &p, double eps=Math::LengthEps) const override
	Define the point position relative to the curve. More...

double	PointProjection (const MbCartPoint &) const override
	Calculate the point projection to the curve. More...

bool	NearPointProjection (const MbCartPoint &pnt, double xEpsilon, double yEpsilon, double &t, bool ext, MbRect1D *tRange=nullptr) const override
	Find the point projection to the curve. More...

void	PerpendicularPoint (const MbCartPoint &pnt, SArray< double > &tFind) const override
	Find perpendiculars to a curve. More...

bool	GetMiddlePoint (MbCartPoint &) const override
	Calculate a middle point of a curve.

bool	GetWeightCentre (MbCartPoint &) const override
	Calculate the center of gravity of a curve.

bool	operator== (const MbLine &) const

bool	operator!= (const MbLine &) const

bool	IsHorizontal (double eps=Math::AngleEps) const

bool	IsVertical (double eps=Math::AngleEps) const

bool	IsSimilar (const MbLine &) const

bool	IsParallel (const MbLine &other, double epsilon=Math::AngleEps) const

double	DistanceToParallel (const MbLine &) const

void	IntersectHorizontal (double y, SArray< double > &cross) const override
	Find intersections of a curve with horizontal line. More...

void	IntersectVertical (double x, SArray< double > &cross) const override
	Find intersections of a curve with vertical line. More...

void	Inverse (MbRegTransform *iReg=nullptr) override
	Set the opposite direction of curve.

bool	IsClosed () const override
	Define whether the curve is periodic. More...

bool	IsBounded () const override
	Define whether the curve is bounded.

bool	IsStraight (bool ignoreParams=false) const override
	Define whether the curve is rectilinear..

double	GetParamToUnit () const override
	Return increment of parameter, corresponding to the unit length in space.

double	GetParamToUnit (double t) const override
	Return increment of parameter, corresponding to the unit length in space according to parameter.

void	SetPoint (const MbCartPoint &pnt)

void	GetPoint (MbCartPoint &pnt) const

void	GetDirection (MbDirection &dir) const

void	SetDirection (const MbDirection &dir)

void	SetDirection (const MbVector &v)

void	SetAngle (double angle)

double	GetAngle () const

MbNurbs *	NurbsCurve (const MbCurveIntoNurbsInfo &) const override
	Construct a NURBS copy of a curve. More...

MbCurve *	NurbsCurve (const MbNurbsParameters &) const override
	Construct a NURBS copy of a curve. More...

MbContour *	NurbsContour () const override
	Approximate of a curve by the contour from NURBS curves.

size_t	GetCount () const override
	Define the number of splittings for one passage in operations.

ptrdiff_t	IntersectRect (MbRect &rect, MbCartPoint *cross) const

void	Implicit (double &A, double &B, double &C) const

const MbCartPoint &	GetOrigin () const

const MbDirection &	GetDirection () const

MbCartPoint &	SetOrigin ()

MbDirection &	SetDirection ()

MbCartPoint	Origin () const

MbVector	Derive () const

void	GetProperties (MbProperties &) override
	Get properties of the object. More...

void	SetProperties (const MbProperties &) override
	Change properties of the object. More...

void	GetBasisPoints (MbControlData &) const override
	Get control points of object.

void	SetBasisPoints (const MbControlData &) override
	Change the object by control points.

virtual MbCurve *	Trimmed (double t1, double t2, int sense, bool saveParamLenAndLaw=false) const
	Construct a trimmed curve. More...

virtual MbCurve *	Trimmed (double t1, double t2, int sense, const MbDimAccuracy &xyEps, bool saveParamLenAndLaw) const=0
	Construct a trimmed curve with the given two-dimensional accuracy. More...

Public Member Functions inherited from MbCurve
virtual	~MbCurve ()
	Destructor.

MbePlaneType	Type () const override
	Get the group type of the object.

MbePlaneType	Family () const override
	Get family of object.

void	Refresh () override
	Set all temporary (mutable) data of object to undefined (initial) state.

virtual void	PrepareIntegralData (const bool forced) const
	Calculate temporary (mutable) data of an object. More...

size_t	size () const
	Number of objects if object is interpreted as vector of objects.

const MbCurve *	operator[] (size_t) const
	An access operator.

virtual MbResultType	Extend (const MbCurveExtensionParameters &parameters, c3d::PlaneCurveSPtr &resCurve) const
	Extend the curve. More...

bool	IsVisibleInRect (const MbRect &rect, bool exact=false) const override
	Determine visibility of an object in rectangle. More...

virtual bool	IsCompleteInRect (const MbRect &rect) const
	Determine whether an object is fully visible in rectangle. More...

double	DistanceToPoint (const MbCartPoint &toP) const override
	Calculate the distance to a point.

bool	DistanceToPointIfLess (const MbCartPoint &toP, double &d) const override
	Calculate the distance to a point. More...

virtual double	GetPeriod () const
	Return period. More...

virtual bool	IsPeriodic () const
	Define whether the curve is periodic. More...

bool	IsTouch (double eps=Math::LengthEps) const
	Determine whether a curve is closed regardless of the smoothness of the closure. More...

void	Tangent (double &t, MbVector &v) const
	Calculate tangent vector (normalized).

void	Tangent (double &t, MbDirection &d) const
	Calculate tangent vector (normalized).

void	Normal (double &t, MbVector &v) const
	Calculate main normal vector (normalized).

void	Normal (double &t, MbDirection &d) const
	Calculate main normal vector (normalized).

void	_Tangent (double t, MbVector &v) const
	Calculate tangent vector (normalized).

void	_Tangent (double t, MbDirection &d) const
	Calculate tangent vector (normalized).

void	_Normal (double t, MbVector &v) const
	Calculate main normal vector (normalized) at curve and its extension.

void	_Normal (double t, MbDirection &d) const
	Calculate main normal vector (normalized) at curve and its extension.

virtual double	Curvature (double t) const
	Calculate curvature of curve.

double	CurvatureDerive (double t) const
	Calculate derivative of curvature by parameter.

double	CurvatureRadius (double t) const
	Calculate radius of curve with a sign.

virtual bool	IsDegenerate (double eps=Math::LengthEps) const
	Define whether the curve is degenerate..

virtual bool	IsSmoothConnected (double angleEps) const
	Define whether joints of contour/curve are smooth.

double	GetParamLength () const
	Calculate the parametric length of a curve.

virtual double	CalculateMetricLength () const
	Calculate the metric length of a curve.

virtual double	CalculateLength (double t1, double t2) const
	Calculate the metric length of a curve. More...

virtual void	ResetTCalc () const
	Reset the current value of parameter.

virtual bool	BeginApprox (double sag, double &tbeg, double &tend, MbCartPoint &pnt, bool &existNextPoint) const
	Start approximation for the drawing. More...

virtual bool	GetNextPoint (double sag, double tend, double &tcur, MbCartPoint &pnt) const
	Calculate the next point. More...

virtual void	CalculatePolygon (double sag, MbPolygon &poligon) const
	Calculate an array of points for drawing. More...

MbNurbs *	NurbsCurve (const MbCurveIntoNurbsInfo *nInfo=nullptr) const
	Construct a NURBS copy of a curve. More...

virtual MbCurve *	Trimmed (double t1, double t2, int sense, bool saveParamLenAndLaw=false) const
	Construct a trimmed curve. More...

virtual MbeState	Deformation (const MbRect &rect, const MbMatrix &matr)
	Deform the curve. More...

virtual bool	IsInRectForDeform (const MbRect &) const
	Determine visibility of a curve in rectangle.

virtual MbeLocation	PointLocation (const MbCartPoint &pnt, double eps=Math::LengthEps) const
	The point position relative to the curve.

MbeNewtonResult	PointProjectionNewton (const MbCartPoint &p, double xEpsilon, double yEpsilon, size_t iterLimit, double &t, bool ext) const
	Find the point projection to the curve. More...

void	PointProjection (const MbCartPoint &pnt, MbCartPoint &on) const
	Calculate the point projection to the curve. More...

void	BasePointProjection (const MbCartPoint &pnt, MbCartPoint &on) const
	Calculate the point projection to the curve. More...

void	PointProjectionAndAngle (MbCartPoint &on, double &angle) const
	Calculate the point projection to the curve. More...

bool	DirectPointProjection (const MbCartPoint &pnt, const MbDirection &dir, MbCartPoint &pp) const
	Calculate the point projection to the curve. More...

virtual bool	SmallestPerpendicular (const MbCartPoint &pnt, double &tProj) const
	Find the nearest perpendicular to the curve. More...

virtual void	TangentPoint (const MbCartPoint &pnt, SArray< double > &tFind) const
	Find tangents to a curve. More...

virtual void	Isoclinal (const MbVector &angle, SArray< double > &tFind) const
	Construct isoclines. More...

void	HorzIsoclinal (SArray< double > &tFind) const
	Construct horizontal isoclines. More...

void	VertIsoclinal (SArray< double > &tFind) const
	Construct vertical isoclines. More...

void	LowestPoint (MbCartPoint &lowestPoint, double &tLowest) const
	Find the lowest point of a curve and the corresponding parameter.

virtual void	SelfIntersect (SArray< MbCrossPoint > &, double metricEps=Math::LengthEps) const
	Find self-intersections of curve. More...

virtual void	OffsetCuspPoint (SArray< double > &tCusps, double dist) const
	Find the special points of an offset curve. More...

virtual bool	GoThroughPoint (MbCartPoint &pnt)
	Create a curve through a point. More...

virtual void	GetStartPoint (MbCartPoint &) const
	Calculate a start point of a curve.

virtual void	GetEndPoint (MbCartPoint &) const
	Calculate an end point of a curve.

virtual bool	GetCentre (MbCartPoint &) const
	Calculate a center of curve.

virtual double	GetRadius (double accuracy=PARAM_REGION) const
	Get the physical radius of the curve or zero if it impossible. More...

virtual bool	GetAxisPoint (MbCartPoint &p) const
	Calculate a point to construct an axis. More...

virtual bool	IsSimilarToCurve (const MbCurve &curve, double precision=PARAM_PRECISION) const
	Define whether the curves are similar for the merge.

void	GetPointsByEvenParamDelta (size_t n, std::vector< MbCartPoint > &pnts) const
	Get n points of a curve with equal intervals by parameter.

void	GetPointsByEvenParamDelta (size_t n, SArray< MbCartPoint > &pnts) const

virtual void	GetPointsByEvenLengthDelta (size_t n, std::vector< MbCartPoint > &pnts) const
	Get n points of a curve with equal intervals by arc length.

void	GetPointsByEvenLengthDelta (size_t n, SArray< MbCartPoint > &pnts) const

bool	IsPointOn (const MbCartPoint &, double eps=Math::LengthEps) const
	Check whether the point is on a curve with the tolerance eps.

bool	IsParamOn (double t, double eps=Math::paramEpsilon) const
	Check whether the parameter is inside a range with the tolerance eps.

void	CorrectCyclicParameter (double &t, double eps=Math::paramRegion) const
	Correct parameter for closed curves. More...

void	CorrectParameter (double &t) const
	Correct parameter. More...

MbCurve *	InverseDuplicate () const
	Create a copy with changed direction.

bool	IsInverseSame (const MbCurve &curve, double accuracy=LENGTH_EPSILON) const
	Define whether an inversed curve is the same.

virtual bool	IsReparamSame (const MbCurve &curve, double &factor) const
	Define whether a reparameterized curve is the same. More...

MbCartPoint	GetLimitPoint (ptrdiff_t number) const
	Calculate the boundary point. More...

void	GetLimitPoint (ptrdiff_t number, MbCartPoint &pnt) const
	Calculate the boundary point. More...

void	GetLimitTangent (ptrdiff_t number, MbVector &v) const
	Calculate a tangent vector to the boundary point. More...

void	GetLimitPointAndTangent (ptrdiff_t number, MbCartPoint &pnt, MbVector &v) const
	Calculate a tangent vector and point at the end of a curve. More...

bool	AreLimitPointsEqual () const
	Are boundary points equal? More...

virtual bool	GetSpecificPoint (const MbCartPoint &from, double &dmax, MbCartPoint &pnt) const
	Return a specific point of a curve. More...

virtual const MbCurve &	GetBasisCurve () const
	Returns the base curve if exists or itself.

virtual MbCurve &	SetBasisCurve ()
	Returns the base curve if exists or itself.

virtual double	GetParamDelta () const
	Return an indent by parameter of a curve.

virtual const MbCurve &	GetSubstrate () const
	Get a substrate or itself.

virtual MbCurve &	SetSubstrate ()
	Get a substrate or itself.

virtual int	SubstrateCurveDirection () const
	Return direction of a substrate relative to a curve or vice versa.

virtual void	SubstrateToCurve (double &) const
	Transform a substrate parameter to the curve parameter.

virtual void	CurveToSubstrate (double &) const
	Transform a curve parameter to the substrate parameter.

virtual double	GetLengthEvaluation () const
	Calculate the metric length of a curve. More...

virtual double	GetTEpsilon (double epsilon) const
	Return the minimal discernible value of parameter with the given tolerance.

virtual double	GetTEpsilon (double t, double epsilon) const
	Return the minimal discernible value of parameter with the given tolerance according to parameter.

virtual double	GetTRegion (double epsilon) const
	Return the minimal discernible value of parameter with the given tolerance.

virtual double	GetTRegion (double t, double epsilon) const
	Return the minimal discernible value of parameter with the given tolerance according to parameter.

virtual double	GetTRegion (double t, const MbDimAccuracy &xyEps) const
	Return the minimal discernible value of parameter with the given two-dimensinal accuracy according to parameter. The method takes into account the direction of the curve at a point.

double	GetTMid () const
	Return the middle of parametric range of a curve.

double	GetTRange () const
	Return the parametric length of a curve.

MbCartPoint	PointOn (double &t) const
	Calculate point on the curve.

MbVector	FirstDer (double &t) const
	Calculate first derivative.

MbDirection	Tangent (double &t) const
	Calculate tangent vector (normalized).

MbDirection	Normal (double &t) const
	Calculate the normal vector.

double	DerLength (double &t) const
	Calculate the length of derivative vector.

virtual void	GetAnalyticalFunctionsBounds (std::vector< double > &params) const
	Get the boundaries of the curve sections that are described by one analytical function. More...

virtual void	BreakPoints (std::vector< double > &vBreaks, double precision=ANGLE_REGION) const
	\ ru Определение точек излома кривой. The determination of curve smoothness break points.

MbProperty &	CreateProperty (MbePrompt name) const override
	Create a custom property.

virtual bool	IsContinuousDerivative (bool &contLength, bool &contDirect, c3d::DoubleVector *params=nullptr, double epsilon=EPSILON) const
	Get properties of the object. More...

virtual bool	SetContinuousDerivativeLength (VERSION version, double epsilon=EPSILON)
	Eliminate the discontinuities of the first derivative at length. More...

bool	IsSpaceNear (const MbCurve &curve, double eps, bool ext, double devSag=5.0 *Math::deviateSag) const
	Check whether the two curves are metrically close. More...

bool	IsSpaceNear (const MbCurve &curve, double xEps, double yEps, bool ext, double xNear, double yNear, double devSag=5.0 *Math::deviateSag) const
	Check whether the two curves are metrically close. More...

SimpleName	GetCurveName () const
	A curve name.

void	SetCurveName (SimpleName newName)
	Set a curve name.

Public Member Functions inherited from MbPlaneItem
virtual	~MbPlaneItem ()
	Destructor.

void	PrepareWrite () const
	Object registration. More...

MbeRefType	RefType () const override
	Get the registration type (for copying, duplication).

virtual void	Rotate (const MbCartPoint &pnt, double angle, MbRegTransform iReg=nullptr, const MbSurface newSurface=nullptr)
	Rotate about a point. More...

Public Member Functions inherited from TapeBase
	TapeBase (RegistrableRec regs=noRegistrable)
	Constructor.

	TapeBase (const TapeBase &)
	Copy-constructor.

virtual	~TapeBase ()
	Destructor.

RegistrableRec	GetRegistrable () const
	Whether the stream class is registrable.

void	SetRegistrable (RegistrableRec regs=registrable) const
	Set the state of registration of the stream class.

virtual const char *	GetPureName (const VersionContainer &) const
	Get the class name.

virtual bool	IsFamilyRegistrable () const
	Whether the object belongs to a registrable family.

Public Member Functions inherited from MbRefItem
refcount_t	GetUseCount () const
	Get count of references (get count of owners of an object).

refcount_t	AddRef () const
	Increase count of references by one.

refcount_t	DecRef () const
	Decrease count of references by one.

refcount_t	Release () const
	Decrease count of references by one and if count of references became zero, then remove itself.

Public Member Functions inherited from MbNestSyncItem
void	Lock () const
	Switch lock on (locking happens only in parallel region).

void	Unlock () const
	Switch lock off if locking has been set.

CommonRecursiveMutex *	GetLock () const
	Get a pointer to the mutex object. Return nullptr if no parallelism. For use in ScopedLock.

Additional Inherited Members
Protected Member Functions inherited from MbCurve
	MbCurve ()
	Default constructor.

	MbCurve (const MbCurve &other)
	Copy-constructor.

Protected Member Functions inherited from MbPlaneItem
	MbPlaneItem ()
	Constructor.

Protected Member Functions inherited from MbRefItem
	MbRefItem ()
	Constructor without parameters.

Protected Attributes inherited from MbCurve
SimpleName	name
	A curve name. The object data is temporary and used internally.

Detailed Description

Line in two-dimensional space.

Straight line behaves as an infinite object although its data has boundary parameter values tmin and tmax. In contrast to curves in the calculation methods of radius-vector and its derivatives the line doesn't correct parameter "t" if it is outside the values tmin and tmax.
Radius-vector of line is described by the vector function
r(t) = origin + (t direction).

Member Function Documentation

◆ IsSimilar()

bool MbLine::IsSimilar ( const MbPlaneItem & item ) const

overridevirtual

Determine whether the objects are similar.

Objects of the same type are considered to be similar if data of the objects can be equated or the data are also similar (pointers). Similar object can be initialized by data of object similar to it (equate one to another without changing of addresses).

Parameters

[in] item - Object for comparison.

Returns: Whether the objects are similar.

Reimplemented from MbPlaneItem.

◆ SetEqual()

bool MbLine::SetEqual ( const MbPlaneItem & item )

overridevirtual

Make the objects equal.

It is possible to make equal only similar objects. Similar object is equated to a given one by changing of numerical data.

Parameters

[in] item - Object for initialization.

Returns: Whether the object is made equal to the given one.

Implements MbPlaneItem.

◆ IsSame()

bool MbLine::IsSame	(	const MbPlaneItem &	item,
		double	accuracy = `LENGTH_EPSILON`
	)		const

overridevirtual

Determine whether objects are equal.

Objects of the same types with similar (equal) data are considered to be equal.

Parameters

[in]	item	- Object for comparison.
[in]	accuracy	- The accuracy.

Returns: Whether the objects are equal.

Implements MbPlaneItem.

◆ Transform()

void MbLine::Transform	(	const MbMatrix &	matr,
		MbRegTransform *	iReg = `nullptr`,
		const MbSurface *	newSurface = `nullptr`
	)

overridevirtual

Transform according to the matrix.

Transform the initial object according to the matrix using the registrator. If the object contains references to the other geometric objects, then the nested objects are transformed according to the matrix. The registrator is used for preventing multiple transformation of the object. The function can be used without the registrator to transform a single object. The registrator must be used to transform a set of interdependent objects to prevent repeated transformation of the nested objects, since it is not ruled out that several objects from the set contain references to one or several common objects subject to transformation.

Parameters

[in]	matr	- A transformation matrix.
[in]	iReg	- Registrator.
[in]	surface	- New base surface of object provided that 'matr' is a transformation matrix from the old surface to a new one. For transformation of projection curve. It isn't considered if the surface is planar.

Implements MbPlaneItem.

◆ Move()

void MbLine::Move	(	const MbVector &	to,
		MbRegTransform *	iReg = `nullptr`,
		const MbSurface *	newSurface = `nullptr`
	)

overridevirtual

Translate along a vector.

Translate a geometric object along the vector using the registrator. If the object contains references to the other objects, then the translation operation is applied to the nested objects. The registrator is used for preventing multiple transformation of the object. The function can be used without the registrator to transform a single object. The registrator must be used to transform a set of interdependent objects to prevent repeated transformation of the nested objects, since it is not ruled out that several objects from the set contain references to one or several common objects subject to translation.

Parameters

[in]	to	- Translation vector.
[in]	iReg	- Registrator.
[in]	surface	- New base surface of object provided that 'matr' is a transformation matrix from the old surface to a new one. For transformation of projection curve. It isn't considered if the surface is planar.

Implements MbPlaneItem.

◆ Rotate()

void MbLine::Rotate	(	const MbCartPoint &	pnt,
		const MbDirection &	angle,
		MbRegTransform *	iReg = `nullptr`,
		const MbSurface *	newSurface = `nullptr`
	)

overridevirtual

Rotate about a point.

Rotate an object about a point by the given angle using the registrator. If the object contains references to the other geometric objects, then the rotation operation is applied to the nested objects too. The registrator is used for preventing multiple transformation of the object. The function can be used without the registrator to transform a single object. The registrator must be used to transform a set of interdependent objects to prevent repeated transformation of the nested objects, since it is not ruled out that several objects from the set contain references to one or several common objects subject to rotation.

Parameters

[in]	pnt	- Fixed point.
[in]	angle	- The rotation angle.
[in]	iReg	- Registrator.
[in]	surface	- New base surface of object provided that 'matr' is a transformation matrix from the old surface to a new one. For transformation of projection curve. It isn't considered if the surface is planar.

Implements MbPlaneItem.

◆ Duplicate()

MbPlaneItem& MbLine::Duplicate ( MbRegDuplicate * iReg = nullptr ) const

overridevirtual

Create a copy.

Create a copy of the object using the registrator. The registrator is used for preventing multiple copying of an object. If the object contains references to other objects, then the included objects are copied too. It is allowed not to pass the registrator to a function. Then the new copy of the object will be created. It is allowed not to use the registrator while copying a single object or a set of disconnected objects. The registrator must be used to copy several correlated objects successively. It is possible that the objects' connection means that the objects contain references to the common objects. Then, while copying without using the registrator, one can get a set of copies which contain references to the different copies of a single included object, what leads to loss of connection between the copies.

Parameters

[in] iReg - Registrator.

Returns: Copy of the object.

Implements MbPlaneItem.

◆ AddYourGabaritMtr()

void MbLine::AddYourGabaritMtr	(	MbRect &	rect,
		const MbMatrix &	matr
	)		const

overridevirtual

Add a bounding box to rectangle.

Add a bounding box to rectangle with taking into account of transformation matrix. If the transformation matrix is not an identity matrix then there is performed a transformation of object's copy by the matrix and after that a bounding box of the transformed object is added to rectangle. A copy is destroyed after using.

Parameters

[out]	rect	- A rectangle with information about bounds.
[in]	matr	- Transformation matrix.

Reimplemented from MbCurve.

◆ CalculateGabarit()

void MbLine::CalculateGabarit ( MbRect & ) const

overridevirtual

Detect the bounding box of a curve.

The sent rectangle becomes empty for getting a bounding box. Then bounding boxes of an object are calculated and saved into a rectangle 'rect'.

Reimplemented from MbCurve.

◆ CalculateLocalGabarit()

void MbLine::CalculateLocalGabarit	(	const MbMatrix &	into,
		MbRect &	local
	)		const

overridevirtual

Calculate bounding box in the local coordinate system.

For getting a bounding box of an object relatively to the local coordinate system, a sent rectangle becomes empty. After that bounding boxes of an object in the local coordinate system are calculated and saved in a rectangle 'rect'.

Parameters

[in]	matr	- A transition matrix from the current coordinate system of the object to the local coordinate system.
[out]	rect	- A rectangle with information about bounds.

Reimplemented from MbCurve.

◆ IsVisibleInRect() [1/2]

bool MbLine::IsVisibleInRect	(	const MbRect &	rect,
		bool	exact = `false`
	)		const

overridevirtual

Determine visibility of an object in rectangle.

It is considered that the object is visible in rectangle if bounds of an object is crossed with the given rectangle or (high requirements to accuracy, exact = true) at least one point of object is in the rectangle.

Parameters

[in]	rect	- Rectangle to check getting to.
[in]	exact	- Check accuracy. If exact = true, then at least one point of object gets to the rectangle. if exact = false, it is sufficient to find intersection between rectangle and bounding box of an object.

Returns: true, if the object is visible in the rectangle, otherwise false.

Implements MbPlaneItem.

◆ DistanceToPointIfLess()

bool MbLine::DistanceToPointIfLess	(	const MbCartPoint &	to,
		double &	d
	)		const

overridevirtual

Calculate the distance to a point.

Calculate distance to object from a given point near the object. Distance is calculated and stored to 'd' variable if it is less then initial value of 'd'. There can be performance benefit in comparison with DistanceToPoint function due to primarily checking the distance from point to bounding box and performing the further calculations only if this distance is not greater than the given one.

Parameters

[in]	to	- Point.
[in,out]	d	- Specified distance from object on input. Distance from point to object on output if operation succeeded.

Returns: True if distance from point to the object is less than the given one, otherwise false. Calculate the distance from a point and change the given value of distance if the distance is less than the given one.

Implements MbPlaneItem.

◆ PointOn()

void MbLine::PointOn	(	double &	t,
		MbCartPoint &	p
	)		const

overridevirtual

Calculate a point on the curve.

Correct parameter when getting out of domain bounds and calculate a point on the curve.

Parameters

[in]	t	- Curve parameter.
[out]	p	- A point on the curve.

Implements MbCurve.

◆ _PointOn()

void MbLine::_PointOn	(	double	t,
		MbCartPoint &	p
	)		const

overridevirtual

Calculate point at curve and its extension.

Calculate a point on the curve including the outside area determination parameter.

Parameters

[in]	t	- Curve parameter.
[out]	p	- A point on the curve.

Reimplemented from MbCurve.

◆ Explore()

void MbLine::Explore	(	double &	t,
		bool	ext,
		MbCartPoint &	pnt,
		MbVector &	fir,
		MbVector *	sec,
		MbVector *	thir
	)		const

overridevirtual

Calculate point and derivatives of object for given parameter.

Values of point and derivatives are calculated on parameter area and on extended curve.

Parameters

[in]	t	- Parameter.
[in]	ext	- On parameters area (false), on extended curve (true).
[out]	pnt	- Point.
[out]	fir	- Derivative with respect to t.
[out]	sec	- Second derivative with respect to t, if not nullptr.
[out]	thir	- Third derivative with respect to t, if not nullptr.

Reimplemented from MbCurve.

◆ DeletePart()

MbeState MbLine::DeletePart	(	double	t1,
		double	t2,
		MbCurve *&	part2
	)

overridevirtual

Delete the piece of a curve.

Delete a part of a curve between parameters t1 and t2. If the curve is split into two parts after deletion, then the initial object corresponds to the start part of a curve, and parameter 'part2' contains the end part of a curve. If the curve remained simply connected, then only the initial object changes.

Parameters

[in]	t1	- Start parameter of trimming.
[in]	t2	- End parameter of trimming.
[in,out]	part2	- The end part of a curve after deletion, if an initial curve is split into parts. It may be the only part after deletions, \ if the curve did not change (e. g. for a curve of MbLine type), in this case the returned value is dp_Degenerated.

Returns: A state of a curve after modification.

Implements MbCurve.

◆ TrimmPart()

MbeState MbLine::TrimmPart	(	double	t1,
		double	t2,
		MbCurve *&	part2
	)

overridevirtual

Keep the piece of a curve.

Leave a part of a curve between parameters t1 and t2.
In a case of success the returned value equals dp_Changed and a curve satisfies to the next conditions:

if an initial curve is closed then the start point of a trimmed curve should correspond to the parameter t1, the end point - to the parameter t2,

if an initial curve is not closed then the start point of a trimmed curve should correspond to the minimum parameter from t1 and t2, the end point - to the maximum one.

Parameters

[in]	t1	- Start parameter of trimming.
[in]	t2	- End parameter of trimming.
[in,out]	part2	- This may be filled by a result of trimming if the curve was not changed. In this case the returned value is dp_Degenerated. Otherwise nullptr is returned.

Returns: A state of a curve after modification:
dp_Degenerated - the curve is degenerated and there are possible three cases: the curve was not changed, because it would degenerate in a result of transformation, or it it was not changed and the result of trimming is 'part2',
dp_NoChanged - the curve was not changes,
dp_Changed - the curve is changed.

Warning: The function is designed for internal use only.

Implements MbCurve.

◆ Trimmed() [1/3]

MbCurve* MbLine::Trimmed	(	double	t1,
		double	t2,
		int	sense,
		const MbDimAccuracy &	xyEps,
		bool	saveParamLenAndLaw
	)		const

overridevirtual

Construct a trimmed curve with the given two-dimensional accuracy.

Constructs a trimmed curve, a start point of which corresponds to a point with parameter t1 and an end point corresponds to a point with parameter t2. Direction of the constructed curve relative to the initial curve may be changed by the parameter 'sense'. If the curve is closed, then there may be obtained a trimmed curve, passing through the start of a curve.
In a case of closed curve (or for an arc - exception) three parameters 'sense', t1 and t2 clearly define the result. In a case of unclosed curve the parameter 'sense' and parameter of trimming should correspond each other:
1) if sense == 1, then t1 < t2,
2) if sense == -1, then t1 > t2,
If there is a discrepancy between 'sense' and parameters of trimming, then 'sense' parameter has higher priority. If parameters t1 and t2 are equal and the curve is closed, then in result a closed curve should be obtained.

Parameters

[in]	t1	- Parameter corresponding to start of a trimmed curve.
[in]	t2	- Parameter corresponding to end of a trimmed curve.
[in]	sense	- Direction of a trimmed curve in relation to an initial curve. sense = 1 - direction does not change. sense = -1 - direction changes to the opposite value.
[in]	xyEps	- Two-dimensional accuracy. It is used for estimations near the points corresponding to the parameters t1 and t2.
[in]	saveParLenAndLaw	- Save parametric length and law.

Returns: A constructed trimmed curve.

Warning: Under development.

Implements MbCurve.

◆ HasLength()

bool MbLine::HasLength ( double & length ) const

overridevirtual

Calculate the metric length of a curve.

Calculate the metric length of a curve and save the result in the variable 'length'.

Parameters

[in,out] length - Calculated length of a curve.

Returns: True - if the length of a curve differs from null. Otherwise returns false.

Implements MbCurve.

◆ GetMetricLength()

double MbLine::GetMetricLength ( ) const

overridevirtual

Calculate the metric length of a curve.

If a length of a curve is already calculated and saved in the object then this function returns the existing result, without repeating of calculations. Otherwise the length is calculated by the function CalculateMetricLength().

Returns: Length of a curve.

Implements MbCurve.

◆ LengthBetween2Points()

virtual double MbLine::LengthBetween2Points	(	MbCartPoint &	p1,
		MbCartPoint &	p2,
		MbCartPoint *	pc = `nullptr`
	)		const

overridevirtual

Calculate minimal length of a curve between two points on it.

If a curve is not closed, then the length between points is clearly defined. If a curve is closed, then there is chosen the shortest path from the two possible paths. For a closed curve the desired part may be defined by the control points pc. In this case the such part of a curve is chosen, which is closer to a control point.

Parameters

[in]	p1	- The first point.
[in]	p2	- The second point
[in]	pc	- A control point

Returns: A length of a curve between points.

Reimplemented from MbCurve.

◆ DistanceAlong()

bool MbLine::DistanceAlong	(	double &	t,
		double	len,
		int	curveDir,
		double	eps = `Math::LengthEps`,
		VERSION	version = `Math::DefaultMathVersion()`
	)		const

overridevirtual

Translate parameter along the curve.

Translate parameter along the curve by the given distance at the given direction. The new value of parameter is saved in the variable t. If the curve is not closed and the length of its part from the point with parameter t to the end at the given direction is less than the required shift, then calculations are performed on extension of the curve, if it possible to construct such extension.

Parameters

[in,out]	t	- Input - the initial value of parameter. Output - the new value of parameter.
[in]	len	- The value of shift along the curve.
[in]	curveDir	- The offset direction. If curveDir is non-negative, then the shift is directed to the side of increasing of parameter. Otherwise - to the side of decreasing of parameter.
[in]	eps	- Computational tolerance.
[in]	version	- Version.

Returns: True - if the operation is performed successfully, otherwise false.

Reimplemented from MbCurve.

◆ Step()

double MbLine::Step	(	double	t,
		double	sag
	)		const

overridevirtual

Calculate parameter step.

Calculate parameter step for the curve's approximation by its sag value. Calculation of the step is performed with consideration of curvature radius. A step of curve's approximation is chosen in such way, that the deviation of a curve from its polygon does not exceed the given sag value.

Parameters

[in]	t	- A parameter defining the point on a curve, at which a step should be calculated.
[in]	sag	- Maximum feasible sag value.

Returns: A sag value by parameter at given point.

Reimplemented from MbCurve.

◆ DeviationStep()

double MbLine::DeviationStep	(	double	t,
		double	ang
	)		const

overridevirtual

Calculate parameter step.

Calculate parameter step for the curve's approximation by the deviation angle of the tangent vector. A step of curve's approximation is chosen in such way, that angular deviation of the tangent curve at the next point does not exceed the given value ang.

Parameters

[in]	t	- A parameter defining the point on a curve, at which a step should be calculated.
[in]	ang	- The maximum feasible deviation angle of tangent.

Returns: A sag value by parameter at given point.

Reimplemented from MbCurve.

◆ PointRelative()

MbeItemLocation MbLine::PointRelative	(	const MbCartPoint &	pnt,
		double	eps = `Math::LengthEps`
	)		const

overridevirtual

Define the point position relative to the curve.

There is defined on which side from a curve the point is located, by the positive direction of a curve.

Parameters

[in]	pnt	- A given point.
[in]	eps	- A tolerance of detection.

Returns: Iloc_InItem = 1 - if the point is on the left from a curve,
iloc_OnItem = 0 - if the point is on a curve,
iloc_OutOfItem = 1 - if the point is on the right from a curve.

Reimplemented from MbCurve.

◆ PointProjection()

double MbLine::PointProjection ( const MbCartPoint & pnt ) const

overridevirtual

Calculate the point projection to the curve.

Calculate the parameter of the curve corresponding to the projection of the given point on this curve.
This function does not allow the parameter to go beyond the parametric domain of the definition of an unclosed curve, unlike the NearPointProjection function.

Parameters

[in] pnt - A given point.

Returns: The found parameter for the projection of a point onto the curve.

Reimplemented from MbCurve.

◆ NearPointProjection()

bool MbLine::NearPointProjection	(	const MbCartPoint &	pnt,
		double	xEpsilon,
		double	yEpsilon,
		double &	t,
		bool	ext,
		MbRect1D *	tRange = `nullptr`
	)		const

overridevirtual

Find the point projection to the curve.

Find the nearest projection of a point on a curve (in the range of the curve) or on its continuation by the given initial approximation. If the parameter ext = true, then also search for a projection on the continuation of the curve. If the range of change of the 'tRange' parameter is specified, then find the projection in the specified range. A range of parameter may not belong to the domain of a curve. The Newton method is used.

Note: Mathematical kernel provides a thread-safe function implementation for its objects.

Parameters

[in]	pnt	- A given point.
[in]	xEpsilon	- A tolerance of detection of the projection by x axis.
[in]	yEpsilon	- A tolerance of detection of the projection by y axis.
[in,out]	t	- Input - initial approximation, output - parameter of a curve corresponding to the nearest projection.
[in]	ext	- A flag defining whether to seek projection on the extension of the curve.
[in]	tRange	- A range of parameter changing in which the solution should be found.

Returns: Returns true if the found parameter is in a valid range (according to the given ext, tRange parameters), or false - otherwise.

Reimplemented from MbCurve.

◆ PerpendicularPoint()

void MbLine::PerpendicularPoint	(	const MbCartPoint &	pnt,
		SArray< double > &	tFind
	)		const

overridevirtual

Find perpendiculars to a curve.

Find all perpendiculars to a curve from the given point. In this function a curve without extensions is considered.

Parameters

[in]	pnt	- A given point.
[in,out]	tFind	- An array of parameter on a curve, corresponding to the points on a curve, which the perpendiculars are passed through.

Reimplemented from MbCurve.

◆ IntersectHorizontal()

void MbLine::IntersectHorizontal	(	double	y,
		SArray< double > &	cross
	)		const

overridevirtual

Find intersections of a curve with horizontal line.

Parameters

[in]	y	- An ordinate of points of a horizontal line.
[in,out]	cross	- An array of parameters of a curve corresponding to the intersection points.

Reimplemented from MbCurve.

◆ IntersectVertical()

void MbLine::IntersectVertical	(	double	x,
		SArray< double > &	cross
	)		const

overridevirtual

Find intersections of a curve with vertical line.

Parameters

[in]	x	- An abscissa of points of a vertical line.
[in,out]	cross	- An array of parameters of a curve corresponding to the intersection points.

Reimplemented from MbCurve.

◆ IsClosed()

bool MbLine::IsClosed ( ) const

overridevirtual

Define whether the curve is periodic.

Define whether the curve is periodic.
A periodic curve is closed. A curve is considered as periodic if:

start point is coincident with end point;
derivatives in start point and end point coincide;
if there are breaks at curve (in cases when a curve is contour or polyline), then derivatives may not coincide; in Bezier curve derivatives should coincide by direction, but they may differ by absolute value.
Curves:
MbLine,
MbLineSegment,
MbCosinusoid,
MbContour (if it contains only a single segment of one of the listed types)
are not considered periodic when the start and end points coincide. The IsClosed() method always returns false for them.
Returns
True if a curve is closed.

Implements MbCurve.

◆ NurbsCurve() [1/2]

MbNurbs* MbLine::NurbsCurve ( const MbCurveIntoNurbsInfo & nInfo ) const

overridevirtual

Construct a NURBS copy of a curve.

Constructs a NURBS curve which approximates a given curve inside the range [t1, t2]. with a given direction. If it is possible, constructs the accurate curve, perhaps with multiple knots. The number of knots for NURBS is defined depending on the curve.

Parameters

[in,out]	nurbs	- A constructed NURBS-curve.
[in]	t1	- Parameter corresponding to start of approximated part of a curve.
[in]	t2	- Parameter corresponding to end of approximated part of a curve.
[in]	sense	- Does the direction of parameter increasing along the NURBS curve coincide with direction of the initial curve. 'sense' > 0 - direction coincide.
[in]	nInfo	- Parameters of conversion of a curve to NURBS.

Returns: The constructed NURBS curve or nullptr in a case of failure.

Implements MbCurve.

◆ NurbsCurve() [2/2]

MbCurve* MbLine::NurbsCurve ( const MbNurbsParameters & tParameters ) const

overridevirtual

Construct a NURBS copy of a curve.

Constructs a NURBS curve which approximates a given curve with the given parameters. In parameters the degree and the number of knots of a spline and the range of curve's parameters changing may be set. If the flag of accurate approximation is not set in parameters then NURBS without multiple knots is constructed.

Parameters

[in] tParameters - Parameters for the construction of a NURBS copy of the curve.

Returns: The constructed NURBS curve or nullptr in a case of failure.

Reimplemented from MbCurve.

◆ GetProperties()

void MbLine::GetProperties ( MbProperties & properties )

overridevirtual

Get properties of the object.

Get internal data (properties) of an object for viewing and modification.

Parameters

[in] properties - Container for internal data of an object.

Implements MbPlaneItem.

◆ SetProperties()

void MbLine::SetProperties ( const MbProperties & properties )

overridevirtual

Change properties of the object.

Change internal data (properties) of object is performed by copying of corresponding values from the given object.

Parameters

[in] properties - Container for internal data of an object.

Implements MbPlaneItem.

◆ IsVisibleInRect() [2/2]

bool MbCurve::IsVisibleInRect

override

Determine visibility of an object in rectangle.

Determine whether an object is visible in the given rectangle. There is a possibility to perform a fast check or more thorough check when the second parameter has a corresponding value.

Parameters

[in]	rect	- A given two-dimensional rectangle.
[in]	exact	- Whether to perform a more thorough check.

Returns: true, if the object is fully or partially contained in the rectangle, otherwise false.

◆ Trimmed() [2/3]

virtual MbCurve* MbCurve::Trimmed

Construct a trimmed curve.

Constructs a trimmed curve, a start point of which corresponds to a point with parameter t1 and an end point corresponds to a point with parameter t2. Direction of the constructed curve relative to the initial curve may be changed by the parameter 'sense'. If the curve is closed, then there may be obtained a trimmed curve, passing through the start of a curve.
In a case of closed curve (or for an arc - exception) three parameters 'sense', t1 and t2 clearly define the result. In a case of unclosed curve the parameter 'sense' and parameter of trimming should correspond each other:
1) if sense == 1, then t1 < t2,
2) if sense == -1, then t1 > t2,
If there is a discrepancy between 'sense' and parameters of trimming, then 'sense' parameter has higher priority. If parameters t1 and t2 are equal and the curve is closed, then in result a closed curve should be obtained.

Parameters

[in]	t1	- Parameter corresponding to start of a trimmed curve.
[in]	t2	- Parameter corresponding to end of a trimmed curve.
[in]	sense	- Direction of a trimmed curve in relation to an initial curve. sense = 1 - direction does not change. sense = -1 - direction changes to the opposite value.
[in]	saveParLenAndLaw	- Save parametric length and law.

Returns: A constructed trimmed curve.

◆ Trimmed() [3/3]

virtual MbCurve* MbCurve::Trimmed

Construct a trimmed curve with the given two-dimensional accuracy.

Constructs a trimmed curve, a start point of which corresponds to a point with parameter t1 and an end point corresponds to a point with parameter t2. Direction of the constructed curve relative to the initial curve may be changed by the parameter 'sense'. If the curve is closed, then there may be obtained a trimmed curve, passing through the start of a curve.
In a case of closed curve (or for an arc - exception) three parameters 'sense', t1 and t2 clearly define the result. In a case of unclosed curve the parameter 'sense' and parameter of trimming should correspond each other:
1) if sense == 1, then t1 < t2,
2) if sense == -1, then t1 > t2,
If there is a discrepancy between 'sense' and parameters of trimming, then 'sense' parameter has higher priority. If parameters t1 and t2 are equal and the curve is closed, then in result a closed curve should be obtained.

Parameters

[in]	t1	- Parameter corresponding to start of a trimmed curve.
[in]	t2	- Parameter corresponding to end of a trimmed curve.
[in]	sense	- Direction of a trimmed curve in relation to an initial curve. sense = 1 - direction does not change. sense = -1 - direction changes to the opposite value.
[in]	xyEps	- Two-dimensional accuracy. It is used for estimations near the points corresponding to the parameters t1 and t2.
[in]	saveParLenAndLaw	- Save parametric length and law.

Returns: A constructed trimmed curve.

Warning: Under development.

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

cur_line.h

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ IsSimilar()

◆ SetEqual()

◆ IsSame()

◆ Transform()

◆ Move()

◆ Rotate()

◆ Duplicate()

◆ AddYourGabaritMtr()

◆ CalculateGabarit()

◆ CalculateLocalGabarit()

◆ IsVisibleInRect() [1/2]

◆ DistanceToPointIfLess()

◆ PointOn()

◆ _PointOn()

◆ Explore()

◆ DeletePart()

◆ TrimmPart()

◆ Trimmed() [1/3]

◆ HasLength()

◆ GetMetricLength()

◆ LengthBetween2Points()

◆ DistanceAlong()

◆ Step()

◆ DeviationStep()

◆ PointRelative()

◆ PointProjection()

◆ NearPointProjection()

◆ PerpendicularPoint()

◆ IntersectHorizontal()

◆ IntersectVertical()

◆ IsClosed()

◆ NurbsCurve() [1/2]

◆ NurbsCurve() [2/2]

◆ GetProperties()

◆ SetProperties()

◆ IsVisibleInRect() [2/2]

◆ Trimmed() [2/3]

◆ Trimmed() [3/3]