Elliptical arc in three-dimensional space. More...

#include <cur_arc3d.h>

Inheritance diagram for MbArc3D:

Collaboration diagram for MbArc3D:

Public Member Functions
	MbArc3D (const MbCartPoint3D &pc, const MbCartPoint3D &p1, const MbCartPoint3D &p2, int initSense=0)
	Constructor of an ellipse, a circle or an elliptical or circular arc. More...

	MbArc3D (const MbCartPoint3D &p0, const MbCartPoint3D &p1, const MbCartPoint3D &p2, int n, bool closed)
	Constructor of a circle or a circular arc. More...

	MbArc3D (const MbCartPoint3D &pc, const MbCartPoint3D &p1, const MbCartPoint3D &p2, const MbVector3D &aZ, int initSense)
	Constructor of a circle or a circular arc. More...

	MbArc3D (const MbCartPoint3D &p0, const MbVector3D &vZ, const MbVector3D &vX, double aa, double bb, double angle)
	Constructor of an elliptical arc. More...

	MbArc3D (const MbCartPoint3D &p1, const MbCartPoint3D &p2, double a_4, MbVector3D &vZ)
	Constructor of a circular arc. More...

	MbArc3D (const MbCartPoint3D &p1, const MbCartPoint3D &p2, const MbVector3D &dirInPoint, bool insecond)
	Constructor of a circle by two points and direction to the center from one of them. More...

	MbArc3D (const MbPlacement3D &place, double aa, double bb, double angle)
	Constructor of an elliptical arc. More...

	MbArc3D (const MbArc3D &init, double t1, double t2, int initSense, const MbDimAccuracy &xyzEps=MbDimAccuracy::threeDimAcc)
	Constructor of an elliptical arc. More...

	MbArc3D (const MbArc3D &init, MbCartPoint3D p1, MbCartPoint3D p2, int initSense)
	Constructor of an elliptical arc. More...

	MbArc3D (const MbArc &ellipse, const MbPlacement3D &place)
	Constructor by a local system and two-dimensional elliptical arc. More...

bool	Init (const MbCartPoint3D &p0, const MbCartPoint3D &p1, const MbCartPoint3D &p2, int n, bool closed)
	Initialization of a circular arc by three points; (n == 0) - a circle or an arc by the center and two points, (n == 1) - a circle or an arc by three points. Return true if successful.

bool	Init (double a_2, const MbCartPoint3D &p1, const MbCartPoint3D &p2, MbVector3D &vZ)
	Initialization of a circular arc by the starting and the end points and 1/2 of the arc opening angle. Return true if successful.

void	Init (const MbArc &ellipse, const MbPlacement3D &pos)
	Initialization of an arc by 2D-arc and local coordinate system.

bool	Init (const MbCartPoint3D &p1, const MbCartPoint3D &p2, const MbVector3D &dirInPoint, bool insecond)
	Initialization of a circle by two points and direction to the center in one of them. Returns true if successful.

void	Inverse (MbRegTransform *iReg=nullptr) override
	Change direction of a curve.

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	MetricStep (double t, double length) const override
	Calculate parameter step. More...

bool	NearPointProjection (const MbCartPoint3D &, double &t, bool ext, MbRect1D *tRange=nullptr) const override
	Find the point projection to the curve. More...

MbNurbs3D *	NurbsCurve (const MbCurveIntoNurbsInfo &) const override
	Construct a NURBS copy of a curve. More...

MbCurve3D *	NurbsCurve (const MbNurbsParameters &) const override
	Construct a NURBS copy of a curve. More...

MbCurve3D *	Trimmed (double t1, double t2, int sense, const MbDimAccuracy &xyzEps, bool saveParamLenAndLaw) const override
	Construct a trimmed curve with the given two-dimensional accuracy. More...

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

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

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

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

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

void	GetPointsByEvenLengthDelta (size_t n, std::vector< MbCartPoint3D > &pnts) const override
	Get n points of a curve with equal intervals by arc length.

MbCurve *	GetMap (const MbMatrix3D &, MbRect1D pRgn=nullptr, VERSION version=Math::DefaultMathVersion(), bool coincParams=nullptr) const override
	Construct a planar projection of a piece of a space curve. More...

MbCurve *	GetMapPsp (const MbMatrix3D &, double zNear, MbRect1D *pRgn=nullptr) const override
	Construct a planar projection of a piece of a space curve. More...

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

bool	GetCircleAxis (MbAxis3D &) const override
	Get an axis of a circle which is geometrically coincident to the given curve. More...

bool	GetPlaneCurve (MbCurve *&curve2d, MbPlacement3D &place, bool saveParams, PlanarCheckParams params=PlanarCheckParams()) const override
	Get planar curve and placement if the space curve is planar. More...

void	AddYourGabaritTo (MbCube &) const override
	Expand sent bounding box (a.k.a. gabarit), so that it included the object. More...

void	CalculateGabarit (MbCube &) const override
	Calculate bounding box of a curve.

void	CalculateLocalGabarit (const MbMatrix3D &, MbCube &) const override
	To compute bounding box in a local coordinate system. More...

bool	IsShift (const MbSpaceItem &, MbVector3D &, bool &isSame, double accuracy=LENGTH_EPSILON) const override
	Whether the object is a shift.

bool	IsSimilarToCurve (const MbCurve3D &curve, double precision=METRIC_PRECISION) const override
	Whether the curves to union (joining) are similar.

void	SetRadiusA (double aa)
	Set the major semiaxis.

void	SetRadiusB (double bb)
	Set the minor semiaxis.

void	SetRadius (double r)
	Set circle radius.

double	GetRadiusA () const
	Get the major semiaxis.

double	GetRadiusB () const
	Get the minor semiaxis.

void	SetLimitPoint (ptrdiff_t number, const MbCartPoint3D &)
	Replace a start (1) or end (2) point of the arc.

double	GetAngle () const
	Get the end angle of the arc.

void	SetAngle (double ang)
	Change the end angle of the arc.

bool	IsCircle (double eps=METRIC_REGION) const
	Whether the arc of an ellipse is an arc of a circle.

double	CheckParam (double &t) const
	Set the parameter into the region of the legal values.

void	ParamToAngle (double &t) const
	Convert parameter of curve to the angle.

void	AngleToParam (double &t) const
	Convert an angle of curve to a parameter of curve.

double	GetTrim1 () const
	Parameters of start point.

double	GetTrim2 () const
	Parameters of end point.

bool	MakeTrimmed (double t1, double t2)
	Setting of the parameters of trimming with keeping the curve direction.

void	AlignXAxis ()
	Rotate the placement of a circular arc so as the ox-axis points to the start point of the arc.

bool	IsPlanar (double accuracy=METRIC_EPSILON) const override
	Whether the curve is planar?

bool	GetPlacement (MbPlacement3D &place, PlanarCheckParams params=PlanarCheckParams()) const override
	Fill the placement if a curve is planar.

void	GetCentre (MbCartPoint3D &) const override
	Give the curve center.

void	GetWeightCentre (MbCartPoint3D &) const override
	Give the gravity center of a curve.

MbResultType	Extend (const MbCurveExtensionParameters3D &parameters, c3d::SpaceCurveSPtr &resCurve) const override
	Extend the curve. More...

bool	Normalize ()
	Orthonormalize the local coordinate system.

virtual MbCurve3D *	Trimmed (double t1, double t2, int sense, bool saveParamLenAndLaw=false) const
	Construct a trimmed curve. More...

virtual MbCurve3D *	Trimmed (double t1, double t2, int sense, const MbDimAccuracy &xyzEps, bool saveParamLenAndLaw) const
	Construct a trimmed curve with the given two-dimensional accuracy. More...

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

MbSpaceItem &	Duplicate (MbRegDuplicate *=nullptr) const override
	Create a copy of the object. More...

void	Transform (const MbMatrix3D &, MbRegTransform *=nullptr) override
	Convert the object according to the matrix. More...

void	Move (const MbVector3D &, MbRegTransform *=nullptr) override
	Move an object along a vector. More...

void	Rotate (const MbAxis3D &, double angle, MbRegTransform *=nullptr) override
	Rotate an object around an axis at a given angle. More...

bool	IsSame (const MbSpaceItem &other, double accuracy=LENGTH_EPSILON) const override
	Determine whether an object is equal. More...

bool	SetEqual (const MbSpaceItem &) override
	Make objects equal if they are similar. More...

double	DistanceToPoint (const MbCartPoint3D &) const override
	Determine the distance to the point. More...

bool	IsSpaceSame (const MbSpaceItem &item, double eps=METRIC_REGION) const override
	Are the objects identical in space?

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

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

void	GetBasisPoints (MbControlData3D &) const override
	Get control points of object.

void	SetBasisPoints (const MbControlData3D &) override
	Change the object by control points.

Functions for curve domain description
double	GetTMax () const override
	Get the maximum value of parameter.

double	GetTMin () const override
	Get the minimum value of parameter.

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

double	GetPeriod () const override
	Return period. If a curve is not periodic then 0.

Functions for working in the domain of a curve.
PointOn, FirstDer, SecondDer, ThirdDer,... functions correct parameter when it runs out the domain.
void	PointOn (double &t, MbCartPoint3D &) const override
	Calculate a point on the curve. More...

void	FirstDer (double &t, MbVector3D &) const override
	Calculate first derivative.

void	SecondDer (double &t, MbVector3D &) const override
	Calculate second derivative.

void	ThirdDer (double &t, MbVector3D &) const override
	Calculate third derivative.

void	Normal (double &t, MbVector3D &) const override
	Calculate main normal vector.

Functions for working inside and outside of the curve domain.
_PointOn, _FirstDer, _SecondDer, _ThirdDer,... functions don't correct parameter when it runs out the domain. The bounded curve is extended due to the equations of curve.
void	_PointOn (double t, MbCartPoint3D &) const override
	Calculate point at curve and its extension. More...

void	_FirstDer (double t, MbVector3D &) const override
	Calculate first derivative at curve and its extension.

void	_SecondDer (double t, MbVector3D &) const override
	Calculate second derivative at curve and its extension.

void	_ThirdDer (double t, MbVector3D &) const override
	Calculate third derivative at curve and its extension.

void	_Normal (double t, MbVector3D &) const override
	Calculate main normal vector (normalized) 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, MbCartPoint3D &pnt, MbVector3D &fir, MbVector3D sec, MbVector3D thir) const override
	Calculate point and derivatives of object for given parameter. More...

Public Member Functions inherited from MbCurve3D
virtual	~MbCurve3D ()
	Destructor.

virtual void	Accept (Visitor &visitor)
	Implementation of a function initializing a visit of an object.

size_t	size () const
	Size of curve interpreted as vector of curves.

const MbCurve3D *	operator[] (size_t) const
	An access operator.

MbeSpaceType	Type () const override
	Get the group object type.

MbeSpaceType	Family () const override
	Get family of objects.

virtual MbCurve3D &	InverseDuplicate () const
	Create a copy with changed direction.

double	DistanceToPoint (const MbCartPoint3D &) const override
	Determine the distance to the point. More...

void	AddYourGabaritTo (MbCube &) const override
	Expand sent bounding box (a.k.a. gabarit), so that it included the object. More...

void	Refresh () override
	Translate all the time (mutable) data objects in an inconsistent (initial) state.

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

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

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

virtual void	Tangent (double &t, MbVector3D &) const
	Calculate tangent vector (normalized).

virtual void	BNormal (double &t, MbVector3D &) const
	Calculate binormal vector.

virtual void	_Tangent (double t, MbVector3D &) const
	Calculate tangent vector (normalized) at curve and its extension.

virtual void	_BNormal (double t, MbVector3D &) const
	Calculate binormal vector (normalized) at curve and its extension.

virtual void	FastApproxExplore (double &t, MbCartPoint3D &pnt, MbVector3D &fir, MbVector3D *sec) const
	Calculate point and derivatives on the curve. More...

double	CurveStep (const double &t, const MbStepData &stepData) const
	Calculate parameter step. More...

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

virtual const MbCurve3D &	GetBasisCurve () const
	Returns the base curve if exists or itself.

virtual MbCurve3D &	SetBasisCurve ()
	Returns the base curve if exists or itself.

virtual void	ThirdMetricDer (double t, MbVector3D &vect) const
	Calculate second derivative of tangent.

MbNurbs3D *	NurbsCurve (const MbCurveIntoNurbsInfo *nInfo=nullptr) const
	Construct a NURBS copy of a curve. More...

virtual size_t	NurbsCurveMinPoints (const MbNurbsParameters &tParameters, double epsilon=c3d::METRIC_DELTA) const
	Define the number of knots of a NURBS curve which is required to approximate the curve with the given tolerance. More...

virtual MbCurve3D *	Trimmed (double t1, double t2, int sense, bool saveParamLenAndLaw=false) const
	Construct a trimmed curve. More...

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

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

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

void	CalculateLocalGabarit (const MbMatrix3D &into, MbCube &cube) const override
	To compute bounding box in a local coordinate system. More...

virtual bool	IsDegenerate (double eps=METRIC_PRECISION) const
	Check whether the curve is degenerated.calculate.

virtual bool	IsStraight (bool ignoreParams=false) const
	Whether the line is straight?

virtual bool	IsSmoothConnected (double angleEps) const
	Are joints of contour/curve smooth?

virtual void	ChangeCarrier (const MbSpaceItem &item, MbSpaceItem &init)
	Change the carrier. For surface curves.

virtual bool	ChangeCarrierBorne (const MbSpaceItem &item, MbSpaceItem &init, const MbMatrix &matr)
	Change the carrier. More...

MbProperty &	CreateProperty (MbePrompt name) const override
	Create your own property with the name.

void	CalculateMesh (const MbStepData &stepData, const MbFormNote &note, MbMesh &mesh) const override
	Build polygonal copy mesh. More...

virtual void	CalculatePolygon (const MbStepData &stepData, MbPolygon3D &polygon) const
	Calculate an array of points for drawing. More...

virtual MbeNewtonResult	PointProjectionNewton (const MbCartPoint3D &p, size_t iterLimit, double &t, bool ext) const
	Find the point projection to the curve. More...

virtual MbeNewtonResult	IsoclinalNewton (const MbVector3D &dir, size_t iterLimit, double &t) const
	Find isoclines of a curve. More...

virtual void	GetIsoclinal (const MbVector3D &nor, SArray< double > &tIso) const
	Find all isoclines of a curve. More...

virtual double	DistanceToCurve (const MbCurve3D &curve2, double &t1, double &t2) const
	Calculate the nearest distance to a curve.

virtual double	DistanceToPlace (const MbPlacement3D &place, double &t0, double &angle) const
	The nearest point of a curve by the placement.

virtual MbCurve *	GetProjection (const MbPlacement3D &place, VERSION version) const
	Construct a planar projection of a space curve to a plane. More...

void	GetPointsByEvenParamDelta (size_t n, std::vector< MbCartPoint3D > &pnts) const
	Get n points of a curve with equal intervals by parameter.

void	GetPointsByEvenParamDelta (size_t n, SArray< MbCartPoint3D > &pnts) const

void	GetPointsByEvenLengthDelta (size_t n, SArray< MbCartPoint3D > &pnts) const

void	GetBasisPoints (MbControlData3D &) const override
	Get control points of object.

void	SetBasisPoints (const MbControlData3D &) override
	Change the object by control points.

virtual bool	IsContinuousDerivative (bool &contLength, bool &contDirect, c3d::DoubleVector *params=nullptr, double epsilon=EPSILON) const
	Have the first derivative of the curve the continuous length and direction? More...

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

bool	IsSpaceNear (const MbCurve3D &curve, double eps, bool ext, double devSag=5.0 *Math::deviateSag) const
	Check whether the two curves are metrically close. More...

bool	IsPointOn (const MbCartPoint3D &, double eps=METRIC_PRECISION) const
	Check whether a point is on a curve or not.

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

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

MbCartPoint3D	PointOn (double &t) const
	Calculate point on the curve.

MbVector3D	FirstDer (double &t) const
	Calculate first derivative.

MbVector3D	SecondDer (double &t) const
	Calculate second derivative.

MbVector3D	ThirdDer (double &t) const
	Calculate third derivative.

virtual void	GetCurvatureSpecialPoints (std::vector< c3d::DoublePair > &points) const
	Find all the special points of the curvature function of the curve. More...

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.

MbCartPoint3D	GetLimitPoint (ptrdiff_t number) const
	Calculate the boundary point. More...

void	GetLimitPoint (ptrdiff_t number, MbCartPoint3D &pnt) const
	Calculate the boundary point. More...

MbVector3D	GetLimitTangent (ptrdiff_t number) const
	Calculate a tangent vector to the boundary point. More...

void	GetLimitTangent (ptrdiff_t number, MbVector3D &v) const
	Calculate a tangent vector to the boundary point. More...

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

bool	SetInParamRegion (double &t) const
	Move to the parametric region.

bool	IsParamOn (double t, double eps) const
	Check whether a parameter is in the range of the curve.

bool	IsInverseSame (const MbCurve3D &curve, double accuracy=LENGTH_EPSILON) const
	Whether an inversed curve is the same.

virtual bool	IsReparamSame (const MbCurve3D &curve, double &factor) const
	Define whether a reparameterized curve is the same. More...

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

virtual double	GetParamToUnit (double t) const
	Get increment of parameter, corresponding to the unit length in space.

double	GetTEpsilon () const
	Get the minimum distinguishable value of parameter.

double	GetTEpsilon (double t) const
	Get the minimum distinguishable value of parameter.

double	GetTRegion () const
	Get the minimum distinguishable value of parameter.

double	GetTRegion (double t) const
	Get the minimum distinguishable value of parameter.

double	GetTRegion (double t, const MbDimAccuracy &xyzEps) const
	Get the minimum distinguishable value of parameter with the given three-dimensional accuracy according to parameter.

virtual const MbCurve3D &	GetSubstrate () const
	Get a substrate or itself.

virtual MbCurve3D &	SetSubstrate ()
	Get a substrate or itself.

virtual int	SubstrateCurveDirection () const
	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.

bool	GetPlaneCurve (SPtr< MbCurve > &curve2d, MbPlacement3D &place, bool saveParams, PlanarCheckParams params=PlanarCheckParams()) const
	Get planar curve and placement if the space curve is planar. More...

bool	GetPlaneCurve (SPtr< const MbCurve > &curve2d, MbPlacement3D &place, bool saveParams, PlanarCheckParams params=PlanarCheckParams()) const
	Get planar curve and placement if the space curve is planar. More...

virtual bool	GetSurfaceCurve (MbCurve &curve2d, MbSurface &surface, VERSION version=Math::DefaultMathVersion()) const
	Get surface curve if the space curve is surface (after the using call DeleteItem for arguments)

bool	GetSurfaceCurve (SPtr< MbCurve > &curve2d, SPtr< MbSurface > &surface, VERSION version=Math::DefaultMathVersion()) const
	Get surface curve if the space curve is surface (after the using call DeleteItem for arguments)

bool	GetSurfaceCurve (SPtr< const MbCurve > &curve2d, SPtr< const MbSurface > &surface, VERSION version=Math::DefaultMathVersion()) const
	Get surface curve if the space curve is surface (after the using call DeleteItem for arguments)

void	CalculateGrid (double radius, const MbStepData &stepData, MbMesh &mesh) const
	Approximation of a curve by the flat tube with the given radius.

SimpleName	GetCurveName () const
	A curve name.

void	SetCurveName (SimpleName newName)
	Set a curve name.

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

void	PrepareWrite () const
	Register object. More...

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

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

virtual bool	IsSimilar (const MbSpaceItem &item) const
	Determine whether an object is similar. More...

void	CalculateWire (const MbStepData &stepData, MbMesh &mesh) const

void	CalculateWire (double sag, MbMesh &mesh) const

virtual void	GetBasisItems (RPArray< MbSpaceItem > &)
	Outstanding reference objects in a container sent.

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.

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.

Static Public Member Functions
static MbArc3D *	Create (const MbCartPoint3D &pc, const MbCartPoint3D &p1, const MbCartPoint3D &p2, int initSense=0)
	Create ellipse, a circle or an elliptical or circular arc. More...

static MbArc3D *	Create (const MbCartPoint3D &p0, const MbCartPoint3D &p1, const MbCartPoint3D &p2, int n, bool closed)
	Create circle or a circular arc. More...

static MbArc3D *	Create (const MbCartPoint3D &pc, const MbCartPoint3D &p1, const MbCartPoint3D &p2, const MbVector3D &aZ, int initSense)
	Create circle or a circular arc. More...

static MbArc3D *	Create (const MbCartPoint3D &p0, const MbVector3D &vZ, const MbVector3D &vX, double aa, double bb, double angle)
	Create elliptical arc. More...

static MbArc3D *	Create (const MbCartPoint3D &p1, const MbCartPoint3D &p2, double a_4, MbVector3D &vZ)
	Create circular arc. More...

static MbArc3D *	Create (const MbCartPoint3D &p1, const MbCartPoint3D &p2, const MbVector3D &dirInPoint, bool insecond)
	Create circle by two points and direction to the center from one of them. More...

Protected Member Functions
	MbArc3D ()
	Constructor of a circle with default parameters. More...

Protected Member Functions inherited from MbCurve3D
	MbCurve3D ()
	Default constructor.

	MbCurve3D (const MbCurve3D &other)
	Copy-constructor.

Protected Member Functions inherited from MbSpaceItem
	MbSpaceItem ()
	Default constructor.

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

Protected Attributes
MbPlacement3D	position
	Local coordinate system.

double	a
	Radius of semiaxis along X.

double	b
	Radius of semiaxis along Y.

double	trim1
	The start point parameters.

double	trim2
	The end point parameters.

bool	closed
	Closedness.

MbCube	cube
	Bounding box.

Protected Attributes inherited from MbCurve3D
SimpleName	name
	A curve name. The object data is temporary and used internally.

Detailed Description

Elliptical arc in three-dimensional space.

The elliptical arc is described by two radii a and b and two parameters trim1 and trim2 given in the local coordinate system 'position'.
Parameters 'trim1' and 'trim2' are measured along the arc in direction from position.axisX axis to position.axisY axis. Parameters 'trim1' and 'trim2' will be called parameters of trimming. Values of parameters of trimming equal to 0 and 2pi correspond to a point on position.axisX axis.
Parameter t of curve possesses the values in the range: 0<=t<=trim2-trim1. The curve can be closed. For closed curve: trim2-trim1=2pi.
Radius-vector of the curve in the method PointOn(double&t,MbCartPoint3D&r) is described by the function
r(t) = position.origin + (a cos(trim1+t) position.axisX) + (b sin(trim1+t) position.axisY).
Radii of the curve must be positive: a>0, b>0.
The following inequalities must be satisfied for the parameters of trimming: trim1<trim2.
Local coordinate system 'position' can be both right and left.

Constructor & Destructor Documentation

◆ MbArc3D() [1/11]

MbArc3D::MbArc3D ( )

protected

Constructor of a circle with default parameters.

A circle is created with center in the origin and zero radius.

◆ MbArc3D() [2/11]

MbArc3D::MbArc3D	(	const MbCartPoint3D &	pc,
		const MbCartPoint3D &	p1,
		const MbCartPoint3D &	p2,
		int	initSense = `0`
	)

Constructor of an ellipse, a circle or an elliptical or circular arc.

An arc centered in point 'pc' is created.
The first semiaxis is determines as the distance between points pc and p1. The second semiaxis is determined as the length of projection of the vector from pc to p2 onto the perpendicular to (p1 - pc). The start point of the arc lies on the ray starting from the circle center and passing through point 'p1'. The end point is on the ray from the center passing through the point 'p2'.
Parameter 'initSense' specifies completeness and the arc direction. If initSense == 0, then the complete ellipse or circle is constructed.
If initSense > 0, then the direction of moving is counterclockwise if seeing against the vector product (p1 - pc) and (p2 - pc).
If initSense < 0, , then the direction of moving is counterclockwise if seeing against the vector product (p1 - pc) and(p2 - pc).

Deprecated:: The method is deprecated.

Parameters

[in]	pc	- Center of the ellipse or the circle.
[in]	p1	- A point determining the beginning of the curve and the first semiaxis.
[in]	p2	- A point determining the end of the curve and the second semiaxis.
[in]	initSense	- Determines the completeness and the direction. initSense == 0 - closed curve initSense > 0 - moving counterclockwise, initSense < 0 - clockwise.

◆ MbArc3D() [3/11]

MbArc3D::MbArc3D	(	const MbCartPoint3D &	p0,
		const MbCartPoint3D &	p1,
		const MbCartPoint3D &	p2,
		int	n,
		bool	closed
	)

Constructor of a circle or a circular arc.

Constructor of a circle or a circular arc by one of two methods.

Deprecated:: The method is deprecated.

Parameters

[in]	p0	- Center (n == 0) or starting point (n != 0).
[in]	p1	- Starting point (n == 0) or point the circle passes through (n == 1).
[in]	p2	- A point determining the end of the curve and the second semiaxis.
[in]	n	- The parameter defines the method of arc construction. If n == 0, then a circle or a circular arc have the center in point p0. If n == 1, then a circle or an arc passes through the specified three points. If \|n\| == 2 & closed == false, then an arc passes through p0 and p2 but not p1.
[in]	closed	- Specifies a circle (true) or an arc (false).

◆ MbArc3D() [4/11]

MbArc3D::MbArc3D	(	const MbCartPoint3D &	pc,
		const MbCartPoint3D &	p1,
		const MbCartPoint3D &	p2,
		const MbVector3D &	aZ,
		int	initSense
	)

Constructor of a circle or a circular arc.

A circular arc is created with a center in point 'pc'. Points 'p1' and 'p2' specify the bounds of arc. The start point of the arc lies on point 'p1'. The end point is on the ray passing through the point 'p2'. Parameter 'initSense' specifies the arc direction.

Deprecated:: The method is deprecated.

Parameters

[in]	pc	- Center of circle.
[in]	p1	- A point specifying the beginning of the arc.
[in]	p2	- A point specifying the end of the arc.
[in]	aZ	- A direction of axis Z local coordinate system of the arc.
[in]	initSense	- Arc direction. If initSense > 0, then the orientation is counterclockwise if you look towards the vector aZ. If initSense < 0, then the orientation is clockwise if you look towards the vector aZ. If initSense = 0, then the circle is building.

◆ MbArc3D() [5/11]

MbArc3D::MbArc3D	(	const MbCartPoint3D &	p0,
		const MbVector3D &	vZ,
		const MbVector3D &	vX,
		double	aa,
		double	bb,
		double	angle
	)

Constructor of an elliptical arc.

An elliptical arc is created with the given semiaxes and the local coordinate system. 'angle' determines the arc angle. The angle is measured from the OX axis counterclockwise. The angle is given in radians.

Deprecated:: The method is deprecated.

Parameters

[in]	p0	- The ellipse local coordinate system center.
[in]	vZ	- Z-axis of the local coordinate system of the ellipse.
[in]	vX	- X-axis of the local coordinate system of the ellipse.
[in]	aa	- Radius of semiaxis along X.
[in]	bb	- Radius of semiaxis along Y.
[in]	angle	- An angle specifying the end of the arc.

◆ MbArc3D() [6/11]

MbArc3D::MbArc3D	(	const MbCartPoint3D &	p1,
		const MbCartPoint3D &	p2,
		double	a_4,
		MbVector3D &	vZ
	)

Constructor of a circular arc.

An arc is created with ends at the given points. A circle radius is defined by the given tangent of 1/4 of arc opening angle.

Deprecated:: The method is deprecated.

Parameters

[in]	p1	- Beginning of the arc.
[in]	p2	- End of the arc.
[in]	a4	- Tangent of 1/4 of the arc opening angle.
[in]	vZ	- Axis of the arc.

◆ MbArc3D() [7/11]

MbArc3D::MbArc3D	(	const MbCartPoint3D &	p1,
		const MbCartPoint3D &	p2,
		const MbVector3D &	dirInPoint,
		bool	insecond
	)

Constructor of a circle by two points and direction to the center from one of them.

A circle is created by two points and direction at one of them.

Deprecated:: The method is deprecated.

Parameters

[in]	p1	- The starting point.
[in]	p2	- The end point.
[in]	dirInPoint	- Direction at one of points (p1 or p2) to the center of the circle.
[in]	insecond	- Direction from the first point (insecond == true) to the circle center.

◆ MbArc3D() [8/11]

MbArc3D::MbArc3D	(	const MbPlacement3D &	place,
		double	aa,
		double	bb,
		double	angle
	)

Constructor of an elliptical arc.

An elliptical arc is created with the given semiaxes and the local coordinate system. 'angle' determines the arc angle. The angle is measured from the OX axis counterclockwise. The angle is given in radians.

Parameters

[in]	place	- The local coordinate system of the ellipse.
[in]	aa	- Radius of semiaxis along X.
[in]	bb	- Radius of semiaxis along Y.
[in]	angle	- An angle specifying the end of the arc.

◆ MbArc3D() [9/11]

MbArc3D::MbArc3D	(	const MbArc3D &	init,
		double	t1,
		double	t2,
		int	initSense,
		const MbDimAccuracy &	xyzEps = `MbDimAccuracy::threeDimAcc`
	)

Constructor of an elliptical arc.

An elliptical arc is constructed with the local coordinate system and semiaxes of the given ellipse. t1 and t2 specify the start and the end angles of the arc. The angles are measured from the OX axis counterclockwise. The angles are given in radians. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the direction of moving is counterclockwise.

Parameters

[in]	init	- A pattern ellipse.
[in]	t1	- An angle specifying the beginning of the arc.
[in]	t2	- An angle specifying the end of the arc.
[in]	initSense	- Direction. initSense > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'initSense' can't be equal to zero.
[in]	xyzEps	- Three-dimensional accuracy.

◆ MbArc3D() [10/11]

MbArc3D::MbArc3D	(	const MbArc3D &	init,
		MbCartPoint3D	p1,
		MbCartPoint3D	p2,
		int	initSense
	)

Constructor of an elliptical arc.

An elliptical arc is constructed with the local coordinate system and semiaxes of the given ellipse. Projections of p1 and p2 onto 'init' determines the starting and the end angles of the arc. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the direction of moving is counterclockwise.

Parameters

[in]	init	- A pattern ellipse.
[in]	p1	- A point specifying the beginning of the arc.
[in]	p2	- A point specifying the end of the arc.
[in]	initSense	- Direction. initSense > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'initSense' can't be equal to zero.

◆ MbArc3D() [11/11]

MbArc3D::MbArc3D	(	const MbArc &	ellipse,
		const MbPlacement3D &	place
	)

Constructor by a local system and two-dimensional elliptical arc.

Constructor by a local coordinate system and two-dimensional elliptical arc.

Parameters

[in]	ellipse	- Two-dimensional elliptical arc.
[in]	place	- A local coordinate system.

Member Function Documentation

◆ Create() [1/6]

static MbArc3D* MbArc3D::Create	(	const MbCartPoint3D &	pc,
		const MbCartPoint3D &	p1,
		const MbCartPoint3D &	p2,
		int	initSense = `0`
	)

static

Create ellipse, a circle or an elliptical or circular arc.

An arc centered in point 'pc' is created.
The first semiaxis is determines as the distance between points pc and p1. The second semiaxis is determined as the length of projection of the vector from pc to p2 onto the perpendicular to (p1 - pc). The start point of the arc lies on the ray starting from the circle center and passing through point 'p1'. The end point is on the ray from the center passing through the point 'p2'.
Parameter 'initSense' specifies completeness and the arc direction. If initSense == 0, then the complete ellipse or circle is constructed.
If initSense > 0, then the direction of moving is counterclockwise if seeing against the vector product (p1 - pc) and (p2 - pc).
If initSense < 0, , then the direction of moving is counterclockwise if seeing against the vector product (p1 - pc) and(p2 - pc).

Parameters

[in]	pc	- Center of the ellipse or the circle.
[in]	p1	- A point determining the beginning of the curve and the first semiaxis.
[in]	p2	- A point determining the end of the curve and the second semiaxis.
[in]	initSense	- Determines the completeness and the direction. initSense == 0 - closed curve initSense > 0 - moving counterclockwise, initSense < 0 - clockwise.

Returns: Returns pointer to the created object or null pointer in case of failure.

◆ Create() [2/6]

static MbArc3D* MbArc3D::Create	(	const MbCartPoint3D &	p0,
		const MbCartPoint3D &	p1,
		const MbCartPoint3D &	p2,
		int	n,
		bool	closed
	)

static

Create circle or a circular arc.

Constructor of a circle or a circular arc by one of two methods.

Parameters

[in]	p0	- Center (n == 0) or starting point (n != 0).
[in]	p1	- Starting point (n == 0) or point the circle passes through (n == 1).
[in]	p2	- A point determining the end of the curve and the second semiaxis.
[in]	n	- The parameter defines the method of arc construction. If n == 0, then a circle or a circular arc have the center in point p0. If n == 1, then a circle or an arc passes through the specified three points. If \|n\| == 2 & closed == false, then an arc passes through p0 and p2 but not p1.
[in]	closed	- Specifies a circle (true) or an arc (false).

Returns: Returns pointer to the created object or null pointer in case of failure.

◆ Create() [3/6]

static MbArc3D* MbArc3D::Create	(	const MbCartPoint3D &	pc,
		const MbCartPoint3D &	p1,
		const MbCartPoint3D &	p2,
		const MbVector3D &	aZ,
		int	initSense
	)

static

Create circle or a circular arc.

A circular arc is created with a center in point 'pc'. Points 'p1' and 'p2' specify the bounds of arc. The start point of the arc lies on point 'p1'. The end point is on the ray passing through the point 'p2'. Parameter 'initSense' specifies the arc direction.

Parameters

[in]	pc	- Center of circle.
[in]	p1	- A point specifying the beginning of the arc.
[in]	p2	- A point specifying the end of the arc.
[in]	aZ	- A direction of axis Z local coordinate system of the arc.
[in]	initSense	- Arc direction. If initSense > 0, then the orientation is counterclockwise if you look towards the vector aZ. If initSense < 0, then the orientation is clockwise if you look towards the vector aZ. If initSense = 0, then the circle is building.

Returns: Returns pointer to the created object or null pointer in case of failure.

◆ Create() [4/6]

static MbArc3D* MbArc3D::Create	(	const MbCartPoint3D &	p0,
		const MbVector3D &	vZ,
		const MbVector3D &	vX,
		double	aa,
		double	bb,
		double	angle
	)

static

Create elliptical arc.

An elliptical arc is created with the given semiaxes and the local coordinate system. 'angle' determines the arc angle. The angle is measured from the OX axis counterclockwise. The angle is given in radians.

Parameters

[in]	p0	- The ellipse local coordinate system center.
[in]	vZ	- Z-axis of the local coordinate system of the ellipse.
[in]	vX	- X-axis of the local coordinate system of the ellipse.
[in]	aa	- Radius of semiaxis along X.
[in]	bb	- Radius of semiaxis along Y.
[in]	angle	- An angle specifying the end of the arc.

Returns: Returns pointer to the created object or null pointer in case of failure.

◆ Create() [5/6]

static MbArc3D* MbArc3D::Create	(	const MbCartPoint3D &	p1,
		const MbCartPoint3D &	p2,
		double	a_4,
		MbVector3D &	vZ
	)

static

Create circular arc.

An arc is created with ends at the given points. A circle radius is defined by the given tangent of 1/4 of arc opening angle.

Parameters

[in]	p1	- Beginning of the arc.
[in]	p2	- End of the arc.
[in]	a4	- Tangent of 1/4 of the arc opening angle.
[in]	vZ	- Axis of the arc.

Returns: Returns pointer to the created object or null pointer in case of failure.

◆ Create() [6/6]

static MbArc3D* MbArc3D::Create	(	const MbCartPoint3D &	p1,
		const MbCartPoint3D &	p2,
		const MbVector3D &	dirInPoint,
		bool	insecond
	)

static

Create circle by two points and direction to the center from one of them.

A circle is created by two points and direction at one of them.

Parameters

[in]	p1	- The starting point.
[in]	p2	- The end point.
[in]	dirInPoint	- Direction at one of points (p1 or p2) to the center of the circle.
[in]	insecond	- Direction from the first point (insecond == true) to the circle center.

Returns: Returns pointer to the created object or null pointer in case of failure.

◆ Duplicate()

MbSpaceItem& MbArc3D::Duplicate ( MbRegDuplicate * iReg = nullptr ) const

overridevirtual

Create a copy of the object.

Create a copy of an object using the registrator. Registrator is used to prevent multiple copy of the object. If the object contains references to the other objects, then nested objects are copied as well. It is allowed not to pass registrator into the function. Then new copy of object will be created. While copying of single object or set of not connected objects, it is allowed not to use registrator. Registrator should be used if it is required to copy several connected objects. It is possible, that objects connection is based on the references to common objects. Then, while copying without using of registrator, it is possible to obtain set of copies, that contain references to the different copies of the same nested object, that leads to loss of connection between copies.

Parameters

[in] iReg - Registrator.

Returns: A copy of the object.

Implements MbSpaceItem.

◆ Transform()

void MbArc3D::Transform	(	const MbMatrix3D &	matr,
		MbRegTransform *	iReg = `nullptr`
	)

overridevirtual

Convert the object according to the matrix.

Convert the original object according to the matrix using the registrator. If object contains references to the other geometric objects, then nested objects are transformed according to the matrix. Registrator is needed to prevent multiple object copying. It is allowed to use function without registrator, if it is needed to transform single object. If it is needed to transform a set of connected objects, then one should use registrator to prevent repeating transformation of nested objects, because of the possible situation when several objects contain references to the same common objects, that require to be transformed.

Parameters

[in]	matr	- Transformation matrix.
[in]	iReg	- Registrator.

Implements MbSpaceItem.

◆ Move()

void MbArc3D::Move	(	const MbVector3D &	to,
		MbRegTransform *	iReg = `nullptr`
	)

overridevirtual

Move an object along a vector.

Move an object along a geometric vector using the registrator. If object contains references to the other geometric objects then the move operation is applied to the nested objects. Registrator is needed to prevent multiple copying of the object. It is allowed to use function without registrator, if it is needed to transform a single object. If it is needed to transform a set of connected objects, then one should use registrator to prevent repeating transformation of nested objects, because of the possible situation when several objects contain references to the same common objects, that require to be moved.

Parameters

[in]	to	- Shift vector.
[in]	iReg	- Registrator.

Implements MbSpaceItem.

◆ Rotate()

void MbArc3D::Rotate	(	const MbAxis3D &	axis,
		double	angle,
		MbRegTransform *	iReg = `nullptr`
	)

overridevirtual

Rotate an object around an axis at a given angle.

Rotate an object around an axis at a given angle with the registrator. If object contains references to the other geometric objects then the rotation operation is applied to the nested objects. Registrator is needed to prevent multiple copying of the object. It is allowed to use function without registrator, if it is needed to transform a single object. If it is needed to transform a set of connected objects, then one should use registrator to prevent repeating transformation of nested objects, because of the possible situation when several objects contain references to the same common objects, that require to be rotated.

Parameters

[in]	axis	- The axis of rotation.
[in]	angle	- Rotation.
[in]	iReg	- Registrator.

Implements MbSpaceItem.

◆ IsSame()

bool MbArc3D::IsSame	(	const MbSpaceItem &	other,
		double	accuracy = `LENGTH_EPSILON`
	)		const

overridevirtual

Determine whether an object is equal.

Still considered objects of the same type, all data is the same (equal).

Parameters

[in]	item	- The object to compare.
[in]	accuracy	- The accuracy to compare.

Returns: Whether the objects are equal.

Implements MbSpaceItem.

◆ SetEqual()

bool MbArc3D::SetEqual ( const MbSpaceItem & item )

overridevirtual

Make objects equal if they are similar.

You can still make only a similar objects.

Parameters

[in] item - The object to initialize.

Returns: Object is changed.

Implements MbSpaceItem.

◆ DistanceToPoint()

double MbArc3D::DistanceToPoint ( const MbCartPoint3D & point ) const

overridevirtual

Determine the distance to the point.

Parameters

[in] point - Point.

Returns: Distance to point

Implements MbSpaceItem.

◆ GetProperties()

void MbArc3D::GetProperties ( MbProperties & properties )

overridevirtual

Outstanding properties of the object.

Issue internal data (properties) of the object for viewing and modification.

Parameters

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

Implements MbSpaceItem.

◆ SetProperties()

void MbArc3D::SetProperties ( const MbProperties & properties )

overridevirtual

Change the properties of an object.

Changing the internal data (properties) of the object you are copying the corresponding values from the sent object.

Parameters

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

Implements MbSpaceItem.

◆ IsClosed()

bool MbArc3D::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:
MbLine3D,
MbLineSegment3D,
MbSpiral and inherited classes,
MbBridgeCurve3D,
MbContour3D (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 MbCurve3D.

◆ PointOn()

void MbArc3D::PointOn	(	double &	t,
		MbCartPoint3D &	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 MbCurve3D.

◆ _PointOn()

void MbArc3D::_PointOn	(	double	t,
		MbCartPoint3D &	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 MbCurve3D.

◆ Explore()

void MbArc3D::Explore	(	double &	t,
		bool	ext,
		MbCartPoint3D &	pnt,
		MbVector3D &	fir,
		MbVector3D *	sec,
		MbVector3D *	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 MbCurve3D.

◆ Step()

double MbArc3D::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 from its polygon does not exceed the given value of sag.

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 MbCurve3D.

◆ DeviationStep()

double MbArc3D::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 MbCurve3D.

◆ MetricStep()

double MbArc3D::MetricStep	(	double	t,
		double	length
	)		const

overridevirtual

Calculate parameter step.

Calculate the parameter step for approximation of a curve by the given metric length of a step along a curve.

Parameters

[in]	t	- A parameter defining the point on a curve, at which a step should be calculated.
[in]	len	- Maximum metric length of a step along a curve.

Returns: A sag value by parameter at given point.

Reimplemented from MbCurve3D.

◆ NearPointProjection()

bool MbArc3D::NearPointProjection	(	const MbCartPoint3D &	pnt,
		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.

Parameters

[in]	pnt	- A given point.
[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 MbCurve3D.

◆ NurbsCurve() [1/2]

MbNurbs3D* MbArc3D::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]	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.

Reimplemented from MbCurve3D.

◆ NurbsCurve() [2/2]

MbCurve3D* MbArc3D::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 MbCurve3D.

◆ Trimmed() [1/3]

MbCurve3D* MbArc3D::Trimmed	(	double	t1,
		double	t2,
		int	sense,
		const MbDimAccuracy &	xyzEps,
		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 or periodic curve 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]	xyzEps	- Three-dimensional accuracy.
[in]	saveParLenAndLaw	- Save parametric length and law.

Returns: A constructed trimmed curve.

Warning: Under development.

Reimplemented from MbCurve3D.

◆ GetLengthEvaluation()

double MbArc3D::GetLengthEvaluation ( ) const

overridevirtual

Calculate the metric length of a curve.

The length of a curve is inaccurately calculated, by approximation of polyline. If the more accurate curve's length is required, then use the function CalculateMetricLength().

Reimplemented from MbCurve3D.

◆ DistanceAlong()

bool MbArc3D::DistanceAlong	(	double &	t,
		double	len,
		int	curveDir,
		double	eps = `Math::metricPrecision`,
		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.

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

Reimplemented from MbCurve3D.

◆ GetMap()

MbCurve* MbArc3D::GetMap	(	const MbMatrix3D &	into,
		MbRect1D *	pRegion = `nullptr`,
		VERSION	version = `Math::DefaultMathVersion()`,
		bool *	coincParams = `nullptr`
	)		const

overridevirtual

Construct a planar projection of a piece of a space curve.

Parameters

[in]	into	- The transformation matrix from the global coordinate system into a plane of view.
[in]	pRegion	- A mapped piece of a curve (paramRegion.x = t1, paramRegion.y = t2), by default - the whole curve..
[in]	version	- Version, last by default.
[in,out]	coincParams	- A flag of coincidence between parameterization of initial curve and its projection if coincParams != nullptr then the function tries to create a projection with coincident parameterization if *coincParams = true then parameterization of projection coincides with parameterization of initial curve.

Returns: Two-dimensional projection of a curve

Reimplemented from MbCurve3D.

◆ GetMapPsp()

MbCurve* MbArc3D::GetMapPsp	(	const MbMatrix3D &	into,
		double	zNear,
		MbRect1D *	pRegion = `nullptr`
	)		const

overridevirtual

Construct a planar projection of a piece of a space curve.

Construct a planar projection of a piece of a space curve for the perspective visualization.

Parameters

[in]	into	- The transformation matrix from the global coordinate system into a plane of view.
[in]	zNear	- The parameter of the perspective visualization which is equal to the distance between the observation point and the plane of view (negative).
[in]	pRegion	- A mapped piece of a curve (paramRegion.x = t1, paramRegion.y = t2), by default - the whole curve..

Returns: Two-dimensional projection of a curve

Reimplemented from MbCurve3D.

◆ GetRadius()

double MbArc3D::GetRadius ( double accuracy = METRIC_REGION ) const

overridevirtual

Get the physical radius of the curve or zero if it impossible.

Generally returns 0. A non-zero value may be obtained only when the curve is an arc or is equal to an arc with the set precision (METRIC_REGION by default). \params[in] accuracy - The maximum curve deviation from an arc (METRIC_REGION by default).

Returns: Radius value if it can be obtained or 0.0.

Reimplemented from MbCurve3D.

◆ GetCircleAxis()

bool MbArc3D::GetCircleAxis ( MbAxis3D & axis ) const

overridevirtual

Get an axis of a circle which is geometrically coincident to the given curve.

Parameters

[out] axis - An axis with the origin at circle's center and direction along the normal of circle's plane.

Reimplemented from MbCurve3D.

◆ GetPlaneCurve()

bool MbArc3D::GetPlaneCurve	(	MbCurve *&	curve2d,
		MbPlacement3D &	place,
		bool	saveParams,
		PlanarCheckParams	params = `PlanarCheckParams()`
	)		const

overridevirtual

Get planar curve and placement if the space curve is planar.

Get planar curve and placement if the space curve is planar (after the using call DeleteItem for two-dimensional curves).

Parameters

[out]	curve2d	- The resulting flat curve.
[out]	place	- The coordinate system of the resulting 2D curve.
[in]	saveParams	- The parameter specifying the preservation of the correspondence of the parameterization for the two-dimensional curve. If true - parameterization of curve2d curve must match the parameterization of the original curve this. If false - curve parameterizations may not correspond. The curve2d is more likely to be detected than with the true flag.
[in]	params	- Validation parameters.

Returns: true if a flat curve was created.

Reimplemented from MbCurve3D.

◆ AddYourGabaritTo()

void MbArc3D::AddYourGabaritTo ( MbCube & cube ) const

overridevirtual

Expand sent bounding box (a.k.a. gabarit), so that it included the object.

Expand sent bounding box, so that it included the object.

Parameters

[in,out] cube - The bounding box to expand.

Implements MbSpaceItem.

◆ CalculateLocalGabarit()

void MbArc3D::CalculateLocalGabarit	(	const MbMatrix3D &	into,
		MbCube &	cube
	)		const

overridevirtual

To compute bounding box in a local coordinate system.

To obtain bounding box of object with regar to a local coordinate system, sent box is made to be empty. Then it is computed bounding box of object in a local coordinate system \ and it is stored in box 'cube'

Parameters

[in]	into	- Transformation matrix from object's current coordinate system to a local coordinate system
[in,out]	cube	- Information on bounding box

Implements MbSpaceItem.

◆ Extend()

MbResultType MbArc3D::Extend	(	const MbCurveExtensionParameters3D &	parameters,
		c3d::SpaceCurveSPtr &	resCurve
	)		const

overridevirtual

Extend the curve.

Extend the curve according to the given parameters.

Parameters

[in]	parameters	- Parameters of extension.
[out]	resCurve	- The extended curve or nullptr if extension is impossible.

Returns: Returns error status or rt_Success if all is OK.

Reimplemented from MbCurve3D.

◆ Trimmed() [2/3]

virtual MbCurve3D* MbCurve3D::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 or periodic curve 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 MbCurve3D* MbCurve3D::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 or periodic curve 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]	xyzEps	- Three-dimensional accuracy.
[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_arc3d.h

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ MbArc3D() [1/11]

◆ MbArc3D() [2/11]

◆ MbArc3D() [3/11]

◆ MbArc3D() [4/11]

◆ MbArc3D() [5/11]

◆ MbArc3D() [6/11]

◆ MbArc3D() [7/11]

◆ MbArc3D() [8/11]

◆ MbArc3D() [9/11]

◆ MbArc3D() [10/11]

◆ MbArc3D() [11/11]

Member Function Documentation

◆ Create() [1/6]

◆ Create() [2/6]

◆ Create() [3/6]

◆ Create() [4/6]

◆ Create() [5/6]

◆ Create() [6/6]

◆ Duplicate()

◆ Transform()

◆ Move()

◆ Rotate()

◆ IsSame()

◆ SetEqual()

◆ DistanceToPoint()

◆ GetProperties()

◆ SetProperties()

◆ IsClosed()

◆ PointOn()

◆ _PointOn()

◆ Explore()

◆ Step()

◆ DeviationStep()

◆ MetricStep()

◆ NearPointProjection()

◆ NurbsCurve() [1/2]

◆ NurbsCurve() [2/2]

◆ Trimmed() [1/3]

◆ GetLengthEvaluation()

◆ DistanceAlong()

◆ GetMap()

◆ GetMapPsp()

◆ GetRadius()

◆ GetCircleAxis()

◆ GetPlaneCurve()

◆ AddYourGabaritTo()

◆ CalculateLocalGabarit()

◆ Extend()

◆ Trimmed() [2/3]

◆ Trimmed() [3/3]