MbArc Class Reference

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

#include <cur_arc.h>

Inheritance diagram for MbArc:

Collaboration diagram for MbArc:

Public Member Functions
	MbArc ()
	Constructor of a circle with default parameters. More...
	MbArc (double rad)
	Constructor of a circle by radius. More...
	MbArc (const MbCartPoint &p, double rad)
	Constructor of a circle. More...
	MbArc (const MbCartPoint &pc, const MbCartPoint &on)
	Create a circle. More...
	MbArc (const MbCartPoint &pc, double rad, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
	Constructor of a circular arc. More...
	MbArc (const MbCartPoint &pc, double rad, double t1, double t2, int initSense)
	Constructor of a circular arc. More...
	MbArc (const MbArc &init, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
	Constructor of an elliptic arc based on a sample and bounding points. More...
	MbArc (const MbCartPoint &pc, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
	Constructor of a circular arc. More...
	MbArc (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &p3)
	Constructor of a circular arc. More...
	MbArc (const MbCartPoint &p1, const MbCartPoint &p2, double a4)
	Constructor of a circular arc. More...
	MbArc (double aa, double bb, const MbPlacement &place, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
	Constructor of an elliptical arc. More...
	MbArc (double aa, double bb, const MbPlacement &place, double t1, double t2, int initSense)
	Constructor of an elliptical arc. More...
	MbArc (const MbArc &ellipse, double t1, double t2, int initSense)
	Constructor of an elliptical arc. More...
	MbArc (double aa, double bb, const MbPlacement &pos)
	Constructor of an ellipse. More...
	MbArc (double aa, double bb, const MbCartPoint &c, double angle)
	Constructor of an ellipse. More...
	MbArc (const MbArc &init)
	Copy-constructor.
virtual	~MbArc ()
	Destructor.
Common functions of a geometric object.
MbePlaneType	IsA () const override
	Get the object type.
MbPlaneItem &	Duplicate (MbRegDuplicate *=nullptr) const override
	Create a copy. More...
bool	IsSame (const MbPlaneItem &other, double accuracy=LENGTH_EPSILON) const override
	Determine whether objects are equal. More...
bool	SetEqual (const MbPlaneItem &) override
	Make the objects equal. More...
void	Transform (const MbMatrix &matr, 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...
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...
void	AddYourGabaritTo (MbRect &r) const override
	Extend the given bounding rectangle so that it encloses this object.
void	CalculateGabarit (MbRect &r) const override
	Detect the bounding box of a curve. More...
bool	IsInRectForDeform (const MbRect &r) const override
	Determine visibility of a curve in rectangle.
MbeState	Deformation (const MbRect &, const MbMatrix &) override
	Deform the curve. More...
void	Refresh () override
	Set all temporary (mutable) data of object to undefined (initial) state.
void	PrepareIntegralData (const bool forced) const override
	Calculate temporary (mutable) data of an object. More...
bool	IsVisibleInRect (const MbRect &r, bool exact=false) const override
	Determine visibility of an object in rectangle. More...
bool	IsCompleteInRect (const MbRect &r) const override
	Determine whether an object is fully visible in rectangle. More...
bool	IsVisibleInRect (const MbRect &rect, bool exact=false) const override
	Determine visibility of an object in rectangle. More...
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. More...
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, MbCartPoint &) const override
	Calculate a point on the curve. More...
void	FirstDer (double &t, MbVector &) const override
	Calculate first derivative.
void	SecondDer (double &t, MbVector &) const override
	Calculate second derivative.
void	ThirdDer (double &t, MbVector &) const override
	Calculate third derivative.
virtual void	Normal (double &t, MbVector &) const
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, MbCartPoint &) const override
	Calculate point at curve and its extension. More...
void	_FirstDer (double t, MbVector &) const override
	Calculate first derivative at curve and its extension.
void	_SecondDer (double t, MbVector &) const override
	Calculate second derivative at curve and its extension.
void	_ThirdDer (double t, MbVector &) const override
	Calculate third derivative at curve and its extension.
virtual void	_Normal (double t, MbVector &) const
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...
Functions of moving along the 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...
Common functions of the curve
void	Inverse (MbRegTransform *iReg=nullptr) override
	Set the opposite direction of curve.
double	GetMetricLength () const override
	Calculate the metric length of a curve. 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.
double	CalculateLength (double t1, double t2) const override
	Calculate the metric length of a curve. 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	PointProjection (const MbCartPoint &pnt) 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	TangentPoint (const MbCartPoint &pnt, SArray< double > &tFind) const override
	Find tangents to a curve. More...
void	PerpendicularPoint (const MbCartPoint &pnt, SArray< double > &tFind) const override
	Find perpendiculars to a curve. More...
bool	SmallestPerpendicular (const MbCartPoint &pnt, double &tProj) const override
	Find the nearest perpendicular to the curve. More...
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...
bool	GetCentre (MbCartPoint &c) const override
	Return the center of an ellipse or a circle.
virtual const MbCartPoint &	GetCentre () const
	Return the center of an ellipse or a circle.
bool	GetMiddlePoint (MbCartPoint &p) const override
	Calculate a middle point of a curve.
bool	GetWeightCentre (MbCartPoint &p) const override
	Calculate the center of gravity of a curve.
double	GetRadius (double accuracy=PARAM_REGION) const override
	Get the physical radius of the curve or zero if it impossible. More...
bool	IsSimilarToCurve (const MbCurve &curve, double precision=PARAM_PRECISION) const override
	Define whether the curves are similar for the merge.
size_t	GetCount () const override
	Define the number of splittings for one passage in operations.
void	GetPointsByEvenLengthDelta (size_t n, std::vector< MbCartPoint > &pnts) const override
	Get n points of a curve with equal intervals by arc length.
bool	HasLength (double &length) const override
	Calculate the metric length of a curve. More...
bool	IsDegenerate (double eps=Math::LengthEps) const override
	Define whether the curve is degenerate..
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.
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...
MbCurve *	Offset (double rad) const override
	Construct the equidistant curve which is shifted by the given value.
MbeItemLocation	PointRelative (const MbCartPoint &pnt, double eps=Math::LengthEps) const override
	Define the point position relative to the curve. More...
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...
bool	ModifyByPoint (size_t ind, const MbCartPoint &pnt)
	Modify the ellipse by a characteristic point. More...
bool	GetSpecificPoint (const MbCartPoint &from, double &dmax, MbCartPoint &pnt) const override
	Return a specific point of a curve. More...
void	Isoclinal (const MbVector &angle, SArray< double > &tFind) const override
	Construct isoclines. More...
bool	GetAxisPoint (MbCartPoint &p) const override
	Calculate a point to construct an axis. More...
MbResultType	Extend (const MbCurveExtensionParameters &parameters, c3d::PlaneCurveSPtr &resCurve) const override
	Extend the curve. More...
bool	IsCircle (double eps=PARAM_REGION) const
	Check whether the ellipse is a circle with a given tolerance.
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...
Functions in the local coordinate system of object placement.
const MbPlacement &	GetPlacement () const
	Get the local coordinate system of an object.
void	SetPlacement (const MbPlacement &pl)
	Modify the local coordinate system of the object.
bool	IsPositionNormal () const
	Determine whether the local coordinate system is orthonormalized.
bool	IsPositionCircular () const
	Determine whether the local coordinate system is orthogonal with X and Y axes equal by length.
bool	IsPositionIsotropic () const
	Determine whether the local coordinate system is orthogonal and isotropic by the axes.
double	GetPositionAngle (const MbCartPoint &p) const
	Calculate the angle in the local coordinate system. More...
void	InitByPositionAngles (double a1, double a2, int initSense, const MbDimAccuracy &xyEps=MbDimAccuracy::twoDimRgn)
	Initialization of the ellipse parameters. More...
Functions for working with data.
double	GetR () const
	Return the radius and the length of semiaxis along X for the ellipse.
double	GetRadiusA () const
	Return the length of semiaxis along X.
double	GetRadiusB () const
	Return the length of semiaxis along Y.
void	SetRadiusA (double aa)
	Set the length of semiaxis along X.
void	SetRadiusB (double bb)
	Set the length of semiaxis along Y.
double	GetAngle () const
	Return the arc opening angle. Set the arc opening angle. The start point of the arc remains unchanged.
void	SetAngle (double ang)
double	GetMajorAxisAngle () const
	Calculate the angle between OX axes of the local and the global coordinate systems.
double	GetTrim1 () const
	Return the parameter of the start point.
double	GetTrim2 () const
	Return the parameter of the end point.
int	GetSense () const
	Determine the flag of coincidence of the direction with the base curve direction.
void	SetTrim1 (double t)
	Set the parameter of the start point.
void	SetTrim2 (double t)
	Set the parameter of the end point.
void	SetRadius (double rad)
	Set the radius of the circular arc.
void	SetCentre (const MbCartPoint &c)
	Set the center.
void	SetDirection (bool clockwise)
	Set the arc orientation.
void	Init (const MbArc &)
	Initialize elliptical arcs with the given arc.
void	Init (const MbCartPoint &pc, double rad)
	Initialize a circle by the center and the radius
void	Init (double t1, double t2)
	Initialize arc by parameters for begin point and end point.
bool	Init3Points (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &p3, bool cl)
	Initialize a circular arc. More...
void	InitCircle (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &p3)
	Initialize a circular arc. More...
void	InitArc (MbCartPoint &pc, const MbCartPoint &p1, const MbCartPoint &p2)
	Initialize a circular arc. More...
void	Init (const MbCartPoint &pc, double rad, const MbCartPoint &p1, const MbCartPoint &p2, bool clockwise)
	Initialize a circular arc. More...
void	Init (const MbCartPoint &pc, const MbCartPoint &p)
	Initialize a circle. More...
void	Init (const MbCartPoint &p1, double angle, double rad)
	Initialize a circle. More...
void	Init (const MbCartPoint &pc, const MbCartPoint &pnt, double angle)
	Initialize a circle. More...
void	Init (const MbCartPoint &pc, double angle1, double angle2, double rad, bool clockwise)
	Initialize a circular arc. More...
void	Init (const MbCartPoint &pc, const MbCartPoint &pnt, bool firstPoint, double angle, bool clockwise)
	Initialize a circular arc. More...
void	Init (const MbCartPoint &pc, double angle1, const MbCartPoint &p2, double rad, bool clockwise)
	Initialize a circular arc. More...
void	Init (MbArc *obj, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
	Initialize a circular arc. More...
void	Init (const MbCartPoint &p1, const MbCartPoint &p2, double angle, bool firstAngle, bool clockwise)
	Initialize a circular arc. More...
void	Init (MbCartPoint &pc, double angle1, double angle2, const MbCartPoint &pnt, bool firstPoint, bool clockwise)
	Initialize a circular arc. More...
void	Init (MbCartPoint &pc, const MbCartPoint &p, bool firstPoint, double angle, double rad, bool clockwise)
	Initialize a circular arc. More...
void	Init (const MbCartPoint &pc, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
	Initialize a circular arc. More...
bool	Init (double a2, MbCartPoint &p1, MbCartPoint &p2, const DiskreteLengthData *diskrData=nullptr, bool correctFirstPnt=true)
	Initialize a circular arc. More...
void	Init (double aa, double bb, const MbPlacement &place)
	Initialize an ellipse. More...
void	Init (double aa, double bb, const MbCartPoint &pc, double ang)
	Initialize an ellipse. More...
void	Init1 (const MbCartPoint &c, const MbCartPoint &p1, double &len, double &angle)
	Initialize an ellipse. More...
void	Init2 (const MbCartPoint &c, const MbCartPoint &p1, MbCartPoint &p2, double &lenB)
	Initialize an ellipse. More...
void	Init3 (const MbCartPoint &c0, const MbCartPoint &p1, double angle, double &aa, double &bb)
	Initialize an ellipse. More...
void	Init4 (const MbCartPoint &p1, const MbCartPoint &p2, double angle, double &aa, double &bb)
	Initialize an ellipse. More...
void	Init5 (const MbCartPoint &c, const MbCartPoint &p1, const MbCartPoint &p2, double &aa, double &bb, double &angle)
	Initialize an ellipse. More...
void	Init6 (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &p3, double &aa, double &bb, double &angle)
	Initialize an ellipse. More...
void	Init7 (const MbCartPoint &pc, MbCartPoint p1, MbCartPoint p2, MbCartPoint p3, double &aa, double &bb, double &angle)
	Initialize an ellipse. More...
void	Init8 (const MbCartPoint &p1, const MbDirection &dir1, const MbCartPoint &p2, const MbDirection &dir2, const MbCartPoint &p3, double &aa, double &bb, double &angle)
	Initialize an ellipse. More...
void	Init (double aa, double bb, const MbPlacement &place, double t1, double t2, int initSense)
	Initialize an elliptical arc. More...
void	Init (double aa, double bb, const MbPlacement &place, const MbCartPoint &p1, const MbCartPoint &p2, bool clockwise)
	Initialize an elliptical arc. More...
void	Init4 (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &pB, const MbCartPoint &pE, bool clockwise=false)
	Initialize an elliptical arc. More...
bool	OnSector (const MbCartPoint &pnt) const
	Determine whether the ray from the center to the point is in the arc's sector.
bool	OnSector (double angle) const
	Determine whether the ray hits the arc's sector. More...
void	SetLimitPoint (ptrdiff_t number, const MbCartPoint &pnt)
	Replace the arc's point. More...
bool	IsClockwise () const
	Return the arc direction: true - clockwise, false - counterclockwise.
double	GetLimitAngle (ptrdiff_t number) const
	Return the angle of the end point. More...
void	SetLimitAngle (ptrdiff_t number, const MbCartPoint &pnt)
	Modify the end angle of the arc. More...
double	CheckParam (double &t) const
	Set the parameter to the range of the allowable values.
void	ParamToAngle (double &t) const
	Convert the parameter of the curve to the angle.
void	AngleToParam (double &t) const
	Convert the curve angle to the curve parameter.
void	ParameterInto (double &t) const
	Convert parameter of the base curve to the local parameter.
void	ParameterFrom (double &t) const
	Convert the local parameter to the parameter of the base curve.
bool	IsBaseParamOn (double t, double eps=Math::paramEpsilon) const
	Determine whether the parameter of the base curve is in range of the trimmed curve.
void	PointOnBaseEllipse (double &t, MbCartPoint &pnt) const
	Evaluate a point on ellipse. More...
double	PointProjectionOnBaseEllipse (const MbCartPoint &pnt) const
	Find the projection of a point onto the ellipse. More...
void	MakeAsBaseEllipse ()
	Initialize as complete ellipse.
void	CopyBaseEllipse (const MbArc &init)
	Copy the base ellipse.
bool	IsSelfIntersectOffset (double d) const
	Determine whether the ellipse offset has self-intersections. More...
bool	ParametricToCanonicConic (double &A, double &B, double &C, double &D, double &E, double &F, double &X1, double &Y1, double &X2, double &Y2) const
bool	Normalize ()
	Orthonormalize the local coordinate system.
void	GetControlPoints (SArray< MbCartPoint > &points)
	Fill the array with the control points.
void	NormalizeTransform (const MbMatrix &mt)
	Orthonormalize the placement when transforming.
ptrdiff_t	EllipticIntersect (const MbLine &pLine, double cross[2], double eps0=PARAM_PRECISION) const
	Determine the parameters of intersection of a line with an ellipse. More...
const MbArc &	operator= (const MbArc &init)
	Overrides the assignment operator.
void	GetProperties (MbProperties &properties) override
	Get properties of the object. More...
void	SetProperties (const MbProperties &properties) 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.
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.
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 void	AddYourGabaritMtr (MbRect &rect, const MbMatrix &matr) const
	Add a bounding box to rectangle. More...
virtual void	CalculateLocalGabarit (const MbMatrix &into, MbRect &local) const
	Calculate bounding box in the local coordinate system. More...
bool	IsVisibleInRect (const MbRect &rect, bool exact=false) const override
	Determine visibility of an object 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 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.
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	IsBounded () const
	Define whether the curve is bounded.
virtual bool	IsStraight (bool ignoreParams=false) const
	Define whether the curve is rectilinear..
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 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 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...
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.
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
void	GetPointsByEvenLengthDelta (size_t n, SArray< MbCartPoint > &pnts) const
virtual double	LengthBetween2Points (MbCartPoint &p1, MbCartPoint &p2, MbCartPoint *pc=nullptr) const
	Calculate minimal length of a curve between two points on it. More...
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 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	GetParamToUnit () const
	Return increment of parameter, corresponding to the unit length in space.
virtual double	GetParamToUnit (double t) const
	Return increment of parameter, corresponding to the unit length in space according to parameter.
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...
virtual bool	IsSimilar (const MbPlaneItem &item) const
	Determine whether the objects are similar. 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.

Static Public Member Functions
static MbArc *	Create (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &p3)
	Create circular arc. More...
static MbArc *	Create (const MbCartPoint &p1, const MbCartPoint &p2, double a4)
	Create circular arc. More...

Protected Member Functions
double	GetParamEpsilon (double eps=Math::LengthEps) const
	Get the parameter accuracy.
void	SetClosed ()
	Make closed.
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
MbPlacement	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.
int	sense
	Flag of coincidence with direction from axisX to axisY (sense==0 is not allowed).
bool	circle
	Whether the object is a circle (true) or an ellipse (false).
bool	closed
	Whether the object is a closed curve (true) or an arc (false).
MbRect	rect
	Auxiliary data. More...
atomic_double	metricLength
	Metric length of curve.
Protected Attributes inherited from MbCurve
SimpleName	name
	A curve name. The object data is temporary and used internally.

Detailed Description

Elliptical arc in two-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+(sense)t) position.axisX) + (b sin(trim1+(sense)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 if sense==1 and trim1>trim2 if sense==-1.
The local coordinate system 'position' can be both right and left. If the local coordinate system is right and sense=+1 or the local coordinate system is left and sense=-1, then the arc is oriented counterclockwise.

Constructor & Destructor Documentation

MbArc() [1/15]

MbArc::MbArc

(

)

Constructor of a circle with default parameters.

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

MbArc() [2/15]

MbArc::MbArc

(

double

rad

)

Constructor of a circle by radius.

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

Parameters

[in]

rad

- Radius.

MbArc() [3/15]

MbArc::MbArc	(	const MbCartPoint &	p,
		double	rad
	)

Constructor of a circle.

A circle is created with center in point 'p' and with the given radius.

Parameters

[in]	p	- Center of circle.
[in]	rad	- Radius.

MbArc() [4/15]

MbArc::MbArc	(	const MbCartPoint &	pc,
		const MbCartPoint &	on
	)

Create a circle.

A circle is created with center in point 'pc'. The radius is determined as the distance between points 'pc' and 'on'.

Parameters

[in]	pc	- Center of circle.
[in]	on	- Point on circle.

MbArc() [5/15]

MbArc::MbArc	(	const MbCartPoint &	pc,
		double	rad,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		int	initSense
	)

Constructor of a circular arc.

A circular arc is created with a center in point 'p' and with a given radius. Points 'p1' and 'p2' specify the bounds of arc. 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 passing through the point 'p2'. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters

[in]	pc	- Center of circle.
[in]	rad	- Radius.
[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 - counterclockwise, initSense < 0 - clockwise. initSense cannot be equal to zero.

MbArc() [6/15]

MbArc::MbArc	(	const MbCartPoint &	pc,
		double	rad,
		double	t1,
		double	t2,
		int	initSense
	)

Constructor of a circular arc.

A circular arc is created with a center in point 'p' and with a given radius. 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 orientation is counterclockwise.

Parameters

[in]	pc	- Center of circle.
[in]	rad	- Radius.
[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 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

MbArc() [7/15]

MbArc::MbArc	(	const MbArc &	init,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		int	initSense
	)

Constructor of an elliptic arc based on a sample and bounding points.

An arc based on the given sample of circle or ellipse is created. Points 'p1' and 'p2' specify the bounds of arc. 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 passing through the point 'p2'. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters

[in]	init	- A sample circle or 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 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

MbArc() [8/15]

MbArc::MbArc	(	const MbCartPoint &	pc,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		int	initSense
	)

Constructor of a circular arc.

An arc of a circle centered in point 'pc'. The radius is determined as the distance between points 'pc' and 'p1'. Points 'p1' and 'p2' specify the bounds of arc. 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 passing through the point 'p2'. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters

[in]	pc	- Center of circle.
[in]	p1	- A point determining the beginning of the arc and the radius.
[in]	p2	- A point specifying the end of the arc.
[in]	initSense	- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

MbArc() [9/15]

MbArc::MbArc	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		const MbCartPoint &	p3
	)

Constructor of a circular arc.

A circular arc is created passing through 3 given points. Points p1 and p3 are the end points. Direction of moving along the arc is defined so as point p2 lay on the arc.

Deprecated:

The method is deprecated.

Parameters

[in]	p1	- Beginning of the arc.
[in]	p2	- A point on the arc.
[in]	p3	- End of the arc.

MbArc() [10/15]

MbArc::MbArc	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		double	a4
	)

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.

MbArc() [11/15]

MbArc::MbArc	(	double	aa,
		double	bb,
		const MbPlacement &	place,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		int	initSense
	)

Constructor of an elliptical arc.

An elliptical arc is created with the given semiaxes and the local coordinate system. Points 'p1' and 'p2' specify the bounds of arc. 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 passing through the point 'p2'. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters

[in]	aa	- Radius of semiaxis along X.
[in]	bb	- Radius of semiaxis along Y.
[in]	place	- The local coordinate system of the 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 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

MbArc() [12/15]

MbArc::MbArc	(	double	aa,
		double	bb,
		const MbPlacement &	place,
		double	t1,
		double	t2,
		int	initSense
	)

Constructor of an elliptical arc.

An elliptical arc is created with the given semiaxes and the local coordinate system. 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 orientation is counterclockwise.

Parameters

[in]	aa	- Radius of semiaxis along X.
[in]	bb	- Radius of semiaxis along Y.
[in]	place	- The local coordinate system of the 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 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

MbArc() [13/15]

MbArc::MbArc	(	const MbArc &	ellipse,
		double	t1,
		double	t2,
		int	initSense
	)

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 orientation is counterclockwise.

Parameters

[in]	ellipse	- 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 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

MbArc() [14/15]

MbArc::MbArc	(	double	aa,
		double	bb,
		const MbPlacement &	pos
	)

Constructor of an ellipse.

An ellipse is created with the given local coordinate system and semiaxes.

Parameters

[in]	aa	- Radius of semiaxis along X.
[in]	bb	- Radius of semiaxis along Y.
[in]	pos	- The local coordinate system of the ellipse.

MbArc() [15/15]

MbArc::MbArc	(	double	aa,
		double	bb,
		const MbCartPoint &	c,
		double	angle
	)

Constructor of an ellipse.

An ellipse is created with the given semiaxes. The local coordinate system of the ellipse has the origin in point 'c'; OX axis of the local coordinate system forms angle 'angle' with the OX axis of the current coordinate system. Direction of turning from the current coordinate system axis to the axis of the new coordinate system.

Parameters

[in]	aa	- Radius of semiaxis along X.
[in]	bb	- Radius of semiaxis along Y.
[in]	c	- Origin of local coordinate system of ellipse.
[in]	angle	- An angle between OX axes of the local and the current coordinate systems.

Member Function Documentation

Create() [1/2]

static MbArc* MbArc::Create ( const MbCartPoint &  p1, const MbCartPoint &  p2, const MbCartPoint &  p3  )

static

Create circular arc.

A circular arc is created passing through 3 given points. Points p1 and p3 are the end points. Direction of moving along the arc is defined so as point p2 lay on the arc.

Parameters

[in]	p1	- Beginning of the arc.
[in]	p2	- A point on the arc.
[in]	p3	- End of the arc.

Create() [2/2]

static MbArc* MbArc::Create ( const MbCartPoint &  p1, const MbCartPoint &  p2, double  a4  )

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.

Duplicate()

MbPlaneItem& MbArc::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.

IsSame()

bool MbArc::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.

SetEqual()

bool MbArc::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.

Transform()

void MbArc::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 MbArc::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 MbArc::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.

DistanceToPointIfLess()

bool MbArc::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.

CalculateGabarit()

void MbArc::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.

Deformation()

MbeState MbArc::Deformation ( const MbRect &  rect, const MbMatrix &  matr  )

overridevirtual

Deform the curve.

If the bounding rectangle of a curve intersects the given one, then the curve is transformed according to the matrix with a help of 'Transform' function.

Parameters

[in]	rect	- A rectangle, in which the visibility of a curve is checked.
[in]	matr	- A deformation matrix.

Returns

A state of a curve after deformation.

Reimplemented from MbCurve.

PrepareIntegralData()

void MbArc::PrepareIntegralData ( const bool  forced ) const

overridevirtual

Calculate temporary (mutable) data of an object.

Calculate the temporary data of an object depending of the "forced" parameter. Calculate only data that was not calculated earlier if parameter "forced" is equal false. Recalculate all temporary data of an object if parameter "forced" is equal true.

Parameters

[in]

forced

- Forced recalculation.

Reimplemented from MbCurve.

IsVisibleInRect() [1/2]

bool MbArc::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.

IsCompleteInRect()

bool MbArc::IsCompleteInRect ( const MbRect &  rect ) const

overridevirtual

Determine whether an object is fully visible in rectangle.

An object is fully contained in the given rectangle if its bounding rectangle is included in the given rectangle.

Parameters

[in]

rect

- Rectangle to check inclusion to.

Returns

true, if the object is fully contained in the rectangle, otherwise false.

Reimplemented from MbCurve.

IsClosed()

bool MbArc::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.

GetPeriod()

double MbArc::GetPeriod ( ) const

overridevirtual

Return period.

Return the period value if a curve can be closed. Let unclosed curve return null.

Returns

The value of period for a closed curve or null - for unclosed curve.

Reimplemented from MbCurve.

PointOn()

void MbArc::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 MbArc::_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 MbArc::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.

Step()

double MbArc::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 MbArc::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.

GetMetricLength()

double MbArc::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.

GetLengthEvaluation()

double MbArc::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 MbCurve.

CalculateLength()

double MbArc::CalculateLength ( double  t1, double  t2  ) const

overridevirtual

Calculate the metric length of a curve.

Calculate the metric length of unclosed curve from parameter t1 to parameter t2. The condition t1 < t2 should satisfied.

Parameters

[in]	t1	- Start parameter of a curve section.
[in]	t2	- End parameter of a curve section.

Returns

Length of a curve.

Reimplemented from MbCurve.

DistanceAlong()

bool MbArc::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.

PointProjection()

double MbArc::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 MbArc::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.

TangentPoint()

void MbArc::TangentPoint ( const MbCartPoint &  pnt, SArray< double > &  tFind  ) const

overridevirtual

Find tangents to a curve.

Find all tangents to a curve from the given point. A point may belong to a curve. In this function a curve without extensions is considered.

Parameters

[in]	pnt	- A given point.
[in,out]	tFind	- An array of parameters of a curve, corresponding to the tangent points.

Reimplemented from MbCurve.

PerpendicularPoint()

void MbArc::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.

SmallestPerpendicular()

bool MbArc::SmallestPerpendicular ( const MbCartPoint &  pnt, double &  tProj  ) const

overridevirtual

Find the nearest perpendicular to the curve.

Find the nearest perpendicular to the curve from the given point. In this function perpendiculars to an extension of a curve are not considered.

Parameters

[in]	pnt	- A given point.
[in,out]	tProj	- Parameter on a curve, corresponding to the point on a curve, which the perpendicular is passed through.

Returns

True if the required perpendicular is constructed.

Reimplemented from MbCurve.

IntersectHorizontal()

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

overridevirtual

Find intersections of a curve with horizontal line.

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

overridevirtual

Find intersections of a curve with vertical line.

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.

GetRadius()

double MbArc::GetRadius ( double  accuracy = PARAM_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 (PARAM_REGION by default). \params[in] accuracy - The maximum curve deviation from an arc (PARAM_REGION by default).

Returns

Radius value if it can be obtained or 0.0.

Reimplemented from MbCurve.

HasLength()

bool MbArc::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.

NurbsCurve() [1/2]

MbNurbs* MbArc::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* MbArc::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.

Trimmed() [1/3]

MbCurve* MbArc::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.

PointRelative()

MbeItemLocation MbArc::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.

DeletePart()

MbeState MbArc::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 MbArc::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.

ModifyByPoint()

bool MbArc::ModifyByPoint	(	size_t	ind,
		const MbCartPoint &	pnt
	)

Modify the ellipse by a characteristic point.

Parameters

[in]	ind	- Index of a characteristic point. Possible values: 0 - Ellipse center. 1 - The point on ellipse corresponding to 0 degrees. 2 - The point on ellipse corresponding to 90 degrees. 3 - The point on ellipse corresponding to 180 degrees. 4 - The point on ellipse corresponding to 270 degrees.
[in]	pnt	- Characteristic point.

Returns

True - if the operation succeeded. Otherwise returns false.

GetSpecificPoint()

bool MbArc::GetSpecificPoint ( const MbCartPoint &  from, double &  dmax, MbCartPoint &  pnt  ) const

overridevirtual

Return a specific point of a curve.

Return a specific point of a curve if the distance from it to the given point is less than dmax. Specific points of a bounded curve are its start and end points.

Parameters

[in]	from	- A control point
[in,out]	dmax	- Input - maximum distance for search of specific point. Output - a distance from the point 'from' to the found specific point.
[in,out]	pnt	- Tangent vector.

Returns

True - if the specific point is found.

Reimplemented from MbCurve.

Isoclinal()

void MbArc::Isoclinal ( const MbVector &  angle, SArray< double > &  tFind  ) const

overridevirtual

Construct isoclines.

Construct lines at an angle to the axis OX and tangent to the curve.

Parameters

[in]	angle	- A vector defining an inclination angle of line to the axis OX.
[in,out]	tFind	- An array of parameters of a curve, corresponding to the tangent points.

Reimplemented from MbCurve.

GetAxisPoint()

bool MbArc::GetAxisPoint ( MbCartPoint &  p ) const

overridevirtual

Calculate a point to construct an axis.

Calculates a point to construct an axis, if a curve may be constructed by rotation of a point around an axis.

Returns

true, if such axis exists.

Reimplemented from MbCurve.

Extend()

MbResultType MbArc::Extend ( const MbCurveExtensionParameters &  parameters, c3d::PlaneCurveSPtr &  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 MbCurve.

GetPositionAngle()

double MbArc::GetPositionAngle

(

const MbCartPoint &

p

)

const

Calculate the angle in the local coordinate system.

Calculate the angle between OX axis of the local coordinate system and the ray starting from the origin of local coordinate system and passing through point p.

Parameters

[in]

p

- A given point.

Returns

Value of angle.

InitByPositionAngles()

void MbArc::InitByPositionAngles	(	double	a1,
		double	a2,
		int	initSense,
		const MbDimAccuracy &	xyEps = MbDimAccuracy::twoDimRgn
	)

Initialization of the ellipse parameters.

Parameters are calculated subject to the directions and angles corresponding to the beginning and the end of the arc calculated in the local coordinate system.

Parameters

[in]	a1	- The angle corresponding to the beginning of the arc.
[in]	a2	- The angle corresponding to the end of the arc.
[in]	initSense	- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.
[in]	xyEps	- The xyEps.x component corresponds to x-axis accuracy, xyEps.y corresponds to y-axis accuracy.

Returns

Value of angle.

Init3Points()

bool MbArc::Init3Points	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		const MbCartPoint &	p3,
		bool	cl
	)

Initialize a circular arc.

Initialize a circular arc passing through all 3 given points. Points p1 and p3 are the end points. If the arc is not closed, then the direction of moving along the arc is defined so as the point p2 lies on the arc.

Parameters

[in]	p1	- Beginning of the arc.
[in]	p2	- A point on the arc.
[in]	p3	- End of the arc.
[in]	cl	- Closedness attribute.

Returns

True if initialization completed successfully.

InitCircle()

void MbArc::InitCircle	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		const MbCartPoint &	p3
	)

Initialize a circular arc.

Initialize a circular arc passing through all 3 given points. Points p1 and p3 are the end points. The direction of moving along the arc is defined so as the point p2 lies on the arc.

Parameters

[in]	p1	- Beginning of the arc.
[in]	p2	- A point on the arc.
[in]	p3	- End of the arc.

InitArc()

void MbArc::InitArc	(	MbCartPoint &	pc,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2
	)

Initialize a circular arc.

A new position of the arc center is specified, the arc center will be located on the bisector of the opening angle.

Parameters

[in]	pc	- Center of circle.
[in]	p1	- Beginning of the arc.
[in]	p2	- End of the arc.

Init() [1/17]

void MbArc::Init	(	const MbCartPoint &	pc,
		double	rad,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		bool	clockwise
	)

Initialize a circular arc.

The center and the radius of the circle is being modified. Points 'p1' and 'p2' specify the bounds of arc. 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 passing through the point 'p2'. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters

[in]	pc	- Center of circle.
[in]	rad	- Radius.
[in]	p1	- A point specifying the beginning of the arc.
[in]	p2	- A point specifying the end of the arc.
[in]	clockwise	- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

Init() [2/17]

void MbArc::Init	(	const MbCartPoint &	pc,
		const MbCartPoint &	p
	)

Initialize a circle.

The source object is changed to a circle with center in point 'pc'. The radius is determined as a distance between points pc and p.

Parameters

[in]	pc	- Center of circle.
[in]	p	- Point on circle.

Init() [3/17]

void MbArc::Init	(	const MbCartPoint &	p1,
		double	angle,
		double	rad
	)

Initialize a circle.

The source object is changed to a circle passing through point p1 with the given radius. Angle 'angle' specifies a line the circle's center lies on. It is the angle between a ray starting from point p1 and directed to the circle's center and OX axis.

Parameters

[in]	p1	- Point on circle.
[in]	angle	- An angle specifying the position of the center on the circle.
[in]	rad	- Radius.

Init() [4/17]

void MbArc::Init	(	const MbCartPoint &	pc,
		const MbCartPoint &	pnt,
		double	angle
	)

Initialize a circle.

The source object is changed to a circle with the given center and passing through point pnt. The radius is determined as the distance between points pc and pnt.

Parameters

[in]	pc	- Center of circle.
[in]	pnt	- Point on circle.
[in]	angle	- Get the start parameter.

Init() [5/17]

void MbArc::Init	(	const MbCartPoint &	pc,
		double	angle1,
		double	angle2,
		double	rad,
		bool	clockwise
	)

Initialize a circular arc.

The source object is changed to a circular arc with the given center and radius. angle1 and angle2 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 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters

[in]	pc	- Center of circle.
[in]	angle1	- An angle specifying the beginning of the arc.
[in]	angle2	- An angle specifying the end of the arc.
[in]	rad	- Radius.
[in]	clockwise	- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

Init() [6/17]

void MbArc::Init	(	const MbCartPoint &	pc,
		const MbCartPoint &	pnt,
		bool	firstPoint,
		double	angle,
		bool	clockwise
	)

Initialize a circular arc.

The source object is changed to a circular arc with the given center and passing through point pnt. The radius is determined as the distance between points pc and pnt. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters

[in]	pc	- Center of circle.
[in]	pnt	- End point of the circular arc.
[in]	firstPoint	- Flag determining whether the point pnt is the start point.
[in]	angle	- The angle between the radius to the second point and the OX axis.
[in]	clockwise	- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

Init() [7/17]

void MbArc::Init	(	const MbCartPoint &	pc,
		double	angle1,
		const MbCartPoint &	p2,
		double	rad,
		bool	clockwise
	)

Initialize a circular arc.

The source object is changed to a circular arc with the given center and radius. The end point of the arc is determined as intersection of ray (pc, p2) and the circle. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters

[in]	pc	- Center of circle.
[in]	angle1	- The start parameter of the circle.
[in]	p2	- A point specifying the angle of the circular arc end.
[in]	rad	- Radius.
[in]	clockwise	- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. initSense can't be equal to zero.

Init() [8/17]

void MbArc::Init	(	MbArc *	obj,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		int	initSense
	)

Initialize a circular arc.

The source object is changed to a circular arc corresponding to a given object. The start and the end point of the arc is determined as intersection of rays passing from the center to points p1 and p2 with the circle. The end point of the arc is determined as intersection of ray (pc, p2) and the circle. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters

[in]	obj	- A pattern object.
[in]	p1	- A point determining the angle of the beginning of the circular arc.
[in]	p2	- A point specifying the angle of the circular arc end.
[in]	initSense	- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

Init() [9/17]

void MbArc::Init	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		double	angle,
		bool	firstAngle,
		bool	clockwise
	)

Initialize a circular arc.

In the result of the operation the circular arc is obtained which starts at point p1 and ends at point p2. For one of points the angle between the direction from the point to the circle center and the OX axis is specified. Parameter firstAngle determines for which of points the angle is specified. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters

[in]	p1	- The start point of the circular arc.
[in]	p2	- The end point of the circular arc.
[in]	angle	- The angle between the direction from the point to the circle center and OX axis.
[in]	firstAngle	- Flag determining for which point the angle is specified. firstAngle == true - for the first one.
[in]	clockwise	- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

Init() [10/17]

void MbArc::Init	(	MbCartPoint &	pc,
		double	angle1,
		double	angle2,
		const MbCartPoint &	pnt,
		bool	firstPoint,
		bool	clockwise
	)

Initialize a circular arc.

In the result of the operation a circular arc is obtained one of ends of which is point pnt. For this point the angle between the line directed from the point to the circle center and OX axis is specified. Find projection pc onto this line to determine the circle center.
The second angle specifies the second end of the arc. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters

[in,out]	pc	- On input - the given point, on output - the circle center.
[in]	angle1	- Angle between the direction from the starting point of the arc to the circle center and OX axis.
[in]	angle2	- Angle between the direction from the end point of the arc to the circle center and OX axis.
[in]	pnt	- End point of the circular arc.
[in]	firstPoint	- Flag determining whether the point pnt is a starting point.
[in]	clockwise	- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

Init() [11/17]

void MbArc::Init	(	MbCartPoint &	pc,
		const MbCartPoint &	p,
		bool	firstPoint,
		double	angle,
		double	rad,
		bool	clockwise
	)

Initialize a circular arc.

The source object is changed to the circular arc with the given radius and passing through point p. The circle center should be defined so as it is as close to the given point pc as possible. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters

[in,out]	pc	- On input - the given point, on output - the circle center.
[in]	p	- End point of the circular arc.
[in]	firstPoint	- Flag determining whether the point pnt is a starting point.
[in]	angle	- The angle between the radius to the second point and the OX axis.
[in]	rad	- Radius.
[in]	clockwise	- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

Init() [12/17]

void MbArc::Init	(	const MbCartPoint &	pc,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		int	initSense
	)

Initialize a circular arc.

In the result of the operation the circular arc is obtained with the center in point pc. The radius is determined as the distance between points 'pc' and 'p1'. Directions from the center to points p1 and p2 specify the angles determining the start and the end of the circle. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters

[in]	pc	- Center of circle.
[in]	p1	- A point specifying the direction to the beginning of the circular arc.
[in]	p2	- A point specifying the direction to the end of the circular arc.
[in]	initSense	- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

Init() [13/17]

bool MbArc::Init	(	double	a2,
		MbCartPoint &	p1,
		MbCartPoint &	p2,
		const DiskreteLengthData *	diskrData = nullptr,
		bool	correctFirstPnt = true
	)

Initialize a circular arc.

The initialization is performed by the starting and end points and 1/2 of the arc opening angle. If diskrData != nullptr, the radius is rounded and the first or the second point is corrected (depends on correctFirstPnt).

Parameters

[in]	a2	- 1/2 of the circular arc opening angle.
[in,out]	p1	- The starting point of the arc. Can be corrected after rounding the radius.
[in,out]	p2	- The end point of the arc. Can be corrected after rounding the radius.
[in]	diskrData	- The structure for rounding the radius.
[in]	correctFirstPnt	- Determines which point to be corrected after the rounding. correctFirstPnt == true - the first point is to be corrected.

Returns

True if initialization completed successfully.

Init() [14/17]

void MbArc::Init	(	double	aa,
		double	bb,
		const MbPlacement &	place
	)

Initialize an ellipse.

In the result of the operation the ellipse is obtained with the given local coordinate system and semiaxes.

Parameters

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

Init() [15/17]

void MbArc::Init	(	double	aa,
		double	bb,
		const MbCartPoint &	pc,
		double	ang
	)

Initialize an ellipse.

In the result of the operation the ellipse is obtained with the specified semiaxes. The ellipse local coordinate system has origin in point pc; OX axis of the local coordinate system forms angle ang with OX axis of the current coordinate system. The turning direction - from the axis of the current coordinate system to the axis of the new coordinate system.

Parameters

[in]	aa	- Radius of semiaxis along X.
[in]	bb	- Radius of semiaxis along Y.
[in]	pc	- Origin of local coordinate system of ellipse.
[in]	ang	- An angle between OX axes of the local and the current coordinate systems.

Init1()

void MbArc::Init1	(	const MbCartPoint &	c,
		const MbCartPoint &	p1,
		double &	len,
		double &	angle
	)

Initialize an ellipse.

In the result of the operation an ellipse is obtained with center in point c. The length of ellipse semiaxis along X-axis is determined as the distance between points c and p1. The length of the second semiaxis is 0. The angle between OX axes of the ellipse's local coordinate system and the current coordinate system.

Parameters

[in]	c	- The ellipse center.
[in]	p1	- A point on ellipse.
[out]	len	- The length of semiaxis along X.
[out]	angle	- An angle between OX axes of the local and the current coordinate systems.

Init2()

void MbArc::Init2	(	const MbCartPoint &	c,
		const MbCartPoint &	p1,
		MbCartPoint &	p2,
		double &	lenB
	)

Initialize an ellipse.

In the result of the operation an ellipse is obtained with center in point c. Point p1 determines the direction of OX axis of ellipse's local coordinate system and the length of semiaxis along X. Point p2 determines the length of semiaxis along Y as the distance from the point to the OX axis of the local coordinate system. Point p2 is changed so as it lies on intersection of the ellipse with OY axis of the local coordinate system.

Parameters

[in]	c	- The ellipse center.
[in]	p1	- A point on ellipse specifies OX axis.
[in,out]	p2	- Specifies the length of semiaxis along Y. On output - point on intersection of ellipse with OY axis of the local coordinate system.
[out]	lenB	- The length of semiaxis along Y.

Init3()

void MbArc::Init3	(	const MbCartPoint &	c0,
		const MbCartPoint &	p1,
		double	angle,
		double &	aa,
		double &	bb
	)

Initialize an ellipse.

In the result of the operation an ellipse is obtained inscribed into the rotated rectangle specified by the point of center c, the vertex p1 and the slope angle 'angle'. OX-axis of the local coordinate system of the ellipse will be oriented according to the angle 'angle'.

Parameters

[in]	c0	- The center of the rectangle.
[in]	p1	- The rectangle vertex.
[in]	angle	- Slope angle of the rectangle.
[out]	aa	- The length of semiaxis along X.
[out]	bb	- The length of semiaxis along Y.

Init4() [1/2]

void MbArc::Init4	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		double	angle,
		double &	aa,
		double &	bb
	)

Initialize an ellipse.

In the result of the operation an ellipse is obtained inscribed into the rotated rectangle specified by two diagonal points p1 and p2 and the slope angle 'angle'. OX-axis of the local coordinate system of the ellipse will be oriented according to the angle 'angle'.

Parameters

[in]	p1	- The rectangle vertex.
[in]	p2	- The rectangle vertex.
[in]	angle	- Slope angle of the rectangle.
[out]	aa	- The length of semiaxis along X.
[out]	bb	- The length of semiaxis along Y.

Init5()

void MbArc::Init5	(	const MbCartPoint &	c,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		double &	aa,
		double &	bb,
		double &	angle
	)

Initialize an ellipse.

In the result of the operation an ellipse is obtained inscribed into the parallelogram given by three points: center of parallelogram (c), middle of one of its sides (p1) and one of vertices of this side (p2). OX-axis of the local coordinate system of the ellipse will pass through the point p2.

Parameters

[in]	c	- The center of parallelogram.
[in]	p1	- The middle of a side of the parallelogram.
[in]	p2	- A vertex of the parallelogram.
[out]	aa	- The length of semiaxis along X.
[out]	bb	- The length of semiaxis along Y.
[out]	angle	- An angle between OX axes of the local and the current coordinate systems.

Init6()

void MbArc::Init6	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		const MbCartPoint &	p3,
		double &	aa,
		double &	bb,
		double &	angle
	)

Initialize an ellipse.

In the result of the operation an ellipse is obtained inscribed into the parallelogram given by three vertices. OX-axis of the local coordinate system of the ellipse will be parallel to the segment [p1 p2].

Parameters

[in]	p1	- A vertex of the parallelogram.
[in]	p2	- A vertex of the parallelogram.
[in]	p3	- A vertex of the parallelogram.
[out]	aa	- The length of semiaxis along X.
[out]	bb	- The length of semiaxis along Y.
[out]	angle	- An angle between OX axes of the local and the current coordinate systems.

Init7()

void MbArc::Init7	(	const MbCartPoint &	pc,
		MbCartPoint	p1,
		MbCartPoint	p2,
		MbCartPoint	p3,
		double &	aa,
		double &	bb,
		double &	angle
	)

Initialize an ellipse.

In the result of the operation an ellipse is obtained constructed by the center pc and three points on it p1, p2, p3

Parameters

[in]	pc	- The ellipse center.
[in]	p1	- A point on ellipse.
[in]	p2	- A point on ellipse.
[in]	p3	- A point on ellipse.
[out]	aa	- The length of semiaxis along X.
[out]	bb	- The length of semiaxis along Y.
[out]	angle	- An angle between OX axes of the local and the current coordinate systems.

Init8()

void MbArc::Init8	(	const MbCartPoint &	p1,
		const MbDirection &	dir1,
		const MbCartPoint &	p2,
		const MbDirection &	dir2,
		const MbCartPoint &	p3,
		double &	aa,
		double &	bb,
		double &	angle
	)

Initialize an ellipse.

For ellipse construction we have two points on ellipse and tangent lines at these points and the third point on the ellipse.

Parameters

[in]	p1	- A point on ellipse.
[in]	dir1	- The direction of tangent line to ellipse at point p1.
[in]	p2	- A point on ellipse.
[in]	dir2	- The direction of tangent line to ellipse at point p2.
[in]	p3	- A point on ellipse.
[out]	aa	- The length of semiaxis along X.
[out]	bb	- The length of semiaxis along Y.
[out]	angle	- An angle between OX axes of the local and the current coordinate systems.

Init() [16/17]

void MbArc::Init	(	double	aa,
		double	bb,
		const MbPlacement &	place,
		double	t1,
		double	t2,
		int	initSense
	)

Initialize an elliptical arc.

In the result of the operation an elliptical arc is obtained with the specified semiaxes and the local coordinate system. 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 orientation is counterclockwise.

Parameters

[in]	aa	- Radius of semiaxis along X.
[in]	bb	- Radius of semiaxis along Y.
[in]	place	- The local coordinate system of the 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 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

Init() [17/17]

void MbArc::Init	(	double	aa,
		double	bb,
		const MbPlacement &	place,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		bool	clockwise
	)

Initialize an elliptical arc.

In the result of the operation an elliptical arc is obtained with the specified semiaxes and the local coordinate system. Points 'p1' and 'p2' specify the bounds of arc. 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 passing through the point 'p2'. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters

[in]	aa	- Radius of semiaxis along X.
[in]	bb	- Radius of semiaxis along Y.
[in]	place	- The local coordinate system of the ellipse.
[in]	p1	- A point specifying the beginning of the arc.
[in]	p2	- A point specifying the end of the arc.
[in]	clockwise	- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

Init4() [2/2]

void MbArc::Init4	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		const MbCartPoint &	pB,
		const MbCartPoint &	pE,
		bool	clockwise = false
	)

Initialize an elliptical arc.

Ellipse is inscribed into the rectangle given by two diagonal points p1 and p2. Sides of the rectangle are parallel to the axes of the current coordinate system. The projections of points pB and pE onto ellipse determine the start and the end of the arc. 'clockwise' determines moving form the start point to the end point clockwise or counterclockwise.

Parameters

[in]	p1	- The rectangle vertex.
[in]	p2	- The rectangle vertex.
[in]	pB	- A point specifying the beginning of the arc.
[in]	pE	- A point specifying the end of the arc.
[in]	clockwise	- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

OnSector()

bool MbArc::OnSector

(

double

angle

)

const

Determine whether the ray hits the arc's sector.

It is analyzed if the ray starting from the center and forming the angle 'angle' with OX-axis of the current coordinate system hits the arc's sector.

Parameters

[in]

angle

- The angle between the direction being analyzed and the OX-axis of the current coordinate system.

Returns

True if the direction hits the arc's sector.

SetLimitPoint()

void MbArc::SetLimitPoint	(	ptrdiff_t	number,
		const MbCartPoint &	pnt
	)

Replace the arc's point.

The reconstruction of the elliptical arc by the end points is performed keeping the arc opening angle.

Parameters

[in]	number	- The index of end point of the arc. 1 - start of arc, 2 - end of arc.
[in]	pnt	- A new point.

GetLimitAngle()

double MbArc::GetLimitAngle ( ptrdiff_t  number ) const

inline

Return the angle of the end point.

The angle of the end point of the arc is measured relative to the OX-axis of the current coordinate system.

Parameters

[in]

number

- The index of end point of the arc. 1 - start of arc, 2 - end of arc.

Returns

The angle between the direction from the center to the end point and OX-axis of the current coordinate system.

SetLimitAngle()

void MbArc::SetLimitAngle ( ptrdiff_t  number, const MbCartPoint &  pnt  )

inline

Modify the end angle of the arc.

Parameters

[in]	number	- The index of end point of the arc. 1 - start of arc, 2 - end of arc.
[in]	pnt	- The point specifying the direction to the new end of the arc.

Returns

The angle between the direction from the center to the end point and OX-axis of the current coordinate system.

PointOnBaseEllipse()

void MbArc::PointOnBaseEllipse	(	double &	t,
		MbCartPoint &	pnt
	)		const

Evaluate a point on ellipse.

The point is evaluated on a closed ellipse regardless of whether the object is an ellipse or is an elliptical arc.

Parameters

[in]	t	- Parameter.
[out]	pnt	- The required point.

PointProjectionOnBaseEllipse()

double MbArc::PointProjectionOnBaseEllipse

(

const MbCartPoint &

pnt

)

const

Find the projection of a point onto the ellipse.

A point is projected onto the closed ellipse regardless of whether the object is an ellipse or an elliptical arc.

Parameters

[in]

pnt

- A point to project.

Returns

Parameter corresponding to the projected point.

IsSelfIntersectOffset()

bool MbArc::IsSelfIntersectOffset

(

double

d

)

const

Determine whether the ellipse offset has self-intersections.

Parameters

[in]

d

- Offset distance.

Returns

True if it has self-intersections.

EllipticIntersect()

ptrdiff_t MbArc::EllipticIntersect	(	const MbLine &	pLine,
		double	cross[2],
		double	eps0 = PARAM_PRECISION
	)		const

Determine the parameters of intersection of a line with an ellipse.

Parameters

[in]	pLine	- Line.
[out]	cross	- Array with parameters of ellipse at intersection points.

Returns

Count of intersection points.

GetProperties()

void MbArc::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 MbArc::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.

Member Data Documentation

rect

MbRect MbArc::rect

mutableprotected

Auxiliary data.

Auxiliary data are used for fast calculations.
Bounding rectangle.

---

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

• cur_arc.h