Bezier spline in two-dimensional space. More...

#include <cur_bezier.h>

Inheritance diagram for MbBezier:

Collaboration diagram for MbBezier:

Public Member Functions
DEPRECATE_DECLARE	MbBezier (bool closed, const SArray< MbCartPoint > &points)
	Constructor by array of all points. More...

DEPRECATE_DECLARE	MbBezier (const SArray< MbCartPoint > &initList, bool cls, int initForm=0)
	Constructor by poles. More...

virtual	~MbBezier ()
	Destructor.

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

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

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

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

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

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

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

Spline initialization functions.
void	Init (const SArray< MbCartPoint > &initList, bool cls)
	Initialize a curve by poles and closedness. More...

void	Init (const MbBezier &initCurve)
	Initialize a curve by a given Bezier curve. More...

void	Init (const MbArc &arc)
	Initialize a curve by a circle arc. More...

void	InitCtrlPoints (const SArray< MbCartPoint > &initList)
	Initialize a curve by control points. More...

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

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

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

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

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

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

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 the motion 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 curve
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...

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...

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

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

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

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

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

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...

Common functions of a polygonal curve
size_t	GetPointsCount () const override
	Return the number of non-coincedent control points.

void	GetPoint (ptrdiff_t index, MbCartPoint &pnt) const override
	Get control point. More...

ptrdiff_t	GetNearPointIndex (const MbCartPoint &pnt) const override
	Get the point index which is nearest to the given.

void	GetRuleInterval (ptrdiff_t index, double &t1, double &t2) const override
	Get the range of influence of point of the curve. More...

void	Rebuild () override
	Rebuild curve.

void	SetClosed (bool cls) override
	Set attribute of closedness.

void	LtSetClosed (bool cls)

void	RemovePoint (ptrdiff_t index) override
	Remove control point with given index.

void	RemovePoints () override
	Remove all points.

void	AddPoint (const MbCartPoint &pnt) override
	Add point to the end of the array of control points.

void	InsertPoint (ptrdiff_t index, const MbCartPoint &pnt) override
	Insert a point to the array of control points. More...

void	InsertPoint (double t, const MbCartPoint &pnt, double xEps, double yEps) override
	Insert a point to the array of control points. More...

void	InsertPolePoints (size_t index, const MbCartPoint &leftPnt, const MbCartPoint &basePnt, const MbCartPoint &rightPnt)
	Insert a pole, specified by three pointss, by index. No recalculation of derivatives at the poles. More...

void	ChangePole (ptrdiff_t index, const MbCartPoint &pnt) override
	Replace the pole. More...

void	ChangePoint (ptrdiff_t index, const MbCartPoint &pnt) override
	Replace a point. More...

bool	CheckParam (double &t, ptrdiff_t &i0, ptrdiff_t &i1, double &t0, double &t1) const override
	Drive a parameter into the curve domain. More...

double	GetParam (ptrdiff_t i) const override
	Get parameter corresponding to the point with specified index.

size_t	GetParamsCount () const override
	Get count of parameters.

void	GetTList (SArray< double > &params) const override

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

MbeState	Deformation (const MbRect &, const MbMatrix &) override
	Deform the curve. More...

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

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

void	AddPoint (MbCartPoint &pnt, double dl, double dr, double angle)
	Add point and derivatives to the end of array. More...

void	ConvexHull (ptrdiff_t seg, SArray< MbCartPoint > &poly) const
	Determine the convex hull of the curve segment. More...

void	OffsetCuspPoint (SArray< double > &tCusps, double dist) const override
	Determination of singular points of the offset curve.

void	GetSegments (RPArray< MbBezier > &segments) const
	Return an array of separate segments of the Bezier-curve.

void	ExeptEqualPoints ()
	Delete coincident points.

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

MbContour *	CreateContour () const
	Create a contour from the NURBS curve.

bool	Break (MbBezier &trimPart, double t1, double t2, const MbDimAccuracy &xyEps=MbDimAccuracy::twoDimAcc) const
	Allocate a part of the Bezier curve. More...

void	SetBezierSplines ()
	Calculate parameters of the Bezier curve.

int	GetFormType () const
	Return the spline shape.

void	SetFormType (int newForm)
	Set the spline shape.

ptrdiff_t	GetSplinesCount () const
	The number of splines.

void	Trimm (MbBezier &trimm, double t1, double t2, int sense) const
	Break a part of the Bezier curve. More...

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

bool	BasicFunctions (double &t, CcArray< double > &values, ptrdiff_t &left) const
	Calculate all base functions in the point. More...

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

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

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

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

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

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

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

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

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

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

MbeState	Deformation (const MbRect &, const MbMatrix &) override
	Deform the curve. More...

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

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

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

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

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

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

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

virtual void	SetBegEndDerivesEqual ()
	Set equal derivatives at the ends.

virtual void	ClosedBreak ()
	Make curve open, keeping coincidence of the beginning and the end.

virtual bool	ChangePointsValue (const SArray< MbCartPoint > &pntList)
	Change control points. More...

virtual void	AddAfter (const MbCartPoint &pnt, ptrdiff_t index)
	Insert a point to the array of control points. More...

virtual void	InsertPoint (double t, const MbCartPoint &pnt, const MbVector &v, double xEps, double yEps)
	Insert a point to the array of control points. More...

size_t	GetPointListCount () const
	Get count of control points.

ptrdiff_t	GetPointListMaxIndex () const
	Get maximal index of array of control points.

template<class PointsVector >
void	GetPoints (PointsVector &pnts) const
	Get array of control points.

void	GetPointList (SArray< MbCartPoint > &pnts) const
	Get array of control points.

void	GetPointList (c3d::ParamPointsVector &pnts) const
	Get array of control points.

bool	ReplacePoints (const SArray< MbCartPoint > &pnts)
	Replace the set of control points.

bool	ReplacePoints (const std::vector< MbCartPoint > &pnts)
	Replace the set of control points.

const MbCartPoint &	GetPointList (size_t i) const
	Get control point with the given index.

MbCartPoint &	SetPointList (size_t i)
	Get control point with the given index.

ptrdiff_t	GetUppIndex () const
	Get the maximal index of array of control points.

size_t	GetSegmentsCount () const
	Get count of ranges.

template<class SegmentsVector >
void	GetLineSegments (SegmentsVector &segments, double eps=PARAM_PRECISION) const
	Get the array of segments.

bool	NurbsParam (double epsilon, double &pmin, double &pmax, ptrdiff_t &i1, double &t1, ptrdiff_t &i2, double &t2) const
	Get information for NurbsCurve function. More...

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

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

MbePlaneType	Family () const override
	Get family of object.

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

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

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

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

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...

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

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

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

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

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

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

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

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

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

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

virtual void	_PointOn (double t, MbCartPoint &p) const
	Calculate point at curve and its extension. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual MbCurve *	Offset (double rad) const
	Construct the equidistant curve which is shifted by the given value.

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

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

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

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...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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	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.

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 MbBezier *	Create (const MbBezier &other)
	Create copy of spline. More...

static MbBezier *	Create (const SArray< MbCartPoint > &initList)
	Create spline by four points. More...

static MbBezier *	Create (bool closed, const SArray< MbCartPoint > &points)
	Create spline by array of all points. More...

static MbBezier *	Create (const MbBezier &pCurve, ptrdiff_t iseg)
	Create spline by segment of Bezier curve. More...

static MbBezier *	Create (const SArray< MbCartPoint > &initList, bool cls, int initForm=0)
	Create spline by poles. More...

static MbBezier *	Create (const MbArc &arc)
	Create spline by circle arc. More...

Protected Member Functions
	MbBezier (const MbBezier &pCurve)
	Copy-constructor.

	MbBezier (const SArray< MbCartPoint > &initList)
	Constructor by four points. More...

	MbBezier (const MbBezier &pCurve, ptrdiff_t iseg)
	Constructor by segment of Bezier curve. More...

	MbBezier (const MbArc &arc)
	Constructor by circle arc. More...

bool	CanChangeClosed () const override
	Determine whether it is possible to change an attribute of closedness.

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

	MbPolyCurve (const MbPolyCurve &pCurve)
	Copy-constructor.

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.

Additional Inherited Members
Protected Attributes inherited from MbPolyCurve
SArray< MbCartPoint >	pointList
	Set of control points.

ptrdiff_t	uppIndex
	Count of curve pieces (is equal to count of control points minus one).

bool	closed
	An attribute of curve closedness.

MbRect	rect
	Bounding rectangle.

atomic_double	metricLength
	Metric length of a spline.

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

Detailed Description

Bezier spline in two-dimensional space.

Bezier spline in two-dimensional space is defined by control points pointList.
Bezier spline is composite curve formed by connected among themselves Bezier curves with third degree. Each third-degree Bezier curve is constructed by four adjacent control points pointList. First and last control point from pointList for unclosed Bezier spline are not used Thus Bezier spline passes through each control point with index 3n+1, where n is integer. The value of parameter along each third-degree Bezier curve is incremented. The parameter of Bezier spline changes from zero to k, where k is the number of tree-degree Bezier curves which form spline. In general case the first derivative of Bezier spline can be discontinuous by length and direction.

Constructor & Destructor Documentation

◆ MbBezier() [1/5]

DEPRECATE_DECLARE MbBezier::MbBezier	(	bool	closed,
		const SArray< MbCartPoint > &	points
	)

Constructor by array of all points.

Constructor by array of all points(poles and rockers), for creation from three-dimensional curve MbBezier3D.

Deprecated:: The method is deprecated.

Parameters

[in]	closed	- Is curve closed?
[in]	points	- An array of points. It must be obtained from point array of three-dimensional curve MbBezier3D which is planar, by projecting them onto the plane of the curve. The number of points must be multiple of three. The minimal number of points is six.

◆ MbBezier() [2/5]

DEPRECATE_DECLARE MbBezier::MbBezier	(	const SArray< MbCartPoint > &	initList,
		bool	cls,
		int	initForm = `0`
	)

Constructor by poles.

Constructor by poles. initList array contains only poles.

Deprecated:: The method is deprecated.

Parameters

[in]	initList	- An array of curve poles. Minimal number of points in array equals two.
[in]	cls	- A curve closedness.
[in]	initForm	- The shape of spline. Possible values: 0 - The standard form. 1 - More convex form of curve.

◆ MbBezier() [3/5]

MbBezier::MbBezier ( const SArray< MbCartPoint > & initList )

protected

Constructor by four points.

Parameters

[in] initList - An array of points. Number of points must be equal to four. When number of points is more then four classical cubic bezier is created for each sequential four points. The smoothness of result curve can be broken.

◆ MbBezier() [4/5]

MbBezier::MbBezier	(	const MbBezier &	pCurve,
		ptrdiff_t	iseg
	)

protected

Constructor by segment of Bezier curve.

Constructor by segment of a given Bezier curve.

Parameters

[in]	pCurve	- A given curve.
[in]	iseg	- A number of curve segment.

◆ MbBezier() [5/5]

MbBezier::MbBezier ( const MbArc & arc )

protected

Constructor by circle arc.

There was constructed a Bezier curve which approximates a given arc of a circle.

Parameters

[in] arc - Circle arc.

Member Function Documentation

◆ Create() [1/6]

static MbBezier* MbBezier::Create ( const MbBezier & other )

static

Create copy of spline.

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

◆ Create() [2/6]

static MbBezier* MbBezier::Create ( const SArray< MbCartPoint > & initList )

static

Create spline by four points.

Parameters

[in] initList - An array of points. Number of points must be equal to four. When number of points is more then four classical cubic bezier is created for each sequential four points. The smoothness of result curve can be broken.

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

◆ Create() [3/6]

static MbBezier* MbBezier::Create	(	bool	closed,
		const SArray< MbCartPoint > &	points
	)

static

Create spline by array of all points.

Create spline by array of all points(poles and rockers), for creation from three-dimensional curve MbBezier3D.

Parameters

[in]	closed	- Is curve closed?
[in]	points	- An array of points. It must be obtained from point array of three-dimensional curve MbBezier3D which is planar, by projecting them onto the plane of the curve. The number of points must be multiple of three. The minimal number of points is six.

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

◆ Create() [4/6]

static MbBezier* MbBezier::Create	(	const MbBezier &	pCurve,
		ptrdiff_t	iseg
	)

static

Create spline by segment of Bezier curve.

Create spline by segment of a given Bezier curve.

Parameters

[in]	pCurve	- A given curve.
[in]	iseg	- A number of curve segment.

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

◆ Create() [5/6]

static MbBezier* MbBezier::Create	(	const SArray< MbCartPoint > &	initList,
		bool	cls,
		int	initForm = `0`
	)

static

Create spline by poles.

Create spline by poles. initList array contains only poles.

Parameters

[in]	initList	- An array of curve poles. Minimal number of points in array equals two.
[in]	cls	- A curve closedness.
[in]	initForm	- The shape of spline. Possible values: 0 - The standard form. 1 - More convex form of curve.

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

◆ Create() [6/6]

static MbBezier* MbBezier::Create ( const MbArc & arc )

static

Create spline by circle arc.

There was constructed a Bezier curve which approximates a given arc of a circle.

Parameters

[in] arc - Circle arc.

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

◆ SetEqual()

bool MbBezier::SetEqual ( const MbPlaneItem & item )

overridevirtual

Make the objects equal.

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

Parameters

[in] item - Object for initialization.

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

Implements MbPlaneItem.

◆ IsSame()

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

overridevirtual

Determine whether objects are equal.

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

Parameters

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

Returns: Whether the objects are equal.

Implements MbPlaneItem.

◆ Transform()

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

overridevirtual

Rotate about a point.

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

Parameters

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

Implements MbPlaneItem.

◆ Duplicate()

MbPlaneItem& MbBezier::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.

◆ Init() [1/3]

void MbBezier::Init	(	const SArray< MbCartPoint > &	initList,
		bool	cls
	)

Initialize a curve by poles and closedness.

Initialize a curve by poles and closedness. initList array contains only poles.

Parameters

[in]	initList	- An array of curve poles.
[in]	cls	- A curve closedness.

◆ Init() [2/3]

void MbBezier::Init ( const MbBezier & initCurve )

Initialize a curve by a given Bezier curve.

Parameters

[in] initCurve - A given curve.

◆ Init() [3/3]

void MbBezier::Init ( const MbArc & arc )

Initialize a curve by a circle arc.

There was constructed a Bezier curve which approximates a given arc of a circle.

Parameters

[in] arc - Circle arc.

◆ InitCtrlPoints()

void MbBezier::InitCtrlPoints ( const SArray< MbCartPoint > & initList )

Initialize a curve by control points.

Initialize a curve by control points. The array initList contains poles and "rocker arms".

Parameters

[in] initList - An array of control points of curve.

◆ PointOn()

void MbBezier::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.

◆ Explore()

void MbBezier::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 MbBezier::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 MbBezier::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.

◆ NurbsCurve() [1/2]

MbNurbs* MbBezier::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* MbBezier::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* MbBezier::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.

◆ GetProperties()

void MbBezier::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 MbBezier::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.

◆ GetPoint()

void MbBezier::GetPoint	(	ptrdiff_t	index,
		MbCartPoint &	pnt
	)		const

overridevirtual

Get control point.

Returns control point of the curve by its index. If the index is negative - returns the first point. If the index is greater than the maximum available, then the last point is returned.

Parameters

[in]	index	- Index of control point.
[out]	pnt	- Control point.

Reimplemented from MbPolyCurve.

◆ GetRuleInterval()

void MbBezier::GetRuleInterval	(	ptrdiff_t	index,
		double &	t1,
		double &	t2
	)		const

overridevirtual

Get the range of influence of point of the curve.

Determines which range of curve parameter will be affected by changing of the control point with 'index' index.

Parameters

[in]	index	- Index of control point.
[out]	t1	- Minimal parameter of the range of influence.
[out]	t2	- Maximal parameter of the range of influence.

Implements MbPolyCurve.

◆ InsertPoint() [1/2]

void MbBezier::InsertPoint	(	ptrdiff_t	index,
		const MbCartPoint &	pnt
	)

overridevirtual

Insert a point to the array of control points.

Insert the given point by index.

Parameters

[in]	pnt	- A given point.
[in]	index	- Index to insert a point by.

Implements MbPolyCurve.

◆ InsertPoint() [2/2]

void MbBezier::InsertPoint	(	double	t,
		const MbCartPoint &	pnt,
		double	xEps,
		double	yEps
	)

overridevirtual

Insert a point to the array of control points.

Insert a point which corresponds to parameter 't' of the curve. If parameter 't' differs from the parameter of some point less than by the given tolerance, then the new point isn't inserted, already existent point close by parameter is replaced.

Parameters

[in]	t	- Parameter of the new point.
[in]	pnt	- A given point.
[in]	xEps	- Tolerance in x direction.
[in]	yEps	- Tolerance in y direction.

Implements MbPolyCurve.

◆ InsertPolePoints()

void MbBezier::InsertPolePoints	(	size_t	index,
		const MbCartPoint &	leftPnt,
		const MbCartPoint &	basePnt,
		const MbCartPoint &	rightPnt
	)

Insert a pole, specified by three pointss, by index. No recalculation of derivatives at the poles.

#basePnt is the characteristic point. The vector from #basePnt to the left point #leftPnt specifies the derivative to the left of the characteristic point, the vector from #basePnt to the right point #rightPnt specifies the derivative to the right of the characteristic point. To maintain the continuity of the directional derivative, the three specified points must lie on one straight line. To maintain the continuity of the derivative with respect to the magnitude, the distances from the characteristic point to the points on the right and left must be equal.

Parameters

[in]	index	- Pole index.
[in]	leftPnt	- Point to the left of the characteristic point.
[in]	basePnt	- Characteristic point
[in]	rightPnt-	Point to the right of the characteristic point.

◆ ChangePole()

void MbBezier::ChangePole	(	ptrdiff_t	index,
		const MbCartPoint &	pnt
	)

overridevirtual

Replace the pole.

Replaces characteristic point with a given index.

Parameters

[in]	index	- An index of changed point.
[in]	pnt	- A given point.

Reimplemented from MbPolyCurve.

◆ ChangePoint()

void MbBezier::ChangePoint	(	ptrdiff_t	index,
		const MbCartPoint &	pnt
	)

overridevirtual

Replace a point.

Parameters

[in]	index	- Index of a point to be changed.
[in]	pnt	- A given point.

Reimplemented from MbPolyCurve.

◆ CheckParam()

bool MbBezier::CheckParam	(	double &	t,
		ptrdiff_t &	i0,
		ptrdiff_t &	i1,
		double &	t0,
		double &	t1
	)		const

overridevirtual

Drive a parameter into the curve domain.

Check parameter. If it is out of the range of the curve parameters, then in case of closed curve drive it into the definition domain with changing by period. In case of open curve - make equal to the nearest boundary parameter. Determine indices of control points the given parameter is between, and also determine their parametric values.

Parameters

[in,out]	t	- On input - the given parameter. On output - parameter in the curve definition domain.
[out]	i0	- Index of control point to the left of the given parameter.
[out]	i1	- Index of control point to the right of the given parameter.
[out]	t0	- Parameter of control point to the left of the given parameter.
[out]	t1	- Parameter of control point to the right of the given parameter.

Returns: True if the operation succeeded.

Implements MbPolyCurve.

◆ CalculateGabarit()

void MbBezier::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.

◆ DeletePart()

MbeState MbBezier::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 MbBezier::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.

◆ Deformation()

MbeState MbBezier::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.

◆ TangentPoint()

void MbBezier::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.

◆ AddPoint()

void MbBezier::AddPoint	(	MbCartPoint &	pnt,
		double	dl,
		double	dr,
		double	angle
	)

Add point and derivatives to the end of array.

Add pole to the end of curve, and the movement of neighboring points (no poles), to ensure the direction of the tangent to the curve at the pole and derivatives lengths in the pole.

Parameters

[in]	pnt	- A given point.
[in]	dl	- Derivative length in pole on the left.
[in]	dr	- Derivative length in pole on the right.
[in]	angle	- The angle between the direction of the tangent and the OX-axis of the current coordinate system.

◆ ConvexHull()

void MbBezier::ConvexHull	(	ptrdiff_t	seg,
		SArray< MbCartPoint > &	poly
	)		const

Determine the convex hull of the curve segment.

Parameters

[in]	seg	- A number of curve segment.
[out]	poly	- Array of points which constitute the convex hull of the segment.

◆ Break()

bool MbBezier::Break	(	MbBezier &	trimPart,
		double	t1,
		double	t2,
		const MbDimAccuracy &	xyEps = `MbDimAccuracy::twoDimAcc`
	)		const

Allocate a part of the Bezier curve.

The new curve is created - a part of the Bezier curve between t1 and t2 parameters.

Parameters

[out]	trimPart	- Created curve.
[in]	t1	- A beginning parameter.
[in]	t2	- An end parameter.
[in]	xyEps	- The xyEps.x component corresponds to x-axis accuracy, xyEps.y corresponds to y-axis accuracy.

Returns: True - if construction has been successfully.

◆ Trimm()

void MbBezier::Trimm	(	MbBezier &	trimm,
		double	t1,
		double	t2,
		int	sense
	)		const

Break a part of the Bezier curve.

The new curve is created - a part of the Bezier curve between t1 and t2 parameters.

Parameters

[out]	trimm	- Created curve.
[in]	t1	- A beginning parameter.
[in]	t2	- An end parameter.
[in]	sense	- Whether the direction of the resulting curve coincides with the direction of the original curve.

◆ DistanceToPointIfLess()

bool MbBezier::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.

◆ BasicFunctions()

bool MbBezier::BasicFunctions	(	double &	t,
		CcArray< double > &	values,
		ptrdiff_t &	left
	)		const

Calculate all base functions in the point.

For a given parameter, are calculated all base functions of the spline and the index of the first characteristic point which determines the behavior of the spline at a given parameter.

Parameters

[in]	t	- A parameter.
[out]	values	- An array with values of base functions in the point.
[in]	left	- An index of characteristic point.

Returns: True - if operation has been successfully.

◆ DistanceAlong()

bool MbBezier::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.

◆ IsContinuousDerivative()

bool MbBezier::IsContinuousDerivative	(	bool &	contLength,
		bool &	contDirect,
		c3d::DoubleVector *	params = `nullptr`,
		double	epsilon = `EPSILON`
	)		const

overridevirtual

Get properties of the object.

Set properties of the object. Get the basis points of the curve.

Have the first derivative of the curve the continuous length and direction?

Are absent any discontinuities at length or at direction of first derivative of the curve?

Parameters

[out]	contLength	- The length is continuous (true/false).
[out]	contDirect	- The direction of the first derivative is continuous (true/false).
[out]	params	- The parameters of the points at which the direction break occurs.
[in]	epsilon	- The accuracy of the calculation.

Reimplemented from MbCurve.

◆ SetContinuousDerivativeLength()

bool MbBezier::SetContinuousDerivativeLength	(	VERSION	version,
		double	epsilon = `EPSILON`
	)

overridevirtual

Eliminate the discontinuities of the first derivative at length.

Eliminate the discontinuities of the first derivatives of the length.

Parameters

[in]	epsilon	- The accuracy of the calculation.
[in]	version	- Math version.

Reimplemented from MbCurve.

◆ Trimmed() [2/3]

virtual MbCurve* MbCurve::Trimmed

Construct a trimmed curve.

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

Parameters

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

Returns: A constructed trimmed curve.

◆ Trimmed() [3/3]

virtual MbCurve* MbCurve::Trimmed

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

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

Parameters

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

Returns: A constructed trimmed curve.

Warning: Under development.

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

cur_bezier.h

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MbBezier() [1/5]

◆ MbBezier() [2/5]

◆ MbBezier() [3/5]

◆ MbBezier() [4/5]

◆ MbBezier() [5/5]

Member Function Documentation

◆ Create() [1/6]

◆ Create() [2/6]

◆ Create() [3/6]

◆ Create() [4/6]

◆ Create() [5/6]

◆ Create() [6/6]

◆ SetEqual()

◆ IsSame()

◆ Transform()

◆ Move()

◆ Rotate()

◆ Duplicate()

◆ Init() [1/3]

◆ Init() [2/3]

◆ Init() [3/3]

◆ InitCtrlPoints()

◆ PointOn()

◆ Explore()

◆ Step()

◆ DeviationStep()

◆ NurbsCurve() [1/2]

◆ NurbsCurve() [2/2]

◆ Trimmed() [1/3]

◆ GetProperties()

◆ SetProperties()

◆ GetPoint()

◆ GetRuleInterval()

◆ InsertPoint() [1/2]

◆ InsertPoint() [2/2]

◆ InsertPolePoints()

◆ ChangePole()

◆ ChangePoint()

◆ CheckParam()

◆ CalculateGabarit()

◆ DeletePart()

◆ TrimmPart()

◆ Deformation()

◆ TangentPoint()

◆ AddPoint()

◆ ConvexHull()

◆ Break()

◆ Trimm()

◆ DistanceToPointIfLess()

◆ BasicFunctions()

◆ DistanceAlong()

◆ IsContinuousDerivative()

◆ SetContinuousDerivativeLength()

◆ Trimmed() [2/3]

◆ Trimmed() [3/3]