NURBS curve in two-dimensional space. More...

#include <cur_nurbs.h>

Inheritance diagram for MbNurbs:

Collaboration diagram for MbNurbs:

Public Member Functions
DEPRECATE_DECLARE	MbNurbs ()

Common functions of 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 &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...

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

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

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

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

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

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

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

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

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

Functions for working in the curve's domain.
Functions PointOn, FirstDer, SecondDer, ThirdDer,... correct parameter when it is out of domain bounds.
void	PointOn (double &t, MbCartPoint &pnt) 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...

void	Derivatives (double &t, bool ext, MbVector &fir, MbVector sec, MbVector thi) const

void	ExtPointOn (double t, MbCartPoint &pnt) const
	Point on the curve extension.

void	ExtFirstDer (double t, MbVector &fd) const
	The first derivative on the curve extension.

void	ExtSecondDer (double t, MbVector &sd) const
	The second derivative on the curve extension.

void	ExtThirdDer (double t, MbVector &td) const
	The third derivative on the curve extension.

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

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

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

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...

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

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

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

MbCurve *	NurbsCurve (const MbNurbsParameters &tParameters) 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...

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

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

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

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

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

void	CalculatePolygon (double sag, MbPolygon &) const override
	Calculate an array of points for drawing. 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	GoThroughPoint (MbCartPoint &p0) override
	Create a curve through a point. More...

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

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

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

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

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

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

void	MakeTangentLine (MbLine *line)
	Touching the spline by line.

void	ConvexHull (ptrdiff_t seg, MbCartPoint *p) const
	Determine the convex hull of the curve segment.

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

bool	ChangePointsValue (const SArray< MbCartPoint > &pntList) override
	Change control points. 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	ResetTCalc () const override
	Reset the current value of parameter.

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

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

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...

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

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

Functions of B-spline.
void	AddPoint (ptrdiff_t index, const MbCartPoint &pnt, double weight)
	Add a point with weight.

void	AddPoint (const MbCartPoint &pnt, double weight)
	Add point to the end of the array.

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

MbNurbs *	Break (double t1, double t2) const
	Break a part.

MbeNurbsCurveForm	GetFormType () const
	Get form of B-spline.

size_t	GetDegree () const
	Get the spline order.

bool	IsRational () const
	Get attribute of rationality, but no regularity of curve.

size_t	GetWeightsCount () const
	Get a size of weights vector.

template<class WeightsVector >
void	GetWeights (WeightsVector &wts, bool justSet=true) const
	Get a weights vector.

double	GetWeight (size_t ind) const
	Get a weights vector element value by index.

double &	SetWeight (size_t ind)
	Get a weights vector element value by index.

size_t	GetKnotsCount () const
	Get a size of knots vector.

template<class KnotsVector >
void	GetKnots (KnotsVector &kts, bool justSet=true) const
	Get a knots vector.

double	GetKnot (size_t ind) const
	Get a knots vector element value by index.

double &	SetKnot (size_t ind)
	Get a knots vector element value by index.

ptrdiff_t	GetUppKnotsIndex () const
	Get the maximal index of knots vector.

void	LtAddPoint (MbCartPoint &pnt, double weight)
	Add point to the end of the array.

void	LtAddPowerPoint (MbCartPoint &pnt)
	Add a control point with degree representation to the end of the array.

void	LtAddKnot (double knot)
	Add a knot to the end of knot vector.

void	LtSetDegree (size_t newDegree)
	Set the spline order.

void	LtSetClosed (bool cls)
	Set the closedness attribute.

void	LtSetData (size_t d, bool c, MbeNurbsCurveForm f)
	Change degree, closedness and type of shape.

bool	LtRebuild ()
	Rebuild the spline.

void	LtInit ()
	Initialization.

bool	LtInitPowerArc ()

bool	LtTrimmed (double t1, double t2, int sense=1)

void	Bezier (MbNurbs &bezierForm) const
	Create a Bezier shape of Nurbs.

bool	Concatenate (MbNurbs &)
	Attach nurbs.

void	SetWeight (ptrdiff_t pointNumber, double newWeight)
	Set weight for control point.

size_t	KnotMultiplicity (ptrdiff_t knotIndex) const
	Get the knot multiplicity.

void	DefineKnotsVector ()
	Determination of basis knot vector.

bool	OpenKnotsVector ()
	Redetermination of the basis knot vector from Close to Open.

bool	CloseKnotsVector ()
	Redetermination of the basis knot vector from Open to Close.

void	CyclicShift (ptrdiff_t interval)
	Shift parameter of closed spline.

void	CyclicShift (double t)

bool	BasicFunctions (double &t, ptrdiff_t k, CcArray< double > &values, ptrdiff_t &left, double &sum)

void	CheckForm ()

MbCurve *	ConvertToConic ()
	Transform a curve into a conic section if it is possible.

bool	SetLimitParam (double newTMin, double newTMax)
	Set the range of parameter.

size_t	InsertKnots (double &newKnot, size_t multiplicity, double relEps)
	Addition of a new knots; returns the number of knots which have been inserted.

ptrdiff_t	RemoveKnot (ptrdiff_t id, ptrdiff_t num, double relEps=Math::paramEpsilon, double absEps=Math::lengthEpsilon)
	Remove multiple internal 'id' knot 'num' times, return count of removals was successfully made.

void	RemoveAllKnots (double relEps=Math::paramEpsilon, double absEps=Math::lengthEpsilon)
	Remove all internal knots if it is possible.

bool	DecomposeCurve ()
	Convert this nurbs to Bezier form; knot vector to clamped.

bool	UnClamped (bool clm)
	Transform knot vector to clamped (if curve is closed and clm = false) or unclamped (if curve is open and clm = true).

void	AddCurve (MbNurbs &, bool bmerge=true)
	Add curve to the end.

template<class NurbsCurves >
void	AddCurves (NurbsCurves &curves)
	Add curves to the end.

bool	BreakC0NURBS4 (RPArray< MbCurve > &, bool bline=true)
	Split the curve. More...

bool	BreakC0 (c3d::PlaneCurvesSPtrVector &, double metricAcc=METRIC_EPSILON, VERSION version=Math::DefaultMathVersion())
	Split NURBS-curve at places where the curve is non-differentiable. Parametrization does not remain.

bool	ExtendNurbs (double, double, bool bmerge=false)
	Extend open NURBS-curve by tangents.

void	FixClosedNurbs ()
	Make curve closed. 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 size_t	GetPointsCount () const
	Get count of control points.

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

virtual ptrdiff_t	GetNearPointIndex (const MbCartPoint &pnt) const
	Get index of the point nearest to the given one.

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

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

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...

virtual void	ChangePole (ptrdiff_t index, const MbCartPoint &pnt)
	Replace a pole. More...

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

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 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...

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 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...

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.

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

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

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

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

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

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

virtual void	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	GetMiddlePoint (MbCartPoint &) const
	Calculate a middle 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

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.

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 MbNurbs *	Create (const MbNurbs &)
	Create copy of spline. More...

template<class PointsVector >
static MbNurbs *	Create (ptrdiff_t initDegree, const PointsVector &initPoints, bool initClosed)
	Create spline. More...

template<class PointsVector , class DoubleVector >
static MbNurbs *	Create (ptrdiff_t initDegree, const PointsVector &initPoints, bool initClosed, const DoubleVector *initWeights)
	Create spline. More...

template<class PointsVector , class DoubleVector >
static MbNurbs *	Create (ptrdiff_t initDegree, bool initClosed, const PointsVector &initPoints, const DoubleVector &initWeights, const DoubleVector &initKnots, MbeNurbsCurveForm initForm=ncf_Unspecified)
	Create spline. More...

static MbNurbs *	CreateThrough (size_t degree, bool cls, const SArray< MbCartPoint > &points, const SArray< double > &params, SArray< double > *aKnots=nullptr)
	Create spline. More...

static MbNurbs *	CreateParasolid (size_t degree, bool closed, bool rational, ptrdiff_t count, const CcArray< double > &verts, ptrdiff_t vertsCount, const CcArray< ptrdiff_t > &mul, ptrdiff_t mulCount, const CcArray< double > &knots, ptrdiff_t knotsCount, double scl)
	Fill NURBS by parasolid data. More...

static MbNurbs *	CreateCube (const MbCartPoint &p1, const MbVector &v1, const MbCartPoint &p2, const MbVector &v2)
	Create spline. More...

static MbNurbs *	CreateArc (const SArray< MbCartPoint > &points)
	Create spline. More...

static MbNurbs *	CreateArc (double a2, const MbCartPoint &p1, const MbCartPoint &p2)
	Create spline. More...

static MbNurbs *	CreateWavyLine (const MbCartPoint &p1, const MbCartPoint &p2, double height, double periode)
	Create spline. More...

Protected Member Functions
template<class PointsVector , class DoubleVector >
	MbNurbs (size_t degree, bool cls, const PointsVector &points, const DoubleVector weights, const DoubleVector knots)
	Constructor. 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.

Functions of NURBS curve initialization.
void	Init (const MbNurbs &)
	Set the spline parameters by a given NURBS curve.

template<class PointsVector >
bool	Init (size_t initDegree, const PointsVector &initPoints, bool initClosed)
	Initialization. More...

template<class PointsVector , class DoubleVector >
bool	Init (size_t initDegree, const PointsVector &initPoints, bool initClosed, const DoubleVector *initWeights)
	Initialization. More...

template<class PointsVector , class DoubleVector >
bool	Init (size_t initDegree, bool initClosed, const PointsVector &initPoints, const DoubleVector &initWeights, const DoubleVector &initKnots, MbeNurbsCurveForm initForm=ncf_Unspecified)
	Initialization. More...

bool	Init (size_t degree, bool cls, const CcArray< double > &points, const CcArray< double > &knots, ptrdiff_t nPoints, ptrdiff_t nKnots)
	Initialization. More...

bool	InitThrough (size_t degree, bool cls, const SArray< MbCartPoint > &points, const SArray< double > &params, SArray< double > *aKnots=nullptr)
	Initialization. More...

bool	InitThrough (size_t degree, bool cls, const c3d::ParamPointsVector &points, const c3d::DoubleVector &params, c3d::DoubleVector *aKnots=nullptr)
	Initialization. More...

bool	InitLine (double t1, const MbCartPoint &p1, double t2, const MbCartPoint &p2)
	Initialization. More...

bool	InitCube (const MbCartPoint &p1, const MbVector &v1, const MbCartPoint &p2, const MbVector &v2)
	Initialization. More...

bool	AttachG (c3d::PntMatingData2D &connectData, bool beg)
	Set conjugation at the end.

bool	RaiseDegree (size_t newDegree, double relEps=Math::paramEpsilon)
	Increase order of curve without changing its geometric shape and parametrization. More...

bool	ReductionDegree (double relEps=Math::paramEpsilon)
	Decrease order of nurbs curve by 1 without changing its geometric shape and parametrization. More...

bool	SetDegree (size_t newDegree)
	Set the spline order. More...

void	DegreeIncrease ()
	Increase the order by 1.

void	SetFormType (MbeNurbsCurveForm f)
	Set the type of shape.

bool	PointOnMultipleKnot (const MbCartPoint &point) const
	The point on a multiple knot.

static MbNurbs *	CreateNURBS2 (const SArray< MbCartPoint > &points, const SArray< double > &params, bool cls)
	Interpolation. More...

static MbNurbs *	CreateNURBS4 (const SArray< MbCartPoint > &, MbeSplineParamType spType, const c3d::PntMatingData2D &begData, const c3d::PntMatingData2D &endData)
	Create cubic NURBS by parameters of conjugation and points which it passes through.

static MbNurbs *	CreateNURBS4 (const SArray< MbCartPoint > &, MbeSplineParamType spType, bool closed, RPArray< c3d::PntMatingData2D > &)
	Create cubic NURBS by interpolation points and data of conjugation at each point.

static MbNurbs *	CreateNURBS4 (const SArray< MbCartPoint > &, const SArray< double > &, bool closed, RPArray< c3d::PntMatingData2D > &)
	Create cubic NURBS by interpolation points, parameters and data of conjugation at each point.

static MbNurbs *	CreateNURBS4 (const SArray< MbCartPoint > &, bool cls, MbeSplineParamType spType, MbeSplineCreateType useInitThrough=sct_Version2)
	Interpolation. More...

static MbNurbs *	CreateNURBS4 (const SArray< MbCartPoint > &points, const SArray< double > &params, bool cls, MbeSplineCreateType useInitThrough=sct_Version2)
	Interpolation. More...

static MbNurbs *	CreateNURBS4 (const SArray< double > &weights, const SArray< MbCartPoint > &points, SArray< double > &params, bool cls)
	Interpolation. More...

static MbNurbs *	CreateNURBS4 (const SArray< MbCartPoint > &points, const SArray< double > &params, const MbVector &, const MbVector &, bool cls, bool bfstS=true, bool bfstN=true)
	Interpolation. More...

static MbNurbs *	CreateNURBS4 (const SArray< MbCartPoint > &points, const SArray< MbVector > &vectors, const SArray< double > &params, bool cls)
	Interpolation. More...

static MbNurbs *	CreateNURBS4 (const MbBezier &)
	Interpolation. More...

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

NURBS curve in two-dimensional space.

NURBS curve is defined by 'pointList' control points, weights of control points ('weights'), knot vector ('knots') and order of spline ('degree').
Abbreviation of NURBS is obtained from the first letters of the Non-Uniform Rational B-Spline phrase. NURBS curve doesn't pass through its control points. 'knots' knot vector has to be not decreasing sequence of real numbers. 'pointList' and 'weights' sets have to contain the same count of elements. For not closed curve 'knots' knot vector has to contain the count of elements of 'pointList' set plus 'degree'. For closed curve 'knots' knot vector has to contain the count of elements of 'pointList' set plus 2*degree-1. Minimal value of spline parameter is equal to value of element of knot vector with degree-1 index. Maximal value of spline parameter is equal to value of element of knot vector with index, which is equal to index of last element minus degree-1. Curve calculation at each point is performed by normalized non-uniform B-splines.
Family of B-splines is defined by given crescent sequence of knot parameters and given order of B-spline.

Constructor & Destructor Documentation

◆ MbNurbs() [1/2]

DEPRECATE_DECLARE MbNurbs::MbNurbs ( )

Deprecated:: The method is deprecated.

◆ MbNurbs() [2/2]

template<class PointsVector , class DoubleVector >

MbNurbs::MbNurbs	(	size_t	degree,
		bool	cls,
		const PointsVector &	points,
		const DoubleVector *	weights,
		const DoubleVector *	knots
	)

protected

Constructor.

Constructor by order, points, parameters and an attribute of closedness. If parameters initDegree and points is invalid then the curve behavior is undefined.

Parameters

[in]	degree	- A spline order. It must be greater than unity. It shouldn't exceed count of control points.
[in]	cls	- A closedness attribute.
[in]	points	- Set of control points. Count of points must be greater than or equal to two.
[in]	weights	- Set of weights for control points. Count of weights must be equal to count of points.
[in]	knots	- Sequence of knot parameters.

Member Function Documentation

◆ Create() [1/4]

static MbNurbs* MbNurbs::Create ( const MbNurbs & )

static

Create copy of spline.

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

◆ Create() [2/4]

template<class PointsVector >

static MbNurbs* MbNurbs::Create	(	ptrdiff_t	initDegree,
		const PointsVector &	initPoints,
		bool	initClosed
	)

inlinestatic

Create spline.

Create spline and set parameters of spline.

Parameters

[in]	initDegree	- A spline order.
[in]	initPoints	- Set of control points.
[in]	initClosed	- A closedness attribute.

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

◆ Create() [3/4]

template<class PointsVector , class DoubleVector >

static MbNurbs* MbNurbs::Create	(	ptrdiff_t	initDegree,
		const PointsVector &	initPoints,
		bool	initClosed,
		const DoubleVector *	initWeights
	)

inlinestatic

Create spline.

Create spline and set parameters of spline.

Parameters

[in]	initDegree	- A spline order.
[in]	initPoints	- Set of control points.
[in]	initClosed	- A closedness attribute.
[in]	initWeights	- Set of weights for control points.

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

◆ Create() [4/4]

template<class PointsVector , class DoubleVector >

static MbNurbs* MbNurbs::Create	(	ptrdiff_t	initDegree,
		bool	initClosed,
		const PointsVector &	initPoints,
		const DoubleVector &	initWeights,
		const DoubleVector &	initKnots,
		MbeNurbsCurveForm	initForm = `ncf_Unspecified`
	)

inlinestatic

Create spline.

Create spline and set parameters of spline.

Parameters

[in]	initDegree	- A spline order.
[in]	initClosed	- A closedness attribute.
[in]	initPoints	- Set of control points.
[in]	initWeights	- Set of weights for control points.
[in]	initKnots	- Non-decreasing sequence of weights.
[in]	initForm	- Type of construction.

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

◆ CreateThrough()

static MbNurbs* MbNurbs::CreateThrough	(	size_t	degree,
		bool	cls,
		const SArray< MbCartPoint > &	points,
		const SArray< double > &	params,
		SArray< double > *	aKnots = `nullptr`
	)

static

Create spline.

Spline passing through given points at given parameters.
In case of closedness it is necessary to pass the array with coincidence of the first and the last points.

Parameters

[in]	degree	- A spline order.
[in]	cls	- A closedness attribute.
[in]	points	- Set of points which the spline passes through.
[in]	params	- Sequence of knot parameters.
[in]	aKnots	- Nondecreasing sequence of knots.

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

◆ CreateParasolid()

static MbNurbs* MbNurbs::CreateParasolid	(	size_t	degree,
		bool	closed,
		bool	rational,
		ptrdiff_t	count,
		const CcArray< double > &	verts,
		ptrdiff_t	vertsCount,
		const CcArray< ptrdiff_t > &	mul,
		ptrdiff_t	mulCount,
		const CcArray< double > &	knots,
		ptrdiff_t	knotsCount,
		double	scl
	)

static

Fill NURBS by parasolid data.

Parameters

[in]	degree	- Order of spline.
[in]	closed	- A closedness attribute.
[in]	rational	- Whether the curve is rational. if true then NURBS is created, false - Bezier curve.
[in]	count	- Count of control points.
[in]	verts	- An array of coordinates of points. If spline is rational, then the fourth coordinate - weight of point.
[in]	vertsCount	- Count of elements in 'verts' array.
[in]	mul	- Array with multiplicity of each knot.
[in]	mulCount	- Count of elements in 'mul' array.
[in]	knots	- Array with values of parameters at knots. Each value is presented only once. Information about knot multiplicity is in the element of 'mul' array with the same index.
[in]	knotsCount	- Count of elements in 'knots' array.
[in]	scl	- A scale factor.

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

◆ CreateCube()

static MbNurbs* MbNurbs::CreateCube	(	const MbCartPoint &	p1,
		const MbVector &	v1,
		const MbCartPoint &	p2,
		const MbVector &	v2
	)

static

Create spline.

Create spline and set parameters of spline.

Parameters

[in]	p1	- The initial point the spline passes through.
[in]	v1	- A tangent vector to the curve at the start point.
[in]	p2	- The final point the spline passes through.
[in]	v2	- A tangent vector to the curve at the end point.

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

◆ CreateArc() [1/2]

static MbNurbs* MbNurbs::CreateArc ( const SArray< MbCartPoint > & points )

static

Create spline.

Constructor of a spline describing the arc of a conic section.

Parameters

[in] points - A set of four points the section passes through. The first and last points define the beginning and ending of the arc respectively.

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

◆ CreateArc() [2/2]

static MbNurbs* MbNurbs::CreateArc	(	double	a2,
		const MbCartPoint &	p1,
		const MbCartPoint &	p2
	)

static

Create spline.

Constructor of a spline describing the arc of a circle.

Parameters

[in]	a2	- A half opening angle.
[in]	p1	- The starting point of the arc.
[in]	p2	- The end point of the arc.

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

◆ CreateWavyLine()

static MbNurbs* MbNurbs::CreateWavyLine	(	const MbCartPoint &	p1,
		const MbCartPoint &	p2,
		double	height,
		double	periode
	)

static

Create spline.

Constructor of a spline describing a wavy line.

Parameters

[in]	p1	- Start point of curve.
[in]	p2	- End point of curve.
[in]	height	- Height of the wave.
[in]	periode	- Period of the wave.

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

◆ Init() [1/4]

template<class PointsVector >

bool MbNurbs::Init	(	size_t	initDegree,
		const PointsVector &	initPoints,
		bool	initClosed
	)

inline

Initialization.

Set parameters of spline.

Parameters

[in]	initDegree	- A spline order.
[in]	initPoints	- Set of control points.
[in]	initClosed	- A closedness attribute.

◆ Init() [2/4]

template<class PointsVector , class DoubleVector >

bool MbNurbs::Init	(	size_t	initDegree,
		const PointsVector &	initPoints,
		bool	initClosed,
		const DoubleVector *	initWeights
	)

inline

Initialization.

Set parameters of spline.

Parameters

[in]	initDegree	- A spline order.
[in]	initPoints	- Set of control points.
[in]	initClosed	- A closedness attribute.
[in]	initWeights	- Set of weights for control points.

◆ Init() [3/4]

template<class PointsVector , class DoubleVector >

bool MbNurbs::Init	(	size_t	initDegree,
		bool	initClosed,
		const PointsVector &	initPoints,
		const DoubleVector &	initWeights,
		const DoubleVector &	initKnots,
		MbeNurbsCurveForm	initForm = `ncf_Unspecified`
	)

inline

Initialization.

Set parameters of spline.

Parameters

[in]	initDegree	- A spline order.
[in]	initClosed	- A closedness attribute.
[in]	initPoints	- Set of control points.
[in]	initWeights	- Set of weights for control points.
[in]	initKnots	- Non-decreasing sequence of weights.
[in]	initForm	- Type of construction.

◆ Init() [4/4]

bool MbNurbs::Init	(	size_t	degree,
		bool	cls,
		const CcArray< double > &	points,
		const CcArray< double > &	knots,
		ptrdiff_t	nPoints,
		ptrdiff_t	nKnots
	)

Initialization.

Set parameters of spline.

Parameters

[in]	degree	- A spline order.
[in]	cls	- A closedness attribute.
[in]	points	- Set of control points.
[in]	knots	- Non-decreasing sequence of knots.
[in]	nPoints	- Count of control points.
[in]	nKnots	- Count of knots.

◆ InitThrough() [1/2]

bool MbNurbs::InitThrough	(	size_t	degree,
		bool	cls,
		const SArray< MbCartPoint > &	points,
		const SArray< double > &	params,
		SArray< double > *	aKnots = `nullptr`
	)

Initialization.

Spline passing through given points at given parameters.
In case of closedness it is necessary to pass the array with coincidence of the first and the last points.

Parameters

[in]	degree	- A spline order.
[in]	cls	- A closedness attribute.
[in]	points	- Set of points which the spline passes through.
[in]	params	- Sequence of knot parameters.
[in]	aKnots	- Nondecreasing sequence of knots.

◆ InitThrough() [2/2]

bool MbNurbs::InitThrough	(	size_t	degree,
		bool	cls,
		const c3d::ParamPointsVector &	points,
		const c3d::DoubleVector &	params,
		c3d::DoubleVector *	aKnots = `nullptr`
	)

Initialization.

Spline passing through given points at given parameters.
In case of closedness it is necessary to pass the array with coincidence of the first and the last points.

Parameters

[in]	degree	- A spline order.
[in]	cls	- A closedness attribute.
[in]	points	- Set of points which the spline passes through.
[in]	params	- Sequence of knot parameters.
[in]	aKnots	- Nondecreasing sequence of knots.

◆ InitLine()

bool MbNurbs::InitLine	(	double	t1,
		const MbCartPoint &	p1,
		double	t2,
		const MbCartPoint &	p2
	)

Initialization.

Initialize a straight spline.

Parameters

[in]	t1	- The initial knot.
[in]	p1	- The initial point the spline passes through.
[in]	t2	- The final knot.
[in]	p2	- The final point the spline passes through.

◆ InitCube()

bool MbNurbs::InitCube	(	const MbCartPoint &	p1,
		const MbVector &	v1,
		const MbCartPoint &	p2,
		const MbVector &	v2
	)

Initialization.

Initialize a cubic curve as a spline.

Parameters

[in]	p1	- The initial point the spline passes through.
[in]	v1	- A tangent vector to the curve at the start point.
[in]	p2	- The final point the spline passes through.
[in]	v2	- A tangent vector to the curve at the end point.

◆ CreateNURBS2()

static MbNurbs* MbNurbs::CreateNURBS2	(	const SArray< MbCartPoint > &	points,
		const SArray< double > &	params,
		bool	cls
	)

static

Interpolation.

Create a planar spline of second-order by points, parameters and attribute of closedness.

◆ CreateNURBS4() [1/6]

static MbNurbs* MbNurbs::CreateNURBS4	(	const SArray< MbCartPoint > &	,
		bool	cls,
		MbeSplineParamType	spType,
		MbeSplineCreateType	useInitThrough = `sct_Version2`
	)

static

Interpolation.

Create a planar spline of fourth order by points, attribute of closedness and parametrization type.
NURBS passes through points. Used boundary condition of knot absence.

◆ CreateNURBS4() [2/6]

static MbNurbs* MbNurbs::CreateNURBS4	(	const SArray< MbCartPoint > &	points,
		const SArray< double > &	params,
		bool	cls,
		MbeSplineCreateType	useInitThrough = `sct_Version2`
	)

static

Interpolation.

Create a planar spline of fourth order by points, parameters and attribute of closedness.
Used boundary condition of knot absence.

◆ CreateNURBS4() [3/6]

static MbNurbs* MbNurbs::CreateNURBS4	(	const SArray< double > &	weights,
		const SArray< MbCartPoint > &	points,
		SArray< double > &	params,
		bool	cls
	)

static

Interpolation.

Create a planar spline of fourth order by weights, points, parameters and attribute of closedness.
Used boundary condition of knot absence.

◆ CreateNURBS4() [4/6]

static MbNurbs* MbNurbs::CreateNURBS4	(	const SArray< MbCartPoint > &	points,
		const SArray< double > &	params,
		const MbVector &	,
		const MbVector &	,
		bool	cls,
		bool	bfstS = `true`,
		bool	bfstN = `true`
	)

static

Interpolation.

Create a planar spline of fourth order by points, parameters and attribute of closedness with boundary conditions - given vectors of first or second derivatives.
Has 2 multiple internal knots, belongs to class of differentiable (but not twice differentiable) functions.

Parameters

[in]	bfstS	- If true, then start boundary condition is the vector of the first derivative, otherwise - the vector of the second derivative.
[in]	bfstN	- If true, then end boundary condition is the vector of first derivative, otherwise - vector of second derivative.

◆ CreateNURBS4() [5/6]

static MbNurbs* MbNurbs::CreateNURBS4	(	const SArray< MbCartPoint > &	points,
		const SArray< MbVector > &	vectors,
		const SArray< double > &	params,
		bool	cls
	)

static

Interpolation.

Create a planar spline of fourth order by points, derivatives, parameters and attribute of closedness.
It has 2 multiple internal knots, belongs to the class of differentiable (but not twice differentiable) functions.

◆ CreateNURBS4() [6/6]

static MbNurbs* MbNurbs::CreateNURBS4 ( const MbBezier & )

static

Interpolation.

Create a planar spline of fourth order by composite Bezier spline of fourth order.
If closedness is necessary - call UnClamped( bezier.IsClosed() ).

◆ RaiseDegree()

bool MbNurbs::RaiseDegree	(	size_t	newDegree,
		double	relEps = `Math::paramEpsilon`
	)

Increase order of curve without changing its geometric shape and parametrization.

Parameters

[in]	newDegree	- New order of spline.
[in]	relEps	- Permissible shape error.

Returns: Returns true if the order of the spline was changed.

◆ ReductionDegree()

bool MbNurbs::ReductionDegree ( double relEps = Math::paramEpsilon )

Decrease order of nurbs curve by 1 without changing its geometric shape and parametrization.

Parameters

[in] relEps - Permissible shape error.

Returns: Returns true if the order of the spline was changed.

◆ SetDegree()

bool MbNurbs::SetDegree ( size_t newDegree )

Set the spline order.

Set the spline order.
When you change the order, the parameterization of the spline is reset to uniform, the shape of the spline changes.

Parameters

[in] newDegree - A new spline order.

Returns: Returns true if the order of the spline was changed.

◆ Duplicate()

MbPlaneItem& MbNurbs::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 MbNurbs::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 MbNurbs::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 MbNurbs::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 MbNurbs::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 MbNurbs::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.

◆ GetProperties()

void MbNurbs::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 MbNurbs::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.

◆ IsClosed()

bool MbNurbs::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.

◆ IsPeriodic()

bool MbNurbs::IsPeriodic ( ) const

overridevirtual

Define whether the curve is periodic.

Define whether the curve is periodic.
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 IsPeriodic() method always returns false for them.
Returns
True if a curve is closed.

Reimplemented from MbCurve.

◆ PointOn()

void MbNurbs::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 MbNurbs::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.

◆ CalculateGabarit()

void MbNurbs::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.

◆ DistanceAlong()

bool MbNurbs::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.

◆ CalculateLength()

double MbNurbs::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.

◆ NurbsCurve() [1/2]

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

◆ IsReparamSame()

bool MbNurbs::IsReparamSame	(	const MbCurve &	curve,
		double &	factor
	)		const

overridevirtual

Define whether a reparameterized curve is the same.

Parameters

[in]	curve	- A curve for comparison.
[out]	factor	- Coefficient of compression of parametric region at the time of transition to the pointed curve.

Reimplemented from MbCurve.

◆ Step()

double MbNurbs::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 MbNurbs::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.

◆ CalculatePolygon()

void MbNurbs::CalculatePolygon	(	double	sag,
		MbPolygon &	poligon
	)		const

overridevirtual

Calculate an array of points for drawing.

Get an array of drawn points with a given sag. If the cure is a contour then knots of a contour are duplicated.

Parameters

[in]	sag	- Maximal value of sag.
[in,out]	poligon	- A polygon of calculated points on a curve.

Reimplemented from MbCurve.

◆ DeletePart()

MbeState MbNurbs::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 MbNurbs::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 MbNurbs::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.

◆ GoThroughPoint()

bool MbNurbs::GoThroughPoint ( MbCartPoint & pnt )

overridevirtual

Create a curve through a point.

Change a curve such that it passes through the given point. Changes should not affect the whole curve. If the curve has any base objects, then the connection with them should not be modified. If the curve cannot be constructed, then the initial curve will not change, false is returned.

Parameters

[in] pnt - A given point.

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

Reimplemented from MbCurve.

◆ TangentPoint()

void MbNurbs::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.

◆ OffsetCuspPoint()

void MbNurbs::OffsetCuspPoint	(	SArray< double > &	tCusps,
		double	dist
	)		const

overridevirtual

Find the special points of an offset curve.

Special points of an offset curve are the points where the curvature radius of the initial curve equals to the value of shift of an offset curve.

Parameters

[in,out]	tCusps	- An array of parameters of special points.
[in]	dist	- Shift of the offset curve.

Reimplemented from MbCurve.

◆ GetRadius()

double MbNurbs::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.

◆ GetAxisPoint()

bool MbNurbs::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.

◆ GetRuleInterval()

void MbNurbs::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 MbNurbs::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 MbNurbs::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.

◆ ChangePoint()

void MbNurbs::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.

◆ ChangePointsValue()

bool MbNurbs::ChangePointsValue ( const SArray< MbCartPoint > & pntList )

overridevirtual

Change control points.

If count of points in the given array is equal to the current count of points, then the array of points is replaced by the new one. If not equal, then the control points are not changed, the function returns false.

Parameters

[in] pntList - The given array of control points.

Returns: True if points have been changed.

Reimplemented from MbPolyCurve.

◆ CheckParam()

bool MbNurbs::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.

◆ DistanceToPointIfLess()

bool MbNurbs::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.

◆ PointProjection()

double MbNurbs::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 MbNurbs::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.

◆ IsContinuousDerivative()

bool MbNurbs::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 MbNurbs::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.

◆ BreakC0NURBS4()

bool MbNurbs::BreakC0NURBS4	(	RPArray< MbCurve > &	,
		bool	bline = `true`
	)

Split the curve.

Split the non-differentiable NURBS-curve of fourth degree at internal knot with multiplicity of three.
If there are no internal knots with multiplicity of three, then the array is filled with copy of curve.
If bline = true, then check the curve for degeneration into a line, if it is a line then transform to a line.

◆ FixClosedNurbs()

void MbNurbs::FixClosedNurbs ( )

Make curve closed.

Make actually closed curve closed.
That is, if the first and the last points of curve are coincident, but curve implemented as open, then one of coincident points is taken away and curve becomes closed.

◆ 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_nurbs.h

Public Member Functions

Static Public Member Functions

Protected Member Functions

Functions of NURBS curve initialization.

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MbNurbs() [1/2]

◆ MbNurbs() [2/2]

Member Function Documentation

◆ Create() [1/4]

◆ Create() [2/4]

◆ Create() [3/4]

◆ Create() [4/4]

◆ CreateThrough()

◆ CreateParasolid()

◆ CreateCube()

◆ CreateArc() [1/2]

◆ CreateArc() [2/2]

◆ CreateWavyLine()

◆ Init() [1/4]

◆ Init() [2/4]

◆ Init() [3/4]

◆ Init() [4/4]

◆ InitThrough() [1/2]

◆ InitThrough() [2/2]

◆ InitLine()

◆ InitCube()

◆ CreateNURBS2()

◆ CreateNURBS4() [1/6]

◆ CreateNURBS4() [2/6]

◆ CreateNURBS4() [3/6]

◆ CreateNURBS4() [4/6]

◆ CreateNURBS4() [5/6]

◆ CreateNURBS4() [6/6]

◆ RaiseDegree()

◆ ReductionDegree()

◆ SetDegree()

◆ Duplicate()

◆ IsSame()

◆ SetEqual()

◆ Transform()

◆ Move()

◆ Rotate()

◆ GetProperties()

◆ SetProperties()

◆ IsClosed()

◆ IsPeriodic()

◆ PointOn()

◆ Explore()

◆ CalculateGabarit()

◆ DistanceAlong()

◆ CalculateLength()

◆ NurbsCurve() [1/2]

◆ NurbsCurve() [2/2]

◆ Trimmed() [1/3]

◆ IsReparamSame()

◆ Step()

◆ DeviationStep()

◆ CalculatePolygon()

◆ DeletePart()

◆ TrimmPart()

◆ Deformation()

◆ GoThroughPoint()

◆ TangentPoint()

◆ OffsetCuspPoint()

◆ GetRadius()

◆ GetAxisPoint()

◆ GetRuleInterval()

◆ InsertPoint() [1/2]

◆ InsertPoint() [2/2]

◆ ChangePoint()

◆ ChangePointsValue()

◆ CheckParam()

◆ DistanceToPointIfLess()

◆ PointProjection()

◆ NearPointProjection()

◆ IsContinuousDerivative()

◆ SetContinuousDerivativeLength()

◆ BreakC0NURBS4()