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

#include <cur_nurbs3d.h>

Inheritance diagram for MbNurbs3D:

Collaboration diagram for MbNurbs3D:

Public Member Functions
void	Init (const MbNurbs3D &)
	Set parameters of the spline.

bool	Init (size_t degree, const SArray< MbCartPoint3D > &points, bool closed, const SArray< double > *weights=nullptr)
	Initialization. More...

bool	Init (size_t degree, bool closed, const SArray< MbCartPoint3D > &points, const SArray< double > &knots)
	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, const SArray< MbCartPoint3D > &points, const SArray< double > &weights, c3d::PntMatingData3D &begData, c3d::PntMatingData3D &endData)
	Initialization. More...

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

bool	InitThrough (size_t degree, bool cls, const SArray< MbCartPoint3D > &points, const SArray< double > &params, SArray< double > *aKnots=nullptr)
	Initialization. More...

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

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

MbeSpaceType	IsA () const override
	Get the type of the object.

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

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

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

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

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

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

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

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

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

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

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

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

void	PointOn (double &t, MbCartPoint3D &) const override
	Calculate a point on the curve. More...

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

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

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

void	Explore (double &t, bool ext, MbCartPoint3D &pnt, MbVector3D &fir, MbVector3D sec, MbVector3D thir) const override
	Calculate point and derivatives of object for given parameter. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

MbNurbs3D *	Trimm (double t1, double t2, int sense) const
	Trim the curve.

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

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

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

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

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

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

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

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

MbNurbs3D *	Break (double t1, double t2) const
	Extract a piece of a curve.

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

void	AddPoint (ptrdiff_t index, const MbCartPoint3D &pnt, double weight)
	Add a point with weight.

void	InsertKnots (double &newKnot, size_t multiplicity, double relEps=Math::paramEpsilon)
	Add a new knot with the given multiplicity.

void	InsertKnotsInRegion (ptrdiff_t idBegin)
	Add new equally spaced knots into the range from idBegin to idBegin+1.

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 which were successfully made.

bool	RemoveKnotAlways (ptrdiff_t id)
	Remove knot 'id' once without checking the accuracy of the curve modification.

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

bool	DecomposeCurve ()
	Transform current NURBS into Bezier curve.

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...

size_t	KnotMultiplicity (size_t knotIndex) const
	Get multiplicity of a knot with a given index.

void	DefineKnotsVector ()
	Definition of the basis knot vector.

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

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

bool	SetLimitParam (double pmin, double pmax)
	Set the range of parameter.

void	AddCurve (MbNurbs3D &, bool bmerge=true)
	Add a curve to the end.

void	AddCurves (const RPArray< MbNurbs3D > &)
	Add curves to the end.

bool	ReparamCurveInBezierForm ()
	Reparameterize a curve according to the length if the curve is obtained from a set of Bezier curves.

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

size_t	GetDegree () const
	Get the order of B-spline.

bool	IsRational () const
	Get the attribute of rationality, but not regularity of a 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.

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

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

bool	AttachG (c3d::PntMatingData3D &connectData, bool beg, bool isWrongAttachG1_K12=false)
	Set conjugation at the end.

bool	BreakC0NURBS4 (RPArray< MbCurve3D > &, bool bline=true) const
	Split the curve. More...

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

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

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

MbCurve3D *	ConvertToConic ()
	Transform a curve into a conic section if it is possible.

bool	BreakC0 (c3d::SpaceCurvesSPtrVector &, double metricAcc=METRIC_EPSILON, VERSION version=Math::DefaultMathVersion())
	Split a NURBS-curve at places where the curve is non-differentiable. If the curve is differentiable, then the curve copy is added.

void	FixClosedNurbs ()
	Make the curve closed. More...

double	GetBSplineParameter (size_t num) const
	Get value of the parameter corresponding to a knot point with 'num' index.

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

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

Public Member Functions inherited from MbPolyCurve3D
MbeSpaceType	Type () const override
	Get the group object type.

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

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

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

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

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

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

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

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

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

bool	IsPlanar (double accuracy=METRIC_EPSILON) const override
	Is a curve planar?

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

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

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

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

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

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

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

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

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

MbeSpaceType	Family () const override
	Get family of objects.

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

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

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

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

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

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

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

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

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

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

virtual void	_PointOn (double t, MbCartPoint3D &p) const
	Calculate point at curve and its extension. More...

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

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

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

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

virtual void	_Normal (double t, MbVector3D &) const
	Calculate main normal vector (normalized) at curve and its extension.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual bool	IsShift (const MbSpaceItem &, MbVector3D &, bool &isSame, double accuracy=LENGTH_EPSILON) const
	Is the object is a shift?

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

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

SimpleName	GetCurveName () const
	A curve name.

void	SetCurveName (SimpleName newName)
	Set a curve name.

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

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

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

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

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

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

void	CalculateWire (double sag, MbMesh &mesh) const

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

	TapeBase (const TapeBase &)
	Copy-constructor.

virtual	~TapeBase ()
	Destructor.

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

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

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

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

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

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

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

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

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

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

Static Public Member Functions
static MbNurbs3D *	Create (const MbNurbs3D &)
	Create copy of spline. More...

static MbNurbs3D *	Create (const MbNurbs &nurbs, const MbPlacement3D &place)
	Create spline. More...

static MbNurbs3D *	Create (size_t degree, const SArray< MbCartPoint3D > &points, bool closed, const SArray< double > *weights=nullptr)
	Create spline. More...

static MbNurbs3D *	Create (size_t degree, bool closed, const SArray< MbCartPoint3D > &points, const SArray< double > &knots)
	Create spline. More...

template<class PointsVector , class DoubleVector >
static MbNurbs3D *	Create (size_t initDegree, bool initClosed, const PointsVector &initPoints, const DoubleVector &initWeights, const DoubleVector &initKnots, MbeNurbsCurveForm initForm=ncf_Unspecified)
	Create spline. More...

static MbNurbs3D *	CreateThrough (size_t degree, bool cls, const SArray< MbCartPoint3D > &points, const SArray< double > &params, SArray< double > *aKnots=nullptr)
	Create spline. More...

static MbNurbs3D *	CreateThrough (size_t degree, bool cls, const c3d::SpacePointsVector &points, const c3d::DoubleVector &params, c3d::DoubleVector *aKnots=nullptr)
	Create spline. More...

static MbNurbs3D *	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 MbNurbs3D *	CreateNURBS4 (const SArray< MbCartPoint3D > &points, MbeSplineParamType spType, const c3d::PntMatingData3D &begData, const c3d::PntMatingData3D &endData, MbeSplineCreateType useInitThrough)
	Create cubic NURBS by parameters of conjugation and points which it passes through.

static MbNurbs3D *	CreateNURBS4 (const SArray< MbCartPoint3D > &points, MbeSplineParamType spType, bool closed, RPArray< c3d::PntMatingData3D > &matingData, MbeSplineCreateType useInitThrough)
	Create cubic NURBS by interpolation points and data of conjugation at each point.

static MbNurbs3D *	CreateNURBS4 (const SArray< MbCartPoint3D > &, const SArray< double > &, bool closed, RPArray< c3d::PntMatingData3D > &, MbeSplineCreateType useInitThrough)
	Create cubic NURBS by interpolation points, parameters and data of conjugation at each point.

static MbNurbs3D *	CreateNURBS4 (const SArray< MbCartPoint3D > &, bool cls, MbeSplineParamType spType, MbeSplineCreateType useInitThrough=sct_Version2)
	Create a cubic NURBS by the attribute of closedness and points which it passes through.

static MbNurbs3D *	CreateNURBS4 (const SArray< MbCartPoint3D > &points, const SArray< double > &params, bool cls, MbeSplineCreateType useInitThrough=sct_Version2)
	Interpolation. More...

static MbNurbs3D *	CreateNURBS4 (const SArray< double > &weights, const SArray< MbCartPoint3D > &points, SArray< double > &params, bool cls)
	Interpolation. More...

static MbNurbs3D *	CreateNURBS4 (const SArray< MbCartPoint3D > &, const SArray< double > &, const MbVector3D &, const MbVector3D &, bool cls, bool bfstS=true, bool bfstN=true)
	Interpolation. More...

static MbNurbs3D *	CreateNURBS4 (const SArray< MbCartPoint3D > &points, const SArray< MbVector3D > &vectors, const SArray< double > &params, bool cls)
	Interpolation. More...

static MbNurbs3D *	CreateNURBS4WithBreak (const SArray< MbCartPoint3D > &, const SArray< MbVector3D > &, const SArray< double > &, bool cls)
	Create a spline of the fourth order taking breaks of curve into account.

static MbNurbs3D *	CreateNURBS4 (const MbBezier3D &)
	Interpolation. More...

static MbNurbs3D *	CreateNURBS (size_t initDegree, const SArray< MbCartPoint3D > &initPoints, const SArray< double > &initParams, bool initClosed, RPArray< c3d::PntMatingData3D > &matingData)
	Create NURBS. More...

Protected Member Functions
	MbNurbs3D (const MbNurbs &, const MbPlacement3D &)
	Constructor. More...

	MbNurbs3D (size_t deg, bool cls, const SArray< MbCartPoint3D > &points, const SArray< double > weights=nullptr, const SArray< double > knots=nullptr)
	Constructor. More...

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

	MbCurve3D (const MbCurve3D &other)
	Copy-constructor.

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

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

Additional Inherited Members
Protected Attributes inherited from MbPolyCurve3D
ptrdiff_t	uppIndex
	Count of curve pieces (is equal to count of control points minus one).

SArray< MbCartPoint3D >	pointList
	Set of control points.

bool	closed
	An attribute of curve closedness.

atomic_double	metricLength
	Metric length of curve.

atomic_double	lengthEvaluation
	Estimated length of a curve.

MbCube	cube
	Bounding box of curve.

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

Detailed Description

NURBS curve in three-dimensional space.

NURBS curve is defined by 'pointList' control points, 'weights' weights of control points, 'knots' knot vector and 'degree' spline order.
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 nondecreasing sequence of real numbers. 'pointList' and 'weights' sets have to contain the same count of elements. For not closed curve knot vector 'knots' has to contain the count of elements of 'pointList' set plus 'degree'. For closed curve knot vector 'knots' has to contain the count of elements of 'pointList' set plus 2*degree-1. Minimal value of spline parameter is equal to value of the element of knot vector with degree-1 index. Maximal value of spline parameter is equal to the value of element of knot vector with index, which is equal to index of the last element minus degree-1. Curve calculation at each point is performed using normalized non-uniform B-splines.
Family of B-splines is defined by the given nondecreasing sequence of knot parameters and the given order of B-spline.

Constructor & Destructor Documentation

◆ MbNurbs3D() [1/2]

MbNurbs3D::MbNurbs3D	(	const MbNurbs &	,
		const MbPlacement3D &
	)

protected

Constructor.

Constructor of planar spline in space.

◆ MbNurbs3D() [2/2]

MbNurbs3D::MbNurbs3D	(	size_t	deg,
		bool	cls,
		const SArray< MbCartPoint3D > &	points,
		const SArray< double > *	weights = `nullptr`,
		const SArray< double > *	knots = `nullptr`
	)

protected

Constructor.

Constructor by order, points, parameters and an attribute of closedness.

Parameters

[in]	deg	- A spline order. Must be greater than unity. Shouldn't exceed the count of control points.
[in]	cls	- 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() [1/5]

static MbNurbs3D* MbNurbs3D::Create ( const MbNurbs3D & )

static

Create copy of spline.

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

◆ Create() [2/5]

static MbNurbs3D* MbNurbs3D::Create	(	const MbNurbs &	nurbs,
		const MbPlacement3D &	place
	)

static

Create spline.

Create spline and set parameters of spline.

Parameters

[in]	nurbs	- The two-dimensional spline.
[in]	place	- Local coordinate system of spline.

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

◆ Create() [3/5]

static MbNurbs3D* MbNurbs3D::Create	(	size_t	degree,
		const SArray< MbCartPoint3D > &	points,
		bool	closed,
		const SArray< double > *	weights = `nullptr`
	)

static

Create spline.

Create spline and set parameters of spline.

Parameters

[in]	degree	- A spline order.
[in]	points	- Set of control points.
[in]	closed	- Closedness attribute.
[in]	weights	- Set of weights for control points.

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

◆ Create() [4/5]

static MbNurbs3D* MbNurbs3D::Create	(	size_t	degree,
		bool	closed,
		const SArray< MbCartPoint3D > &	points,
		const SArray< double > &	knots
	)

static

Create spline.

Create spline and set parameters of spline.

Parameters

[in]	degree	- A spline order.
[in]	closed	- Closedness attribute.
[in]	points	- Set of control points.
[in]	knots	- Nondecreasing sequence of knots.

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

◆ Create() [5/5]

template<class PointsVector , class DoubleVector >

static MbNurbs3D* MbNurbs3D::Create	(	size_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	- Closedness attribute.
[in]	initPoints	- Set of control points.
[in]	initWeights	- Set of weights for control points.
[in]	initKnots	- Nondecreasing sequence of knots.
[in]	initForm	- Type of construction.

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

◆ CreateThrough() [1/2]

static MbNurbs3D* MbNurbs3D::CreateThrough	(	size_t	degree,
		bool	cls,
		const SArray< MbCartPoint3D > &	points,
		const SArray< double > &	params,
		SArray< double > *	aKnots = `nullptr`
	)

static

Create spline.

Spline passing through the given points at the 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	- 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.

◆ CreateThrough() [2/2]

static MbNurbs3D* MbNurbs3D::CreateThrough	(	size_t	degree,
		bool	cls,
		const c3d::SpacePointsVector &	points,
		const c3d::DoubleVector &	params,
		c3d::DoubleVector *	aKnots = `nullptr`
	)

static

Create spline.

Spline passing through the given points at the 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	- 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 MbNurbs3D* MbNurbs3D::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	- Closedness attribute.
[in]	rational	- Whether the curve is rational. if true - 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 is the weight of a 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	- Scale factor.

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

◆ Init() [1/5]

bool MbNurbs3D::Init	(	size_t	degree,
		const SArray< MbCartPoint3D > &	points,
		bool	closed,
		const SArray< double > *	weights = `nullptr`
	)

Initialization.

Set parameters of the spline.

Parameters

[in]	degree	- A spline order.
[in]	points	- Set of control points.
[in]	weights	- Set of weights for control points.
[in]	closed	- Closedness attribute.

◆ Init() [2/5]

bool MbNurbs3D::Init	(	size_t	degree,
		bool	closed,
		const SArray< MbCartPoint3D > &	points,
		const SArray< double > &	knots
	)

Initialization.

Set parameters of the spline.

Parameters

[in]	degree	- A spline order.
[in]	closed	- Closedness attribute.
[in]	points	- Set of control points.
[in]	knots	- Nondecreasing sequence of knots.

◆ Init() [3/5]

template<class PointsVector , class DoubleVector >

bool MbNurbs3D::Init	(	size_t	initDegree,
		bool	initClosed,
		const PointsVector &	initPoints,
		const DoubleVector &	initWeights,
		const DoubleVector &	initKnots,
		MbeNurbsCurveForm	initForm = `ncf_Unspecified`
	)

inline

Initialization.

Set parameters of the spline.

Parameters

[in]	degree	- A spline order.
[in]	closed	- Closedness attribute.
[in]	points	- Set of control points.
[in]	weights	- Set of weights for control points.
[in]	knots	- Nondecreasing sequence of knots.
[in]	initForm	- Type of construction.

◆ Init() [4/5]

bool MbNurbs3D::Init	(	size_t	degree,
		const SArray< MbCartPoint3D > &	points,
		const SArray< double > &	weights,
		c3d::PntMatingData3D &	begData,
		c3d::PntMatingData3D &	endData
	)

Initialization.

Set parameters of the spline.

Parameters

[in]	degree	- A spline order.
[in]	points	- Set of control points.
[in]	weights	- Set of weights for control points.
[in]	begData	- Parameter of conjugation at the start point of the spline.
[in]	endData	- Parameter of conjugation at the end point of the spline.

◆ Init() [5/5]

bool MbNurbs3D::Init	(	size_t	degree,
		bool	closed,
		const CcArray< double > &	points,
		const CcArray< double > &	knots,
		size_t	nPoints,
		size_t	nKnots
	)

Initialization.

Set parameters of the spline.

Parameters

[in]	degree	- A spline order.
[in]	closed	- Closedness attribute.
[in]	points	- Set of control points.
[in]	knots	- Nondecreasing sequence of knots.
[in]	nPoints	- The number of control points.
[in]	endData	- Count of knots.

◆ InitThrough() [1/2]

bool MbNurbs3D::InitThrough	(	size_t	degree,
		bool	cls,
		const SArray< MbCartPoint3D > &	points,
		const SArray< double > &	params,
		SArray< double > *	aKnots = `nullptr`
	)

Initialization.

Spline passing through the given points at the 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	- 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 MbNurbs3D::InitThrough	(	size_t	degree,
		bool	cls,
		const c3d::SpacePointsVector &	points,
		const c3d::DoubleVector &	params,
		c3d::DoubleVector *	aKnots = `nullptr`
	)

Initialization.

Spline passing through the given points at the 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	- Closedness attribute.
[in]	points	- Set of points which the spline passes through.
[in]	params	- Sequence of knot parameters.
[in]	aKnots	- Nondecreasing sequence of knots.

◆ Duplicate()

MbSpaceItem& MbNurbs3D::Duplicate ( MbRegDuplicate * iReg = nullptr ) const

overridevirtual

Create a copy of the object.

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

Parameters

[in] iReg - Registrator.

Returns: A copy of the object.

Implements MbSpaceItem.

◆ IsSame()

bool MbNurbs3D::IsSame	(	const MbSpaceItem &	other,
		double	accuracy = `LENGTH_EPSILON`
	)		const

overridevirtual

Determine whether an object is equal.

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

Parameters

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

Returns: Whether the objects are equal.

Implements MbSpaceItem.

◆ SetEqual()

bool MbNurbs3D::SetEqual ( const MbSpaceItem & item )

overridevirtual

Make objects equal if they are similar.

You can still make only a similar objects.

Parameters

[in] item - The object to initialize.

Returns: Object is changed.

Implements MbSpaceItem.

◆ Transform()

void MbNurbs3D::Transform	(	const MbMatrix3D &	matr,
		MbRegTransform *	iReg = `nullptr`
	)

overridevirtual

Convert the object according to the matrix.

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

Parameters

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

Implements MbSpaceItem.

◆ Move()

void MbNurbs3D::Move	(	const MbVector3D &	to,
		MbRegTransform *	iReg = `nullptr`
	)

overridevirtual

Move an object along a vector.

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

Parameters

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

Implements MbSpaceItem.

◆ Rotate()

void MbNurbs3D::Rotate	(	const MbAxis3D &	axis,
		double	angle,
		MbRegTransform *	iReg = `nullptr`
	)

overridevirtual

Rotate an object around an axis at a given angle.

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

Parameters

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

Implements MbSpaceItem.

◆ GetProperties()

void MbNurbs3D::GetProperties ( MbProperties & properties )

overridevirtual

Outstanding properties of the object.

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

Parameters

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

Implements MbSpaceItem.

◆ SetProperties()

void MbNurbs3D::SetProperties ( const MbProperties & properties )

overridevirtual

Change the properties of an object.

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

Parameters

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

Implements MbSpaceItem.

◆ IsClosed()

bool MbNurbs3D::IsClosed ( ) const

overridevirtual

Define whether the curve is periodic.

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

start point is coincident with end point;
derivatives in start point and end point coincide;
if there are breaks at curve (in cases when a curve is contour or polyline), then derivatives may not coincide; in Bezier curve derivatives should coincide by direction, but they may differ by absolute value.
Curves:
MbLine3D,
MbLineSegment3D,
MbSpiral and inherited classes,
MbBridgeCurve3D,
MbContour3D (if it contains only a single segment of one of the listed types)
are not considered periodic when the start and end points coincide. The IsClosed() method always returns false for them.
Returns
True if a curve is closed.

Implements MbCurve3D.

◆ IsPeriodic()

bool MbNurbs3D::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:
MbLine3D,
MbLineSegment3D,
MbSpiral and inherited classes,
MbBridgeCurve3D,
MbContour3D (if it contains only a single segment of one of the listed types)
are not considered periodic when the start and end points coincide. The IsPeriodic() method always returns false for them.
Returns
True if a curve is closed.

Reimplemented from MbCurve3D.

◆ PointOn()

void MbNurbs3D::PointOn	(	double &	t,
		MbCartPoint3D &	p
	)		const

overridevirtual

Calculate a point on the curve.

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

Parameters

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

Implements MbCurve3D.

◆ Explore()

void MbNurbs3D::Explore	(	double &	t,
		bool	ext,
		MbCartPoint3D &	pnt,
		MbVector3D &	fir,
		MbVector3D *	sec,
		MbVector3D *	thir
	)		const

overridevirtual

Calculate point and derivatives of object for given parameter.

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

Parameters

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

Reimplemented from MbCurve3D.

◆ Step()

double MbNurbs3D::Step	(	double	t,
		double	sag
	)		const

overridevirtual

Calculate parameter step.

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

Parameters

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

Returns: A sag value by parameter at given point.

Reimplemented from MbCurve3D.

◆ DeviationStep()

double MbNurbs3D::DeviationStep	(	double	t,
		double	ang
	)		const

overridevirtual

Calculate parameter step.

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

Parameters

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

Returns: A sag value by parameter at given point.

Reimplemented from MbCurve3D.

◆ NurbsCurve() [1/2]

MbNurbs3D* MbNurbs3D::NurbsCurve ( const MbCurveIntoNurbsInfo & nInfo ) const

overridevirtual

Construct a NURBS copy of a curve.

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

Parameters

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

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

Reimplemented from MbCurve3D.

◆ NurbsCurve() [2/2]

MbCurve3D* MbNurbs3D::NurbsCurve ( const MbNurbsParameters & tParameters ) const

overridevirtual

Construct a NURBS copy of a curve.

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

Parameters

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

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

Reimplemented from MbCurve3D.

◆ Trimmed() [1/3]

MbCurve3D* MbNurbs3D::Trimmed	(	double	t1,
		double	t2,
		int	sense,
		const MbDimAccuracy &	xyzEps,
		bool	saveParamLenAndLaw
	)		const

overridevirtual

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

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

Parameters

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

Returns: A constructed trimmed curve.

Warning: Under development.

Reimplemented from MbCurve3D.

◆ GetRadius()

double MbNurbs3D::GetRadius ( double accuracy = METRIC_REGION ) const

overridevirtual

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

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

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

Reimplemented from MbCurve3D.

◆ GetCircleAxis()

bool MbNurbs3D::GetCircleAxis ( MbAxis3D & axis ) const

overridevirtual

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

Parameters

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

Reimplemented from MbCurve3D.

◆ GetPlaneCurve()

bool MbNurbs3D::GetPlaneCurve	(	MbCurve *&	curve2d,
		MbPlacement3D &	place,
		bool	saveParams,
		PlanarCheckParams	params = `PlanarCheckParams()`
	)		const

overridevirtual

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

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

Parameters

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

Returns: true if a flat curve was created.

Reimplemented from MbCurve3D.

◆ NearPointProjection()

bool MbNurbs3D::NearPointProjection	(	const MbCartPoint3D &	pnt,
		double &	t,
		bool	ext,
		MbRect1D *	tRange = `nullptr`
	)		const

overridevirtual

Find the point projection to the curve.

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

Parameters

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

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

Reimplemented from MbCurve3D.

◆ IsReparamSame()

bool MbNurbs3D::IsReparamSame	(	const MbCurve3D &	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 MbCurve3D.

◆ DistanceAlong()

bool MbNurbs3D::DistanceAlong	(	double &	t,
		double	len,
		int	curveDir,
		double	eps = `Math::metricPrecision`,
		VERSION	version = `Math::DefaultMathVersion()`
	)		const

overridevirtual

Translate parameter along the curve.

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

Parameters

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

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

Reimplemented from MbCurve3D.

◆ CalculateLength()

double MbNurbs3D::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 MbCurve3D.

◆ IsContinuousDerivative()

bool MbNurbs3D::IsContinuousDerivative	(	bool &	contLength,
		bool &	contDirect,
		c3d::DoubleVector *	params = `nullptr`,
		double	epsilon = `EPSILON`
	)		const

overridevirtual

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).
[in]	epsilon	- The accuracy of the calculation.

Reimplemented from MbCurve3D.

◆ SetContinuousDerivativeLength()

bool MbNurbs3D::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 MbCurve3D.

◆ RaiseDegree()

bool MbNurbs3D::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 MbNurbs3D::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.

◆ GetMap()

MbCurve* MbNurbs3D::GetMap	(	const MbMatrix3D &	into,
		MbRect1D *	pRegion = `nullptr`,
		VERSION	version = `Math::DefaultMathVersion()`,
		bool *	coincParams = `nullptr`
	)		const

overridevirtual

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

Parameters

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

Returns: Two-dimensional projection of a curve

Reimplemented from MbCurve3D.

◆ CreateNURBS4() [1/5]

static MbNurbs3D* MbNurbs3D::CreateNURBS4	(	const SArray< MbCartPoint3D > &	points,
		const SArray< double > &	params,
		bool	cls,
		MbeSplineCreateType	useInitThrough = `sct_Version2`
	)

static

Interpolation.

Create an open spline of fourth order by points, parameters and the attribute of closedness.
Used boundary condition of knot absence.

◆ CreateNURBS4() [2/5]

static MbNurbs3D* MbNurbs3D::CreateNURBS4	(	const SArray< double > &	weights,
		const SArray< MbCartPoint3D > &	points,
		SArray< double > &	params,
		bool	cls
	)

static

Interpolation.

Create an open spline of fourth order by points, parameters and the attribute of closedness.
Used boundary condition of knot absence.

◆ CreateNURBS4() [3/5]

static MbNurbs3D* MbNurbs3D::CreateNURBS4	(	const SArray< MbCartPoint3D > &	,
		const SArray< double > &	,
		const MbVector3D &	,
		const MbVector3D &	,
		bool	cls,
		bool	bfstS = `true`,
		bool	bfstN = `true`
	)

static

Interpolation.

Create a spline of the fourth order by points, parameters and the attribute of closedness with boundary conditions - given vectors of the first or the second derivatives.
Has 2 multiple internal knots, belongs to the 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 - vector of first derivative, otherwise - vector of second derivative.

◆ CreateNURBS4() [4/5]

static MbNurbs3D* MbNurbs3D::CreateNURBS4	(	const SArray< MbCartPoint3D > &	points,
		const SArray< MbVector3D > &	vectors,
		const SArray< double > &	params,
		bool	cls
	)

static

Interpolation.

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

◆ CreateNURBS4() [5/5]

static MbNurbs3D* MbNurbs3D::CreateNURBS4 ( const MbBezier3D & )

static

Interpolation.

Create a spline of the fourth order by a composite Bezier spline of the fourth order.
Attention! Parameterization is different from the parameterization of the source Bezier curve.

◆ CreateNURBS()

static MbNurbs3D* MbNurbs3D::CreateNURBS	(	size_t	initDegree,
		const SArray< MbCartPoint3D > &	initPoints,
		const SArray< double > &	initParams,
		bool	initClosed,
		RPArray< c3d::PntMatingData3D > &	matingData
	)

static

Create NURBS.

Create a spline of any order containing the given points with managing of tangent and curvature at these points.

◆ BreakC0NURBS4()

bool MbNurbs3D::BreakC0NURBS4	(	RPArray< MbCurve3D > &	,
		bool	bline = `true`
	)		const

Split the curve.

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

◆ FixClosedNurbs()

void MbNurbs3D::FixClosedNurbs ( )

Make the curve closed.

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

◆ Trimmed() [2/3]

virtual MbCurve3D* MbCurve3D::Trimmed

Construct a trimmed curve.

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

Parameters

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

Returns: A constructed trimmed curve.

◆ Trimmed() [3/3]

virtual MbCurve3D* MbCurve3D::Trimmed

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

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

Parameters

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

Returns: A constructed trimmed curve.

Warning: Under development.

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

cur_nurbs3d.h

Public Member Functions

Static Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MbNurbs3D() [1/2]

◆ MbNurbs3D() [2/2]

Member Function Documentation

◆ Create() [1/5]

◆ Create() [2/5]

◆ Create() [3/5]

◆ Create() [4/5]

◆ Create() [5/5]

◆ CreateThrough() [1/2]

◆ CreateThrough() [2/2]

◆ CreateParasolid()

◆ Init() [1/5]

◆ Init() [2/5]

◆ Init() [3/5]

◆ Init() [4/5]

◆ Init() [5/5]

◆ InitThrough() [1/2]

◆ InitThrough() [2/2]

◆ Duplicate()

◆ IsSame()

◆ SetEqual()

◆ Transform()

◆ Move()

◆ Rotate()

◆ GetProperties()

◆ SetProperties()

◆ IsClosed()

◆ IsPeriodic()

◆ PointOn()

◆ Explore()

◆ Step()

◆ DeviationStep()

◆ NurbsCurve() [1/2]

◆ NurbsCurve() [2/2]

◆ Trimmed() [1/3]

◆ GetRadius()

◆ GetCircleAxis()

◆ GetPlaneCurve()

◆ NearPointProjection()

◆ IsReparamSame()

◆ DistanceAlong()

◆ CalculateLength()

◆ IsContinuousDerivative()

◆ SetContinuousDerivativeLength()

◆ RaiseDegree()

◆ ReductionDegree()

◆ GetMap()

◆ CreateNURBS4() [1/5]

◆ CreateNURBS4() [2/5]

◆ CreateNURBS4() [3/5]

◆ CreateNURBS4() [4/5]

◆ CreateNURBS4() [5/5]

◆ CreateNURBS()

◆ BreakC0NURBS4()

◆ FixClosedNurbs()

◆ Trimmed() [2/3]

◆ Trimmed() [3/3]