C3D Toolkit  Kernel - 117958, Vision - 2.7.6.12

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.
 
MbSpaceItemDuplicate (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...
 
MbNurbs3DNurbsCurve (const MbCurveIntoNurbsInfo &) const override
 Construct a NURBS copy of a curve. More...
 
MbCurve3DNurbsCurve (const MbNurbsParameters &) const override
 Construct a NURBS copy of a curve. More...
 
MbCurve3DTrimmed (double t1, double t2, int sense, bool saveParamLenAndLaw=false) const override
 Construct a trimmed curve. More...
 
double GetRadius (double accuracy=METRIC_REGION) const override
 Get the physical radius of the curve or zero if it impossible. More...
 
bool GetCircleAxis (MbAxis3D &) const override
 Get an axis of a circle which is geometrically coincident to the given curve. More...
 
bool GetPlaneCurve (MbCurve *&curve2d, MbPlacement3D &place, bool saveParams, PlanarCheckParams params=PlanarCheckParams()) const override
 Get planar curve and placement if the space curve is planar. More...
 
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.
 
MbNurbs3DTrimm (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...
 
MbNurbs3DBreak (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.

 
MbCurveGetMap (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).
 
MbCurve3DConvertToConic ()
 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.
 
- 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 MbCurve3Doperator[] (size_t) const
 An access operator.
 
MbeSpaceType Type () const override
 Get the group object type.
 
MbeSpaceType Family () const override
 Get family of objects.
 
virtual MbCurve3DInverseDuplicate () 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 MbCurve3DGetBasisCurve () const
 Returns the base curve if exists or itself.
 
virtual MbCurve3DSetBasisCurve ()
 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.
 
MbNurbs3DNurbsCurve (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...
 
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...
 
MbPropertyCreateProperty (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 MbCurveGetMapPsp (const MbMatrix3D &into, double zNear, MbRect1D *pRegion=nullptr) const
 Construct a planar projection of a piece of a space curve. More...
 
virtual MbCurveGetProjection (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.
 
virtual const MbCurve3DGetSubstrate () const
 Get a substrate or itself.
 
virtual MbCurve3DSetSubstrate ()
 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.
 
CommonRecursiveMutexGetLock () const
 Get a pointer to the mutex object. Return nullptr if no parallelism. For use in ScopedLock.
 

Static Public Member Functions

static MbNurbs3DCreate (const MbNurbs3D &)
 Create copy of spline. More...
 
static MbNurbs3DCreate (const MbNurbs &nurbs, const MbPlacement3D &place)
 Create spline. More...
 
static MbNurbs3DCreate (size_t degree, const SArray< MbCartPoint3D > &points, bool closed, const SArray< double > *weights=nullptr)
 Create spline. More...
 
static MbNurbs3DCreate (size_t degree, bool closed, const SArray< MbCartPoint3D > &points, const SArray< double > &knots)
 Create spline. More...
 
template<class PointsVector , class DoubleVector >
static MbNurbs3DCreate (size_t initDegree, bool initClosed, const PointsVector &initPoints, const DoubleVector &initWeights, const DoubleVector &initKnots, MbeNurbsCurveForm initForm=ncf_Unspecified)
 Create spline. More...
 
static MbNurbs3DCreateThrough (size_t degree, bool cls, const SArray< MbCartPoint3D > &points, const SArray< double > &params, SArray< double > *aKnots=nullptr)
 Create spline. More...
 
static MbNurbs3DCreateThrough (size_t degree, bool cls, const c3d::SpacePointsVector &points, const c3d::DoubleVector &params, c3d::DoubleVector *aKnots=nullptr)
 Create spline. More...
 
static MbNurbs3DCreateParasolid (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 MbNurbs3DCreateNURBS4 (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 MbNurbs3DCreateNURBS4 (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 MbNurbs3DCreateNURBS4 (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 MbNurbs3DCreateNURBS4 (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 MbNurbs3DCreateNURBS4 (const SArray< MbCartPoint3D > &points, const SArray< double > &params, bool cls, MbeSplineCreateType useInitThrough=sct_Version2)
 Interpolation. More...
 
static MbNurbs3DCreateNURBS4 (const SArray< double > &weights, const SArray< MbCartPoint3D > &points, SArray< double > &params, bool cls)
 Interpolation. More...
 
static MbNurbs3DCreateNURBS4 (const SArray< MbCartPoint3D > &, const SArray< double > &, const MbVector3D &, const MbVector3D &, bool cls, bool bfstS=true, bool bfstN=true)
 Interpolation. More...
 
static MbNurbs3DCreateNURBS4 (const SArray< MbCartPoint3D > &points, const SArray< MbVector3D > &vectors, const SArray< double > &params, bool cls)
 Interpolation. More...
 
static MbNurbs3DCreateNURBS4WithBreak (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 MbNurbs3DCreateNURBS4 (const MbBezier3D &)
 Interpolation. More...
 
static MbNurbs3DCreateNURBS (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< MbCartPoint3DpointList
 Set of control points.
 
bool closed
 An attribute of curve closedness.
 
double metricLength
 Metric length of curve.
 
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.

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.

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()

MbCurve3D* MbNurbs3D::Trimmed ( double  t1,
double  t2,
int  sense,
bool  saveParamLenAndLaw = false 
) const
overridevirtual

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.

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.

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.

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.

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.

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.

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.


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