Defines 3D B-Spline curve. More...

#include <cadex/Geom/BSplineCurve.hxx>

Inheritance diagram for cadex::Geom::BSplineCurve:

Public Member Functions
	BSplineCurve ()
	Constructor.

	BSplineCurve (const std::vector< Point > &thePoles, const std::vector< double > &theKnots, const std::vector< int > &theMultiplicities, int theDegree, bool theIsPeriodic=false)
	Constructor.

	BSplineCurve (const std::vector< Point > &thePoles, const std::vector< double > &thePoleWeights, const std::vector< double > &theKnots, const std::vector< int > &theMultiplicities, int theDegree, bool theIsPeriodic=false)
	Constructor.

int	Degree () const
	Returns degree.

int	NumberOfKnots () const
	Returns number of unique knots.

int	NumberOfPoles () const
	Returns number of poles.

double	Knot (int theIndex) const
	Returns a knot value.

std::vector< double >	Knots () const
	Populates a vector of knots.

int	Multiplicity (int theIndex) const
	Returns a knot multiplicity.

std::vector< int >	Multiplicities () const
	Populates a vector of knot multiplicities.

Point	Pole (int theIndex) const
	Returns a pole value.

std::vector< Point >	Poles () const
	Populates a vector of poles.

double	Weight (int theIndex) const
	Returns a weight value.

std::vector< double >	Weights () const
	Populates a vector of weights.

bool	IsRational () const
	Returns true if the B-Spline curve is rational (i.e. has weights).

Public Member Functions inherited from cadex::Geom::Curve
	Curve ()
	Constructor.

CurveType	Type () const

Geom::Continuity	Continuity () const
	Returns a continuity type of the curve.

Point	Value (double theParameter) const
	Evaluates a point on the curve.

Direction	Normal (double theParameter) const
	Returns the normal direction theNormal of parameter theParam.

double	Curvature (double theParameter) const
	Returns the curvature value of parameter theParam.

bool	IsPeriodic () const
	Returns true if the curve is periodic.

double	UMin () const
	Returns a minimum parameter of a definition domain.

double	UMax () const
	Returns a maximum parameter of a definition domain.

void	Domain (double &theUMin, double &theUMax) const
	Returns a definition domain.

bool	IsTrimmed () const
	Returns whether curve is trimmed or not.

void	SetTrim (double theFirst, double theLast)
	Trims curve with [theFirst, theLast] section.

void	Transform (const Transformation &theTransformation)
	Applies transformation matrix to this object.

Curve	Transformed (const Transformation &theTransformation) const
	Returns a copy this object after applying transformation.

void	D0 (double theParameter, Point &theValue) const
	Returns the point theValue of parameter theParam.

void	D1 (double theParameter, Point &theValue, Vector &theD1) const
	Returns the point theValue of parameter theParam and the first derivative theD1.

void	D2 (double theParameter, Point &theValue, Vector &theD1, Vector &theD2) const
	Returns the point theValue of parameter theParam, the first theD1 and second theD2 derivatives.

bool	DN (double theParameter, size_t theDerivativeOrder, Geom::Point &theValue, std::vector< Geom::Vector > &theD) const

void	Mirror (const Point &thePoint)

void	Mirror (const Axis1d &theAxis)

void	Mirror (const Axis3d &theAxis)

Curve	Mirrored (const Point &theRef) const

Curve	Mirrored (const Axis1d &theAxis) const

Curve	Mirrored (const Axis3d &theAxis) const

void	Rotate (const Axis1d &theAxis, double theAngle)

Curve	Rotated (const Axis1d &theAxis, double theAngle) const

void	Translate (const Vector &theVector)

Curve	Translated (const Vector &theVector) const

void	Scale (const Point &thePoint, double theScale)

Curve	Scaled (const Point &thePoint, double theScale) const

Public Member Functions inherited from cadex::BaseObject
size_t	Id () const
	Return unique identifier of public object.

internal::BaseObjectImpl *	Impl () const

bool	IsNull () const

	operator bool () const

template<typename T >
bool	IsOfType () const

template<typename T >
T *	Impl () const
	Reserved for internal use.

Static Public Member Functions
static bool	CompareType (const BaseObject &theObject)

Static Public Member Functions inherited from cadex::Geom::Curve
static bool	CompareType (const BaseObject &theObject)

Static Public Member Functions inherited from cadex::Geom::Geometry
static bool	CompareType (const BaseObject &theObject)

Additional Inherited Members
Public Types inherited from cadex::BaseObject
typedef std::shared_ptr< internal::BaseObjectImpl >	ImplType

Protected Member Functions inherited from cadex::Geom::Curve
	Curve (const ImplType &theImpl)

Protected Member Functions inherited from cadex::Geom::Geometry
	Geometry (const ImplType &theImpl)

Protected Member Functions inherited from cadex::BaseObject
	BaseObject (const ImplType &theImpl)

Detailed Description

Defines 3D B-Spline curve.

B-Spline curve is defined by degree, control points (poles), their weights, unique knots and their multiplicities. The following image depicts an example of a B-Spline curve:

B-Spline curve

For introduction to and mathematical definition of NURBS please refer to external resources, for instance:

A rational B-Spline contains an explicit vector of weights, whereas polynomial does not.

The number of poles must equal the number of weights. The number of poles is defined via the following formulas:

for non-periodic B-Spline: number_of_poles = sum_of_knot_multiplicities - degree - 1;
for periodic B-Spline: number_of_poles = sum_of_knot_multiplicities - start_multiplicity.

B-Splines of degree up to 25 are supported.

Constructor & Destructor Documentation

◆ BSplineCurve() [1/2]

cadex::Geom::BSplineCurve::BSplineCurve	(	const std::vector< Point > &	thePoles,
		const std::vector< double > &	theKnots,
		const std::vector< int > &	theMultiplicities,
		int	theDegree,
		bool	theIsPeriodic = false )

Constructor.

Creates a polynomial B-Spline curve.

Parameters:

theNumberOfPoles defines the length of thePoles and must be >=2;
theNumberOfKnots defines the length of theKnots and theMultiplicities and must be >=2;
theDegree must belong to range [1, 25];
theIsPeriodic specifies if the B-Spline is periodic.

theNumberOfPoles must meet the requirements described above.

◆ BSplineCurve() [2/2]

cadex::Geom::BSplineCurve::BSplineCurve	(	const std::vector< Point > &	thePoles,
		const std::vector< double > &	thePoleWeights,
		const std::vector< double > &	theKnots,
		const std::vector< int > &	theMultiplicities,
		int	theDegree,
		bool	theIsPeriodic = false )

Constructor.

Creates a rational B-Spline curve.

Parameters:

theNumberOfPoles defines the length of thePoles and thePoleWeights and must be >=2;
theNumberOfKnots defines the length of theKnots and theMultiplicities and must be >=2;
theDegree must belong to range [1, 25];
theIsPeriodic specifies if the B-Spline is periodic.

theNumberOfPoles must meet the requirements described above.

Poles are to be provided after division by their weights.

Member Function Documentation

◆ Degree()

int cadex::Geom::BSplineCurve::Degree ( ) const

Returns degree.

Returns the value specified in the constructor.

◆ IsRational()

bool cadex::Geom::BSplineCurve::IsRational ( ) const

Returns true if the B-Spline curve is rational (i.e. has weights).

See also: Weight().

◆ Knot()

double cadex::Geom::BSplineCurve::Knot ( int theIndex ) const

Returns a knot value.

theIndex must be in the range [1, NumberOfKnots()].

See also: Multiplicity().

◆ Knots()

std::vector< double > cadex::Geom::BSplineCurve::Knots ( ) const

Populates a vector of knots.

theKnots must point to a buffer in memory with at least NumberOfKnots() preallocated values.

Returns NumberOfKnots().

See also: Multiplicities().

◆ Multiplicities()

std::vector< int > cadex::Geom::BSplineCurve::Multiplicities ( ) const

Populates a vector of knot multiplicities.

theMultiplicities must point to a buffer in memory with at least NumberOfKnots() preallocated values.

Returns NumberOfKnots().

See also: Knots().

◆ Multiplicity()

int cadex::Geom::BSplineCurve::Multiplicity ( int theIndex ) const

Returns a knot multiplicity.

theIndex must be in the range [1, NumberOfKnots()].

See also: Knot().

◆ NumberOfKnots()

int cadex::Geom::BSplineCurve::NumberOfKnots ( ) const

Returns number of unique knots.

Returns the value specified in the constructor.

◆ NumberOfPoles()

int cadex::Geom::BSplineCurve::NumberOfPoles ( ) const

Returns number of poles.

Returns the value specified in the constructor.

◆ Pole()

Point cadex::Geom::BSplineCurve::Pole ( int theIndex ) const

Returns a pole value.

theIndex must be in the range [1, NumberOfPoles()].

See also: Weight().

◆ Poles()

std::vector< Point > cadex::Geom::BSplineCurve::Poles ( ) const

Populates a vector of poles.

thePoles must point to a buffer in memory with at least NumberOfPoles() preallocated values.

Returns NumberOfPoles().

See also: Weights().

◆ Weight()

double cadex::Geom::BSplineCurve::Weight ( int theIndex ) const

Returns a weight value.

theIndex must be in the range [1, NumberOfPoles()].

For polynomial B-Spline behavior is undefined.

See also: Pole(), IsRational().

◆ Weights()

std::vector< double > cadex::Geom::BSplineCurve::Weights ( ) const

Populates a vector of weights.

theWeights must point to a buffer in memory with at least NumberOfPoles() preallocated values.

Returns NumberOfPoles().

For polynomial B-Spline does nothing and returns 0.

See also: Poles(), IsRational().

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ BSplineCurve() [1/2]

◆ BSplineCurve() [2/2]

Member Function Documentation

◆ Degree()

◆ IsRational()

◆ Knot()

◆ Knots()

◆ Multiplicities()

◆ Multiplicity()

◆ NumberOfKnots()

◆ NumberOfPoles()

◆ Pole()

◆ Poles()

◆ Weight()

◆ Weights()