cadex::ModelData_BSplineCurve Class Reference

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

#include <cadex/ModelData_BSplineCurve.hxx>

Inheritance diagram for cadex::ModelData_BSplineCurve:

Public Types
typedef cadex::internal::ModelData_BSplineCurveImpl	ImplType

Public Member Functions
	ModelData_BSplineCurve ()
	Constructor.
	ModelData_BSplineCurve (const ModelData_Point thePoles[], int theNumberOfPoles, const double theKnots[], int theNumberOfKnots, const int theMultiplicities[], int theDegree, bool theIsPeriodic=false)
	Constructor.
	ModelData_BSplineCurve (const ModelData_Point thePoles[], const double thePoleWeights[], int theNumberOfPoles, const double theKnots[], int theNumberOfKnots, const int theMultiplicities[], int theDegree, bool theIsPeriodic=false)
	Constructor.
	ModelData_BSplineCurve (const Handle_C &)
	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.
int	Knots (double theKnots[]) const
	Populates a vector of knots.
int	Multiplicity (int theIndex) const
	Returns a knot multiplicity.
int	Multiplicities (int theMultiplicities[]) const
	Populates a vector of knot multiplicities.
ModelData_Point	Pole (int theIndex) const
	Returns a pole value.
int	Poles (ModelData_Point thePoles[]) const
	Populates a vector of poles.
bool	IsRational () const
	Returns true if the B-Spline curve is rational (i.e. has weights).
double	Weight (int theIndex) const
	Returns a weight value.
int	Weights (double theWeights[]) const
	Populates a vector of weights.
Public Member Functions inherited from cadex::ModelData_Curve
	ModelData_Curve ()
	Constructor.
	ModelData_Curve (const ModelData_Curve &theOther)
	Constructor.
	ModelData_Curve (ModelData_Curve &&theOther)
	Constructor.
	~ModelData_Curve ()
	Destructor.
ModelData_Curve &	operator= (const ModelData_Curve &theOther)
	Assignment operator.
ModelData_Curve &	operator= (ModelData_Curve &&theOther)
	Move assignment operator.
ModelData_CurveType	Type () const
	Returns a curve type.
bool	IsNull () const
	Returns true if the object has not been initialized yet.
void	Nullify ()
	Resets the object.
	operator bool () const
	Returns if the object has been initialized.
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.
ModelData_Point	Value (double theParameter) const
	Evaluates a point on the curve.
ModelData_Curve	Reversed () const
	Returns a curve with reversed orientation.
void	Transform (const ModelData_Transformation &theTransformation)
	Applies transformation matrix to this object.
ModelData_Curve	Transformed (const ModelData_Transformation &theTransformation) const
	Returns a copy this object after applying transformation.
ModelData_Continuity	Continuity () const
	Returns a continuity type of the curve.
void	D0 (double theParameter, ModelData_Point &theValue) const
	Returns the point theValue of parameter theParam.
void	D1 (double theParameter, ModelData_Point &theValue, ModelData_Vector &theD1) const
	Returns the point theValue of parameter theParam and the first derivative theD1.
void	D2 (double theParameter, ModelData_Point &theValue, ModelData_Vector &theD1, ModelData_Vector &theD2) const
	Returns the point theValue of parameter theParam, the first theD1 and second theD2 derivatives.
bool	DN (double theParameter, size_t theDerivativeOrder, ModelData_Point &theValue, ModelData_Vector theD[]) const
double	Curvature (double theParameter) const
	Returns the curvature value of parameter theParam.
void	Normal (double theParameter, ModelData_Direction &theNormal) const
	Returns the normal direction theNormal of parameter theParam.
void	Mirror (const ModelData_Point &thePoint)
	Mirrors the curve relative to the point.
void	Mirror (const ModelData_Axis1Placement &theAxis)
	Mirrors the curve relative to the axis placement.
void	Mirror (const ModelData_Axis2Placement &theAxis)
	Mirrors the curve relative to the axis placement.
ModelData_Curve	Mirrored (const ModelData_Point &theRef) const
	Returns a copy this curve mirrored along the object.
ModelData_Curve	Mirrored (const ModelData_Axis1Placement &theAxis) const
	Returns a copy this curve mirrored along the object.
ModelData_Curve	Mirrored (const ModelData_Axis2Placement &theAxis) const
	Returns a copy this curve mirrored along the object.
void	Rotate (const ModelData_Axis1Placement &theAxis, double theAngle)
	Rotates the curve around the axis.
ModelData_Curve	Rotated (const ModelData_Axis1Placement &theAxis, double theAngle) const
	Returns a copy this curve rotated along the axis.
void	Translate (const ModelData_Vector &theVector)
	Translates the curve along the vector.
ModelData_Curve	Translated (const ModelData_Vector &theVector) const
	Returns a copy this curve translated along the vector.
void	Scale (const ModelData_Point &thePoint, double theScale)
	Scales the curve with respect to the point.
ModelData_Curve	Scaled (const ModelData_Point &thePoint, double theScale) const
	Returns a copy this curve scaled with respect to the point.

Public Attributes
	operator Handle_C const
Public Attributes inherited from cadex::ModelData_Curve
	operator Handle_C const

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:

• https://en.wikipedia.org/wiki/Non-uniform_rational_B-spline ,
• http://web.cs.wpi.edu/~matt/courses/cs563/talks/nurbs.html ,
• http://www.mactech.com/articles/develop/issue_25/schneider.html ,
• http://mathworld.wolfram.com/B-Spline.html .

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.

Examples

exploring/brepgeometry/Program.cs, exploring/brepgeometry/main.cxx, modeling/brep/Program.cs, and modeling/brep/main.cxx.

Constructor & Destructor Documentation

ModelData_BSplineCurve() [1/3]

cadex::ModelData_BSplineCurve::ModelData_BSplineCurve ( )

inline

Constructor.

Empty constructor.

ModelData_BSplineCurve() [2/3]

cadex::ModelData_BSplineCurve::ModelData_BSplineCurve	(	const ModelData_Point	thePoles[],
		int	theNumberOfPoles,
		const double	theKnots[],
		int	theNumberOfKnots,
		const 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.

ModelData_BSplineCurve() [3/3]

cadex::ModelData_BSplineCurve::ModelData_BSplineCurve	(	const ModelData_Point	thePoles[],
		const double	thePoleWeights[],
		int	theNumberOfPoles,
		const double	theKnots[],
		int	theNumberOfKnots,
		const 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::ModelData_BSplineCurve::Degree

(

)

const

Returns degree.

Returns the value specified in the constructor.

Examples

exploring/brepgeometry/Program.cs, and exploring/brepgeometry/main.cxx.

IsRational()

bool cadex::ModelData_BSplineCurve::IsRational

(

)

const

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

See also

Weight().

Knot()

double cadex::ModelData_BSplineCurve::Knot

(

int

theIndex

)

const

Returns a knot value.

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

See also

Multiplicity().

Examples

exploring/brepgeometry/Program.cs, and exploring/brepgeometry/main.cxx.

Knots()

int cadex::ModelData_BSplineCurve::Knots

(

double

theKnots[]

)

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()

int cadex::ModelData_BSplineCurve::Multiplicities

(

int

theMultiplicities[]

)

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::ModelData_BSplineCurve::Multiplicity

(

int

theIndex

)

const

Returns a knot multiplicity.

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

See also

Knot().

Examples

exploring/brepgeometry/Program.cs, and exploring/brepgeometry/main.cxx.

NumberOfKnots()

int cadex::ModelData_BSplineCurve::NumberOfKnots

(

)

const

Returns number of unique knots.

Returns the value specified in the constructor.

Examples

exploring/brepgeometry/Program.cs, and exploring/brepgeometry/main.cxx.

NumberOfPoles()

int cadex::ModelData_BSplineCurve::NumberOfPoles

(

)

const

Returns number of poles.

Returns the value specified in the constructor.

Examples

exploring/brepgeometry/Program.cs, and exploring/brepgeometry/main.cxx.

Pole()

ModelData_Point cadex::ModelData_BSplineCurve::Pole

(

int

theIndex

)

const

Returns a pole value.

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

See also

Weight().

Examples

exploring/brepgeometry/Program.cs, and exploring/brepgeometry/main.cxx.

Poles()

int cadex::ModelData_BSplineCurve::Poles

(

ModelData_Point

thePoles[]

)

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::ModelData_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().

Examples

exploring/brepgeometry/Program.cs, and exploring/brepgeometry/main.cxx.

Weights()

int cadex::ModelData_BSplineCurve::Weights

(

double

theWeights[]

)

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().