CubicCurveSet Class Reference

Piecewise cubic curves. More...

#include <curveset.h>

Public Member Functions
	CubicCurveSet ()
	Creates an empty piecewise quadric curve.
	CubicCurveSet (const QVector< CubicCurve > &)
	Creates the piecewise cubic curve given a set.
	CubicCurveSet (const QVector< Vector > &, const Vector &=Vector::Null, const Vector &=Vector::Null)
	Creates the piecewise cubic curve given a set of control points with the Cattmul-Rom construction.
	~CubicCurveSet ()
	Empty.
Matrix	GetMatrix (const double &) const
	Compute the Frenet vectors at a given point on the curve.
Frame	GetFrame (const double &) const
	Compute the Frenet frame at a given point on the curve.
int	Size () const
	Return the number of elements of the piecewise cubic curve.
Box	GetBox () const
	Compute the bounding box of the curve.
QuadricCurveSet	Approximate (double) const
	Approximate a piecewise cubic curve by a piecewise quadric curve.
double	GetLength () const
	Return the length of the curve.
double	GetLength (int) const
	Return the length of the sub-curve.
QVector< Vector >	GetDiscretisation (const double &) const
	Generates a discretization of the curve with a linear curvilign absisca parameterization.
QVector< Vector >	GetDiscretisation (const double &, QVector< Vector > &) const
	Generates a discretization of the curve with a linear curvilign absisca parameterization.
int	U (const double &, double &) const
	Compute the parameter of the curve corresponding to the input length.
double	R (const Vector &, double &, int &) const
	Computes the squared distance between a point and a set of cubic curves.

Protected Attributes
QVector< CubicCurve >	curve
	Set of cubic (spline) curves.
QVector< double >	lengths
	Length of every curve (internal optimization).
double	length = 0.0
	Total length (internal optimization).

Detailed Description

Piecewise cubic curves.

Constructor & Destructor Documentation

CubicCurveSet() [1/2]

CubicCurveSet::CubicCurveSet ( const QVector< CubicCurve > & control )

explicit

Creates the piecewise cubic curve given a set.

Parameters

control

Set of cubic curves.

CubicCurveSet() [2/2]

CubicCurveSet::CubicCurveSet ( const QVector< Vector > & control, const Vector & ta = Vector::Null, const Vector & tb = Vector::Null )

explicit

Creates the piecewise cubic curve given a set of control points with the Cattmul-Rom construction.

Parameters

control	Set of points.
ta	Starting tangent vector
tb	Ending tangent vector

Member Function Documentation

Approximate()

QuadricCurveSet CubicCurveSet::Approximate

(

double

gamma

)

const

Approximate a piecewise cubic curve by a piecewise quadric curve.

There are twice as many quadric curves as cubic curves.

See also

CubicCurve::Approximate

Parameters

gamma

Subdision parameter, in [0,1].

GetDiscretisation() [1/2]

QVector< Vector > CubicCurveSet::GetDiscretisation

(

const double &

s

)

const

Generates a discretization of the curve with a linear curvilign absisca parameterization.

Parameters

s	Stepping distance.

GetDiscretisation() [2/2]

QVector< Vector > CubicCurveSet::GetDiscretisation	(	const double &	s,
		QVector< Vector > &	tangents ) const

Generates a discretization of the curve with a linear curvilign absisca parameterization.

Parameters

s	Stepping distance.
tangents	Tangents to the curve at sample points.

GetFrame()

Frame CubicCurveSet::GetFrame

(

const double &

u

)

const

Compute the Frenet frame at a given point on the curve.

Parameters

u	Parameter.

GetLength()

double CubicCurveSet::GetLength ( int k ) const

inline

Return the length of the sub-curve.

Parameters

k	Curve index.

GetMatrix()

Matrix CubicCurveSet::GetMatrix

(

const double &

u

)

const

Compute the Frenet vectors at a given point on the curve.

The columns of the returned matrix contain the tangent, normal and binormal vectors.

Parameters

u	Parameter.

R()

double CubicCurveSet::R	(	const Vector &	p,
		double &	u,
		int &	k ) const

Computes the squared distance between a point and a set of cubic curves.

See also

CubicCurve::R()

Parameters

p	Point.
u	Parameter defining the coordinate of the projection of the argument vertex onto the curve.
k	Index of the curve for which the minimum distance was found.

U()

int CubicCurveSet::U	(	const double &	s,
		double &	u ) const

Compute the parameter of the curve corresponding to the input length.

Parameters

s	Input length.
u	Parameter of the i-th curve.

Returns

Identifier of the curve in the piecewise definition.