CubicCurve2Set Class Reference

Piecewise cubic curves in the plane. More...

#include <curveset.h>

Public Member Functions
	CubicCurve2Set ()
	Creates an empty piecewise quadric curve.
	CubicCurve2Set (const QVector< CubicCurve2 > &)
	Creates the piecewise quadric curve given a set of CubicCurve2.
	CubicCurve2Set (const QVector< Vector2 > &, const Vector2 &=Vector2::Null, const Vector2 &=Vector2::Null)
	Creates the piecewise cubic curve given a set of control points with the Cattmul-Rom construction.
	CubicCurve2Set (const CubicCurveSet &)
	Creates a piecewise cubic curve in the plane from a similar curve.
	~CubicCurve2Set ()
	Empty.
int	Size () const
	Return the number of elements of the piecewise cubic curve.
CubicCurve2	operator() (int) const
	Return the i-th sub-curve.
QVector< Vector2 >	GetDiscretisation (const double &) const
	Generates a discretization of the piecewise cubic curve with a linear curvilign absisca parameterization.
QVector< Vector2 >	GetDiscretisation (const double &, QVector< Vector2 > &) const
	Generates a discretization of the curve with a linear curvilign absisca parameterization.
Box2	GetBox () const
	Compute the bounding box of the curve.
double	GetLength () const
	Return the length of the curve.
double	GetLength (int) const
	Return the length of the sub-curve.
double	Sinuosity () const
	Compute the sinuosity.
bool	Inside (const Vector2 &) const
	Check if a point lies inside the piecewise cubic curve closed contour.
int	U (const double &, double &) const
	Compute the parameter of the curve corresponding to the input length.
double	R (const Vector2 &, double &, int &) const
	Compute the squared distance between a point and a set of cubic curves.
double	Signed (const Vector2 &) const
	Compute the signed distance between a point and a set of cubic curves forming a closed path.
int	Intersect (const Ray2 &ray, int i, double t[3]) const
	Compute the intersection between the set of curves and a ray.
void	UV (const Vector2 &, double &, double &, int &) const
	Compute the inverse mapping for a given input point.
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw the curve.

Protected Attributes
QVector< CubicCurve2 >	curve
	Set of 2D cubic curves.
QVector< double >	lengths
	Length of every curve.
double	length = 0.0
	Total length.

Detailed Description

Piecewise cubic curves in the plane.

The length of every curve CubicCurve2Set::lengths and the total length CubicCurve2Set::length are computed to speed up computations (internal optimization).

Constructor & Destructor Documentation

CubicCurve2Set() [1/3]

CubicCurve2Set::CubicCurve2Set ( const QVector< CubicCurve2 > & control )

explicit

Creates the piecewise quadric curve given a set of CubicCurve2.

Parameters

control

Set of cubic curves.

CubicCurve2Set() [2/3]

CubicCurve2Set::CubicCurve2Set ( const QVector< Vector2 > & control, const Vector2 & ta = Vector2::Null, const Vector2 & tb = Vector2::Null )

explicit

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

Parameters

control	Set of 2D points.
ta	Starting tangent vector.
tb	Ending tangent vector.

CubicCurve2Set() [3/3]

CubicCurve2Set::CubicCurve2Set ( const CubicCurveSet & c )

explicit

Creates a piecewise cubic curve in the plane from a similar curve.

Parameters

c

Curve.

Member Function Documentation

Draw()

void CubicCurve2Set::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush() ) const

Draw the curve.

The brush is not used.

Parameters

scene	Graphics scene.
pen	The pen.
brush	The brush.

GetDiscretisation() [1/2]

QVector< Vector2 > CubicCurve2Set::GetDiscretisation

(

const double &

step

)

const

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

Parameters

step	Stepping distance.

GetDiscretisation() [2/2]

QVector< Vector2 > CubicCurve2Set::GetDiscretisation	(	const double &	step,
		QVector< Vector2 > &	tangents ) const

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

Parameters

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

GetLength()

double CubicCurve2Set::GetLength ( int k ) const

inline

Return the length of the sub-curve.

Parameters

k	Curve index.

Inside()

bool CubicCurve2Set::Inside

(

const Vector2 &

p

)

const

Check if a point lies inside the piecewise cubic curve closed contour.

The curve should be closed.

Parameters

p

Point.

Intersect()

int CubicCurve2Set::Intersect	(	const Ray2 &	ray,
		int	i,
		double	t[3] ) const

Compute the intersection between the set of curves and a ray.

Parameters

ray	The ray.
i	Index.
t	Intersection depths.

operator()()

CubicCurve2 CubicCurve2Set::operator() ( int i ) const

inline

Return the i-th sub-curve.

Parameters

i

Index.

R()

double CubicCurve2Set::R	(	const Vector2 &	p,
		double &	u,
		int &	k ) const

Compute 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.

Signed()

double CubicCurve2Set::Signed

(

const Vector2 &

p

)

const

Compute the signed distance between a point and a set of cubic curves forming a closed path.

See also

CubicCurve2Set::R()

Parameters

p

Point.

Sinuosity()

double CubicCurve2Set::Sinuosity

(

)

const

Compute the sinuosity.

Sinusoity is defined as the ratio between the length of the curve and the distance between end points.

U()

int CubicCurve2Set::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.

UV()

void CubicCurve2Set::UV	(	const Vector2 &	p,
		double &	u,
		double &	v,
		int &	k ) const

Compute the inverse mapping for a given input point.

Parameters

p	Point.
u,v	Inverse Coordinates, u will denote the position along the curve and v the signed distance to the curve.
k	Index of the curve for which the minimum distance was found.