PointCurve2 Class Reference

Piecewise point curve in the plane. More...

#include <curvepoint.h>

Inheritance diagram for PointCurve2:

Public Member Functions
	PointCurve2 ()
	Empty.
	PointCurve2 (const VectorSet2 &, bool=false)
	Creates a curve with points.
	PointCurve2 (const CubicCurve2 &, int, const double &=0.0, const double &=1.0)
	Creates a point curve from a cubic curve.
	PointCurve2 (const QuadricCurve2 &, int, const double &=0.0, const double &=1.0)
	Creates a point curve from a quadric curve.
	PointCurve2 (const QVector< Vector2 > &, bool=false)
	Creates a curve with points.
	PointCurve2 (const QVector< Vector2 > &, const QVector< int > &, bool=false)
	Create a curve from a set of vertexes and a subset of indexes.
	~PointCurve2 ()
	Empty.
int	Size () const
	Return the size of the sampled curve.
Vector2	Tangent (int) const
	Compute the tangent at a given point.
double	Curvature (int) const
	Compute the curvature at a given point.
PointCurve	Transform (const Frame &) const
	Transform the planar point curve into a three dimensional point curve.
bool	IsClosed () const
	Check if the curve is closed.
void	Close ()
	Define the curve as closed.
double	Length () const
	Compute the length of the curve.
double	Sinuosity () const
	Compute the sinuosity.
Polygon2	GetPolygon () const
	Compute the closed bounding polygon.
CubicCurve2Set	ToCubicCurve () const
	Compute the cubic curve passing through all the points of the polyline.
QuadricCurve2Set	ToQuadricCurve () const
	Compute the quadric curve passing through all the points of the polyline.
PointCurve2	Translated (const Vector2 &) const
	Return a translated point curve.
PointCurve2	Transformed (const Frame2 &) const
	Return a transformed point curve.
PointCurve2	Rotated (const double &) const
	Return a rotated point curve.
PointCurve2	Scaled (const Vector2 &) const
	Return a scaled point curve.
double	R (const Vector2 &, double &, int &) const
	Computes the projection of p onto the piecewise linear curve and returns the squared distance.
double	R (const Vector2 &, double &, int &, int &) const
	Computes the projection of p onto the piecewise linear curve, returns the squared distance, and the side with respect to the curve.
void	Draw (QGraphicsScene &, const QPen &=QPen()) const
	Draw the point curve.
Public Member Functions inherited from VectorSet2
	VectorSet2 ()
	Empty.
	VectorSet2 (const QVector< Vector2 > &)
	Create a set of vectors.
	~VectorSet2 ()
	Empty.
VectorSet2	VectorToPoint () const
	Convert a series of displacements into positions.
void	Reverse ()
	Reverse the order of the elements.
int	Size () const
	Return the size of the set.
Vector2	At (int) const
	Access to element.
Vector2 &	operator[] (int)
	Access to element.
Vector2	Barycenter () const
	Compute the barycenter.
void	Vibrate (const double &)
	Randomly move the points.
Box2	GetBox () const
	Compute the bounding box.
Convex2	GetHull () const
	Compute the convex hull of the set.
void	Rotate (const Matrix2 &)
	Rotate all the points.
void	Rotate (const double &)
	Rotate all the points.
void	Translate (const Vector2 &)
	Translate all the points.
void	Scale (const double &)
	Scale all the points.
void	Scale (const Vector2 &)
	Scale all the points.
VectorSet2	Transformed (const Frame2 &) const
	Compute the transformed set.
VectorSet2	Translated (const Vector2 &) const
	Compute the translated set.
VectorSet2	Rotated (const double &) const
	Compute the rotated set.
VectorSet2	Scaled (const Vector2 &) const
	Compute the scaled set.
VectorSet2	Cut (const Box2 &) const
	Return the subset of points that lie inside the box.
VectorSet2	Cut (const Octogon2 &) const
	Return the subset of points that lie inside the octogon.
QVector< Vector2 > &	Get ()
	Access to the internal structure.
const QVector< Vector2 > &	Get () const
	Access to the internal structure.
int	Nearest (const Vector2 &) const
	Compute the index of the nearest point to the argument point.
QVector< Vector2 >	Nearest (const Vector2 &, int) const
	Compute the k-nearest points to the argument point.
QVector< int >	NearestIndexes (const Vector2 &, int) const
	Compute the set of indexes of the k-nearest points to the argument point.
QVector< int >	NearestIndexes (int, int, const double &=Math::Infinity) const
	Compute the set of indexes of the k-nearest points to the argument point in the set.
void	Draw (const double &, QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draws the set of vectors as a set of discs.
VectorSet2	operator+ (const VectorSet2 &) const
	Append a vector set to another one.
void	operator+= (const VectorSet2 &)
	Append a vector set.

Static Public Member Functions
static double	Length (const QVector< Vector2 > &, bool=false)
	Compute the length of a discrete curve.

Protected Attributes
bool	closed = false
	Closed curve flag.
Protected Attributes inherited from VectorSet2
QVector< Vector2 >	v
	Vectors.

Detailed Description

Piecewise point curve in the plane.

Constructor & Destructor Documentation

PointCurve2() [1/5]

PointCurve2::PointCurve2 ( const VectorSet2 & p, bool closed = false )

explicit

Creates a curve with points.

Parameters

p	Set of points.
closed	Flag defining whether the curve is closed (true) or open (false).

PointCurve2() [2/5]

PointCurve2::PointCurve2 ( const CubicCurve2 & c, int n, const double & a = 0.0, const double & b = 1.0 )

explicit

Creates a point curve from a cubic curve.

Parameters

c	Cubic curve.
n	Number of points.
a,b	Internval.

PointCurve2() [3/5]

PointCurve2::PointCurve2 ( const QuadricCurve2 & c, int n, const double & a = 0.0, const double & b = 1.0 )

explicit

Creates a point curve from a quadric curve.

Parameters

c	Quadric curve.
n	Number of points.
a,b	Internval.

PointCurve2() [4/5]

PointCurve2::PointCurve2 ( const QVector< Vector2 > & p, bool closed = false )

explicit

Creates a curve with points.

Parameters

p	Set of points.
closed	Flag defining whether the curve is closed (true) or open (false).

PointCurve2() [5/5]

PointCurve2::PointCurve2 ( const QVector< Vector2 > & p, const QVector< int > & indexes, bool closed = false )

explicit

Create a curve from a set of vertexes and a subset of indexes.

Parameters

p	Array of points.
indexes	Set of indexes.
closed	Flag defining whether the curve is closed (true) or open (false).

Member Function Documentation

Curvature()

double PointCurve2::Curvature

(

int

i

)

const

Compute the curvature at a given point.

Parameters

i	Index of the point on the curve.

Draw()

void PointCurve2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen() ) const

Draw the point curve.

Parameters

scene	Graphics scene.
pen	The pen.

Length()

double PointCurve2::Length ( const QVector< Vector2 > & p, bool closed = false )

static

Compute the length of a discrete curve.

Parameters

p	Array of points.
closed	Boolean.

R() [1/2]

double PointCurve2::R	(	const Vector2 &	p,
		double &	u,
		int &	k ) const

Computes the projection of p onto the piecewise linear curve and returns the squared distance.

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.

R() [2/2]

double PointCurve2::R	(	const Vector2 &	p,
		double &	u,
		int &	k,
		int &	side ) const

Computes the projection of p onto the piecewise linear curve, returns the squared distance, and the side with respect to the curve.

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.
side	Side of the point with respect to the closest segment (1 or -1)

Rotated()

PointCurve2 PointCurve2::Rotated

(

const double &

a

)

const

Return a rotated point curve.

Parameters

a	Rotation angle.

Scaled()

PointCurve2 PointCurve2::Scaled

(

const Vector2 &

s

)

const

Return a scaled point curve.

Parameters

s	Scaling vector.

Sinuosity()

double PointCurve2::Sinuosity

(

)

const

Compute the sinuosity.

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

Tangent()

Vector2 PointCurve2::Tangent

(

int

i

)

const

Compute the tangent at a given point.

Parameters

i

Index.

Transform()

PointCurve PointCurve2::Transform

(

const Frame &

f

)

const

Transform the planar point curve into a three dimensional point curve.

Transformation if performed as follows: (x,y) are mapped to (0,x,y).

Parameters

f

Frame.

Transformed()

PointCurve2 PointCurve2::Transformed

(

const Frame2 &

frame

)

const

Return a transformed point curve.

Parameters

frame

The frame.

Translated()

PointCurve2 PointCurve2::Translated

(

const Vector2 &

t

)

const

Return a translated point curve.

Parameters

t	Translation vector.