QuadraticCurve Class Reference

A quadratic curve. More...

#include <QuadraticCurve.hpp>

Inherits ParametricCurve.

Public Types
enum	Type { Elliptic , Hyperbola , Line , Parabola }
	The four possible curve types. More...
typedef rw::core::Ptr< QuadraticCurve >	Ptr
	Smart pointer type for QuadraticCurve.
typedef rw::core::Ptr< const QuadraticCurve >	CPtr
	Smart pointer type for a const QuadraticCurve.
typedef enum rw::geometry::QuadraticCurve::Type	Type
	The four possible curve types.
Public Types inherited from ParametricCurve
typedef rw::core::Ptr< ParametricCurve >	Ptr
	Smart pointer type for ParametricCurve.
typedef rw::core::Ptr< const ParametricCurve >	CPtr
	Smart pointer type for a const ParametricCurve.
Public Types inherited from Curve
typedef rw::core::Ptr< Curve >	Ptr
	Smart pointer type for Curve.
typedef rw::core::Ptr< const Curve >	CPtr
	Smart pointer type for a const Curve.

Public Member Functions
	QuadraticCurve (const rw::math::Vector3D< double > &c, const rw::math::Vector3D< double > &u, const rw::math::Vector3D< double > &v, const Type &type)
	Construct quadratic curve given by the expression \( \mathbf{p} = \mathbf{c} + r(t) \mathbf{u} + s(t) \mathbf{v} \), where u and v are orthogonal vectors. More...
virtual	~QuadraticCurve ()
	Destrcutor.
QuadraticCurve::Ptr	transform (const rw::math::Transform3D< double > &T) const
	Transform curve. More...
QuadraticCurve::Ptr	transform (const rw::math::Vector3D< double > &P) const
	Transform curve. More...
QuadraticCurve::Ptr	scale (double factor) const
	Get a scaled version of the curve. More...
QuadraticCurve::Ptr	reverse () const
	Make a curve where time variable runs in opposite direction. More...
QuadraticCurve::Ptr	clone () const
	Make a copy of the curve. More...
virtual std::pair< double, double >	extremums (const rw::math::Vector3D< double > &dir) const
	Get extremums of curve in given direction. More...
virtual std::list< rw::math::Vector3D< double > >	discretizeAdaptive (double stepsPerRevolution) const
	Make a discretization of the curve. More...
virtual OBB	obr () const
	Bounding rectangle of curve. More...
virtual std::vector< rw::math::Vector3D< double > >	closestPoints (const rw::math::Vector3D< double > &p) const
	Get the closest points on the curve to a point p. More...
virtual bool	equals (rw::core::Ptr< const rw::geometry::Curve > curve, double eps) const
	Check if this curve is equal to another curve. More...
virtual rw::math::Vector3D< double >	x (double t) const
	Evaluate a point on the curve. More...
virtual rw::math::Vector3D< double >	dx (double t) const
	Evaluate the derivative in a point on the curve. More...
virtual rw::math::Vector3D< double >	ddx (double t) const
	Evaluate the second derivative in a point on the curve. More...
virtual rw::math::Vector3D< double >	operator() (double t) const
	Evaluate a point on the curve. More...
virtual bool	hasLimits () const
	Check if the curve is limited. More...
virtual const std::pair< double, double > &	limits () const
	Get the limits of the curve segment. More...
virtual bool	inLimits (double t) const
	Check if the parameter t is inside the limits set for the curve. More...
virtual void	setLimits (const std::pair< double, double > &limits)
	Set parameter limits for the curve. More...
virtual double	curvature (double t) const
	The curvature in a given point on the curve. More...
virtual std::vector< double >	closestTimes (const rw::math::Vector3D< double > &p) const
	Get the parameter values where the curve is closest to a point p. More...
virtual double	closestTime (const rw::math::Vector3D< double > &p) const
	Get the parameter value where the curve is closest to a point p. More...
const rw::math::Vector3D< double > &	c () const
	The point c. More...
const rw::math::Vector3D< double > &	u () const
	The vector u. More...
const rw::math::Vector3D< double > &	v () const
	The vector v. More...
Type	type () const
	Get the type of curve. More...
QuadraticCurve &	operator= (const QuadraticCurve &rhs)
Public Member Functions inherited from ParametricCurve
	ParametricCurve ()
	Constructor.
virtual	~ParametricCurve ()
	Destructor.
ParametricCurve::Ptr	transform (const rw::math::Transform3D< double > &T) const
	Transform curve. More...
ParametricCurve::Ptr	transform (const rw::math::Vector3D< double > &P) const
	Transform curve. More...
ParametricCurve::Ptr	scale (double factor) const
	Get a scaled version of the curve. More...
ParametricCurve::Ptr	reverse () const
	Make a curve where time variable runs in opposite direction. More...
ParametricCurve::Ptr	clone () const
	Make a copy of the curve. More...
Public Member Functions inherited from Curve
	Curve ()
	Constructor.
virtual	~Curve ()
	Destructor.
rw::core::Ptr< Curve >	transform (const rw::math::Transform3D< double > &T) const
	Transform curve. More...
rw::core::Ptr< Curve >	transform (const rw::math::Vector3D< double > &P) const
	Transform curve. More...
rw::core::Ptr< Curve >	scale (double factor) const
	Get a scaled version of the curve. More...
rw::core::Ptr< Curve >	reverse () const
	Make a curve where time variable runs in opposite direction. More...
rw::core::Ptr< Curve >	clone () const
	Make a copy of the curve. More...

Detailed Description

A quadratic curve.

A quadratic curve is given explicitly by the expression \( \mathbf{p} = \mathbf{c} + r(t) \mathbf{u} + s(t) \mathbf{v} \) where \( \mathbf{c},\mathbf{u},\mathbf{v},\mathbf{p} \in \mathbb{R}^3 \) and \( \mathbf{u}^T \mathbf{v} = 0\) .

The following four types of curves are possible:

• Ellipse: \( (r,s)=(\sin t,\cos t) \)
• Hyperbola: \( (r,s)=(\sinh t,\cosh t) \)
• Line: \( (r,s)=(t,0) \)
• Parabola: \( (r,s)=(t,t^2) \)

Member Enumeration Documentation

Type

enum Type

The four possible curve types.

Enumerator
Elliptic	Ellipse \( \mathbf{p} = \mathbf{c} + \mathbf{u} \sin t + \mathbf{v} < \cos t\)
Hyperbola	Hyperbola \( \mathbf{p} = \mathbf{c} + \mathbf{u} \sinh t + < \mathbf{v} \cosh t\)
Line	Line \( \mathbf{p} = \mathbf{c} + \mathbf{u} t\).
Parabola	Parabola \( \mathbf{p} = \mathbf{c} + \mathbf{u} t + \mathbf{v} t^2\).

Constructor & Destructor Documentation

QuadraticCurve()

QuadraticCurve	(	const rw::math::Vector3D< double > &	c,
		const rw::math::Vector3D< double > &	u,
		const rw::math::Vector3D< double > &	v,
		const Type &	type
	)

Construct quadratic curve given by the expression \( \mathbf{p} = \mathbf{c} + r(t) \mathbf{u} + s(t) \mathbf{v} \), where u and v are orthogonal vectors.

Parameters

c	[in] offset of curve.
u	[in] first direction.
v	[in] second direction.
type	[in] the type of curve.

Member Function Documentation

c()

const rw::math::Vector3D<double>& c ( ) const

inline

The point c.

Returns

the point \( c \in \mathbb{R}^3 \).

clone()

QuadraticCurve::Ptr clone

(

)

const

Make a copy of the curve.

Returns

a new copy of the curve.

closestPoints()

virtual std::vector<rw::math::Vector3D<double> > closestPoints ( const rw::math::Vector3D< double > &  p ) const

virtual

Get the closest points on the curve to a point p.

Notice that the limits are taken into account.

Parameters

p	[in] the point to find closest values for.

Returns

a vector of closest points to p.

Implements ParametricCurve.

closestTime()

virtual double closestTime ( const rw::math::Vector3D< double > &  p ) const

virtual

Get the parameter value where the curve is closest to a point p.

Notice that the limits are taken into account.

Parameters

p	[in] the point to find closest values for.

Returns

the point on the curve closest to p. If multiple points are equally close to p, only one of those points are returned.

Implements ParametricCurve.

closestTimes()

virtual std::vector<double> closestTimes ( const rw::math::Vector3D< double > &  p ) const

virtual

Get the parameter values where the curve is closest to a point p.

Notice that the limits are taken into account.

Parameters

p	[in] the point to find closest values for.

Returns

a list of parameter values.

Implements ParametricCurve.

curvature()

virtual double curvature ( double  t ) const

virtual

The curvature in a given point on the curve.

This function does not take the limits into account.

Parameters

t	[in] the parameter to evaluate the curvature for.

Returns

the curvature.

Implements ParametricCurve.

ddx()

virtual rw::math::Vector3D<double> ddx ( double  t ) const

virtual

Evaluate the second derivative in a point on the curve.

Parameters

t	[in] the parameter to find second derivative for.

Returns

a second derivative vector \( p \in \mathbb{R}^3 \) .

Implements ParametricCurve.

discretizeAdaptive()

virtual std::list<rw::math::Vector3D<double> > discretizeAdaptive ( double  stepsPerRevolution ) const

virtual

Make a discretization of the curve.

The curve must be limited. The discretization is based on the curvature, such that the sampling starts at maximum curvature points (or in limits). The step size to the next point is based on the curvature in the current point.

A line will always give to points, regardless of the chosen number of steps per revolution.

Parameters

stepsPerRevolution

[in] the number of points to sample if the curve is a perfect circle.

Returns

a list of points on the curve.

Implements ParametricCurve.

dx()

virtual rw::math::Vector3D<double> dx ( double  t ) const

virtual

Evaluate the derivative in a point on the curve.

Parameters

t	[in] the parameter to find derivative for.

Returns

a derivative vector \( p \in \mathbb{R}^3 \) .

Implements ParametricCurve.

equals()

virtual bool equals ( rw::core::Ptr< const rw::geometry::Curve >  curve, double  eps  ) const

virtual

Check if this curve is equal to another curve.

Parameters

curve	[in] other curve.
eps	[in] distance threshold.

Returns

true if curves are identical, false otherwise.

Implements ParametricCurve.

extremums()

virtual std::pair<double, double> extremums ( const rw::math::Vector3D< double > &  dir ) const

virtual

Get extremums of curve in given direction.

Notice that the limits are taken into account.

Parameters

dir	[in] direction to get extremums for.

Returns

the minimum and maximum value of the curve in the given direction.

Implements ParametricCurve.

hasLimits()

virtual bool hasLimits ( ) const

inlinevirtual

Check if the curve is limited.

Returns

true if curve is limited, false otherwise.

Implements ParametricCurve.

inLimits()

virtual bool inLimits ( double  t ) const

virtual

Check if the parameter t is inside the limits set for the curve.

Parameters

t	[in] the parameter to check.

Returns

true if inside limits, false otherwise.

Implements ParametricCurve.

limits()

virtual const std::pair<double, double>& limits ( ) const

inlinevirtual

Get the limits of the curve segment.

The returned values are only valid when hasLimits() returns true.

Returns

the minimum and maximum parameter values on the curve.

Implements ParametricCurve.

obr()

virtual OBB obr ( ) const

virtual

Bounding rectangle of curve.

The curve must be limited.

Returns

the bounding rectangle.

Implements ParametricCurve.

operator()()

virtual rw::math::Vector3D<double> operator() ( double  t ) const

virtual

Evaluate a point on the curve.

Parameters

t	[in] the parameter to find point for.

Returns

the vector \( p \in \mathbb{R}^3 \) .

Implements ParametricCurve.

reverse()

QuadraticCurve::Ptr reverse

(

)

const

Make a curve where time variable runs in opposite direction.

Returns

reversed curve.

scale()

QuadraticCurve::Ptr scale

(

double

factor

)

const

Get a scaled version of the curve.

Parameters

factor

[in] the factor to scale with.

Returns

a new scaled curve.

setLimits()

virtual void setLimits ( const std::pair< double, double > &  limits )

virtual

Set parameter limits for the curve.

Parameters

limits

[in] the minimum and maximum parameter values on the curve.

Implements ParametricCurve.

transform() [1/2]

QuadraticCurve::Ptr transform

(

const rw::math::Transform3D< double > &

T

)

const

Transform curve.

Parameters

T	[in] transformation of curve.

Returns

a new transformed curve.

transform() [2/2]

QuadraticCurve::Ptr transform

(

const rw::math::Vector3D< double > &

P

)

const

Transform curve.

Parameters

P	[in] positional offset.

Returns

a new transformed curve.

type()

Type type ( ) const

inline

Get the type of curve.

Returns

the type of curve.

u()

const rw::math::Vector3D<double>& u ( ) const

inline

The vector u.

Returns

the vector \( u \in \mathbb{R}^3 \).

v()

const rw::math::Vector3D<double>& v ( ) const

inline

The vector v.

Returns

the vector \( v \in \mathbb{R}^3 \).

x()

virtual rw::math::Vector3D<double> x ( double  t ) const

virtual

Evaluate a point on the curve.

Parameters

t	[in] the parameter to find point for.

Returns

the vector \( p \in \mathbb{R}^3 \) .

Implements ParametricCurve.

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The documentation for this class was generated from the following file:

• QuadraticCurve.hpp