Interface for parametric curves. A parametric curve, \( \mathbf{p}(t) \in \mathbb{R}^3 \), has its points given as a function of a single parameter, \( t \in \mathbb{R}\). More...

#include <ParametricCurve.hpp>

Inherits Curve.

Inherited by QuadraticCurve.

Public Types
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
	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...

virtual std::pair< double, double >	extremums (const rw::math::Vector3D< double > &dir) const =0
	Get extremums of curve in given direction. More...

virtual std::list< rw::math::Vector3D< double > >	discretizeAdaptive (double stepsPerRevolution) const =0
	Make a discretization of the curve. More...

virtual OBB	obr () const =0
	Bounding rectangle of curve. More...

virtual std::vector< rw::math::Vector3D< double > >	closestPoints (const rw::math::Vector3D< double > &p) const =0
	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 =0
	Check if this curve is equal to another curve. More...

virtual rw::math::Vector3D< double >	x (double t) const =0
	Evaluate a point on the curve. More...

virtual rw::math::Vector3D< double >	dx (double t) const =0
	Evaluate the derivative in a point on the curve. More...

virtual rw::math::Vector3D< double >	ddx (double t) const =0
	Evaluate the second derivative in a point on the curve. More...

virtual rw::math::Vector3D< double >	operator() (double t) const =0
	Evaluate a point on the curve. More...

virtual bool	hasLimits () const =0
	Check if the curve is limited. More...

virtual const std::pair< double, double > &	limits () const =0
	Get the limits of the curve segment. More...

virtual bool	inLimits (double t) const =0
	Check if the parameter t is inside the limits set for the curve. More...

virtual void	setLimits (const std::pair< double, double > &limits)=0
	Set parameter limits for the curve. More...

virtual double	curvature (double t) const =0
	The curvature in a given point on the curve. More...

virtual std::vector< double >	closestTimes (const rw::math::Vector3D< double > &p) const =0
	Get the parameter values where the curve is closest to a point p. More...

virtual double	closestTime (const rw::math::Vector3D< double > &p) const =0
	Get the parameter value where the curve is closest to a point p. 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

Interface for parametric curves. A parametric curve, \( \mathbf{p}(t) \in \mathbb{R}^3 \), has its points given as a function of a single parameter, \( t \in \mathbb{R}\).

Parametric curves have functions for evaluation of points, derivatives and curvature. A parmateric curve can be limited, and it is possible to find closest points with a given point.

Member Function Documentation

◆ clone()

ParametricCurve::Ptr clone ( ) const

inline

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

pure 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 Curve.

Implemented in QuadraticCurve.

◆ closestTime()

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

pure 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.

Implemented in QuadraticCurve.

◆ closestTimes()

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

pure 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.

Implemented in QuadraticCurve.

◆ curvature()

virtual double curvature ( double t ) const

pure 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.

Implemented in QuadraticCurve.

◆ ddx()

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

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

Implemented in QuadraticCurve.

◆ discretizeAdaptive()

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

pure 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 Curve.

Implemented in QuadraticCurve.

◆ dx()

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

pure virtual

Evaluate the derivative in a point on the curve.

Parameters

t	[in] the parameter to find derivative for.

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

Implemented in QuadraticCurve.

◆ equals()

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

pure 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 Curve.

Implemented in QuadraticCurve.

◆ extremums()

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

pure 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 Curve.

Implemented in QuadraticCurve.

◆ hasLimits()

virtual bool hasLimits ( ) const

pure virtual

Check if the curve is limited.

Returns: true if curve is limited, false otherwise.

Implemented in QuadraticCurve.

◆ inLimits()

virtual bool inLimits ( double t ) const

pure 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.

Implemented in QuadraticCurve.

◆ limits()

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

pure virtual

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.

Implemented in QuadraticCurve.

◆ obr()

virtual OBB obr ( ) const

pure virtual

Bounding rectangle of curve.

The curve must be limited.

Returns: the bounding rectangle.

Implements Curve.

Implemented in QuadraticCurve.

◆ operator()()

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

pure virtual

Evaluate a point on the curve.

Parameters

t	[in] the parameter to find point for.

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

Implemented in QuadraticCurve.

◆ reverse()

ParametricCurve::Ptr reverse ( ) const

inline

Make a curve where time variable runs in opposite direction.

Returns: reversed curve.

◆ scale()

ParametricCurve::Ptr scale ( double factor ) const

inline

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 )

pure virtual

Set parameter limits for the curve.

Parameters

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

Implemented in QuadraticCurve.

◆ transform() [1/2]

ParametricCurve::Ptr transform ( const rw::math::Transform3D< double > & T ) const

inline

Transform curve.

Parameters

T	[in] transformation of curve.

Returns: a new transformed curve.

◆ transform() [2/2]

ParametricCurve::Ptr transform ( const rw::math::Vector3D< double > & P ) const

inline

Transform curve.

Parameters

P	[in] positional offset.

Returns: a new transformed curve.

◆ x()

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

pure virtual

Evaluate a point on the curve.

Parameters

t	[in] the parameter to find point for.

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

Implemented in QuadraticCurve.

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

ParametricCurve.hpp

Public Types

Public Member Functions

Detailed Description

Member Function Documentation

◆ clone()

◆ closestPoints()

◆ closestTime()

◆ closestTimes()

◆ curvature()

◆ ddx()

◆ discretizeAdaptive()

◆ dx()

◆ equals()

◆ extremums()

◆ hasLimits()

◆ inLimits()

◆ limits()

◆ obr()

◆ operator()()

◆ reverse()

◆ scale()

◆ setLimits()

◆ transform() [1/2]

◆ transform() [2/2]

◆ x()