Point Class Reference

Detailed Description

A convex set that contains exactly one element.

Also known as a singleton or unit set.

This set is always nonempty, even in the zero-dimensional case.

#include <drake/geometry/optimization/point.h>

Public Member Functions
	Point ()
	Constructs a default (zero-dimensional, nonempty) set.
	Point (const Eigen::Ref< const Eigen::VectorXd > &x)
	Constructs a Point.
	Point (const QueryObject< double > &query_object, GeometryId geometry_id, std::optional< FrameId > reference_frame=std::nullopt, double maximum_allowable_radius=0.0)
	Constructs a Point from a SceneGraph geometry and pose in the reference_frame frame, obtained via the QueryObject.
	~Point () final
const Eigen::VectorXd &	x () const
	Retrieves the point.
void	set_x (const Eigen::Ref< const Eigen::VectorXd > &x)
	Changes the element x describing the set.
bool	PointInSet (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=0) const
	Returns true if the point is within tol of x(), under the L∞-norm.
bool	IsBounded (Parallelism parallelism=Parallelism::None()) const
	Every Point is bounded by construction.
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	Point (const Point &)=default
Point &	operator= (const Point &)=default
	Point (Point &&)=default
Point &	operator= (Point &&)=default
Public Member Functions inherited from ConvexSet
virtual	~ConvexSet ()
std::unique_ptr< ConvexSet >	Clone () const
	Creates a unique deep copy of this set.
int	ambient_dimension () const
	Returns the dimension of the vector space in which the elements of this set are evaluated.
bool	IntersectsWith (const ConvexSet &other) const
	Returns true iff the intersection between this and other is non-empty.
bool	IsBounded (Parallelism parallelism=Parallelism::None()) const
	Returns true iff the set is bounded, e.g., there exists an element-wise finite lower and upper bound for the set.
bool	IsEmpty () const
	Returns true iff the set is empty.
std::optional< Eigen::VectorXd >	MaybeGetPoint () const
	If this set trivially contains exactly one point, returns the value of that point.
std::optional< Eigen::VectorXd >	MaybeGetFeasiblePoint () const
	Returns a feasible point within this convex set if it is nonempty, and nullopt otherwise.
bool	PointInSet (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=0) const
	Returns true iff the point x is contained in the set.
std::pair< VectorX< symbolic::Variable >, std::vector< solvers::Binding< solvers::Constraint > > >	AddPointInSetConstraints (solvers::MathematicalProgram *prog, const Eigen::Ref< const solvers::VectorXDecisionVariable > &vars) const
	Adds a constraint to an existing MathematicalProgram enforcing that the point defined by vars is inside the set.
std::vector< solvers::Binding< solvers::Constraint > >	AddPointInNonnegativeScalingConstraints (solvers::MathematicalProgram *prog, const Eigen::Ref< const solvers::VectorXDecisionVariable > &x, const symbolic::Variable &t) const
	Let S be this convex set.
std::vector< solvers::Binding< solvers::Constraint > >	AddPointInNonnegativeScalingConstraints (solvers::MathematicalProgram *prog, const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &b, const Eigen::Ref< const Eigen::VectorXd > &c, double d, const Eigen::Ref< const solvers::VectorXDecisionVariable > &x, const Eigen::Ref< const solvers::VectorXDecisionVariable > &t) const
	Let S be this convex set.
std::pair< std::unique_ptr< Shape >, math::RigidTransformd >	ToShapeWithPose () const
	Constructs a Shape and a pose of the set in the world frame for use in the SceneGraph geometry ecosystem.
double	CalcVolume () const
	Computes the exact volume for the convex set.
SampledVolume	CalcVolumeViaSampling (RandomGenerator *generator, const double desired_rel_accuracy=1e-2, const int max_num_samples=1e4) const
	Calculates an estimate of the volume of the convex set using sampling and performing Monte Carlo integration.
std::optional< std::pair< std::vector< double >, Eigen::MatrixXd > >	Projection (const Eigen::Ref< const Eigen::MatrixXd > &points) const
	Computes in the L₂ norm the distance and the nearest point in this convex set to every column of points.
bool	has_exact_volume () const
	Returns true if the exact volume can be computed for this convex set instance.

Additional Inherited Members
Protected Member Functions inherited from ConvexSet
	ConvexSet (int ambient_dimension, bool has_exact_volume)
	For use by derived classes to construct a ConvexSet.
template<typename Archive>
void	Serialize (Archive *a)
	Implements non-virtual base class serialization.
virtual std::optional< bool >	DoIsBoundedShortcutParallel (Parallelism) const
	Non-virtual interface implementation for DoIsBoundedShortcutParallel().
virtual std::optional< Eigen::VectorXd >	DoMaybeGetFeasiblePoint () const
	Non-virtual interface implementation for MaybeGetFeasiblePoint().
virtual bool	DoPointInSet (const Eigen::Ref< const Eigen::VectorXd > &x, double tol) const
	Non-virtual interface implementation for PointInSet().
std::optional< symbolic::Variable >	HandleZeroAmbientDimensionConstraints (solvers::MathematicalProgram *prog, const ConvexSet &set, std::vector< solvers::Binding< solvers::Constraint > > *constraints) const
	Instances of subclasses such as CartesianProduct and MinkowskiSum can have constituent sets with zero ambient dimension, which much be handled in a special manner when calling methods such as DoAddPointInSetConstraints.
virtual std::unique_ptr< ConvexSet >	DoAffineHullShortcut (std::optional< double > tol) const
	NVI implementation of DoAffineHullShortcut, which trivially returns null.
	ConvexSet (const ConvexSet &)=default
ConvexSet &	operator= (const ConvexSet &)=default
	ConvexSet (ConvexSet &&)=default
ConvexSet &	operator= (ConvexSet &&)=default
Static Protected Member Functions inherited from ConvexSet
static std::unique_ptr< ConvexSet >	AffineHullShortcut (const ConvexSet &self, std::optional< double > tol)
	When there is a more efficient strategy to compute the affine hull of this set, returns affine hull as an AffineSubspace.

Constructor & Destructor Documentation

Point() [1/5]

Point ( const Point & )

default

Point() [2/5]

Point ( Point && )

default

Point() [3/5]

Point

(

)

Constructs a default (zero-dimensional, nonempty) set.

Point() [4/5]

Point ( const Eigen::Ref< const Eigen::VectorXd > & x )

explicit

Constructs a Point.

Point() [5/5]

Point	(	const QueryObject< double > &	query_object,
		GeometryId	geometry_id,
		std::optional< FrameId >	reference_frame = std::nullopt,
		double	maximum_allowable_radius = 0.0 )

Constructs a Point from a SceneGraph geometry and pose in the reference_frame frame, obtained via the QueryObject.

If reference_frame frame is std::nullopt, then it will be expressed in the world frame.

Exceptions

std::exception

if geometry_id does not correspond to a Sphere or if the Sphere has radius greater than maximum_allowable_radius.

~Point()

~Point ( )

final

Member Function Documentation

IsBounded()

bool IsBounded

(

Parallelism

parallelism = Parallelism::None()

)

const

Every Point is bounded by construction.

Parameters

parallelism

Ignored – no parallelization is used.

Note

See parent class's documentation for more details.

operator=() [1/2]

Point & operator= ( const Point & )

default

operator=() [2/2]

Point & operator= ( Point && )

default

PointInSet()

bool PointInSet	(	const Eigen::Ref< const Eigen::VectorXd > &	x,
		double	tol = 0 ) const

Returns true if the point is within tol of x(), under the L∞-norm.

set_x()

void set_x

(

const Eigen::Ref< const Eigen::VectorXd > &

x

)

Changes the element x describing the set.

Precondition

x must be of size ambient_dimension().

x()

const Eigen::VectorXd & x

(

)

const

Retrieves the point.

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

• drake/geometry/optimization/point.h