Detailed Description

Implements the convex hull of a set of convex sets.

The convex hull of multiple sets is defined as the smallest convex set that contains all the sets. Given non-empty convex sets {X₁, X₂, ..., Xₙ}, the convex hull is the set of all convex combinations of points in the sets, i.e. {∑ᵢ λᵢ xᵢ | xᵢ ∈ Xᵢ, λᵢ ≥ 0, ∑ᵢ λᵢ = 1}.

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

Public Member Functions
	ConvexHull (const ConvexSets &sets, const bool remove_empty_sets=true)
	Constructs the convex hull from a vector of convex sets. More...

	~ConvexHull () final

const ConvexSets &	sets () const
	Returns the participating convex sets. More...

const ConvexSets &	participating_sets () const
	Returns the participating sets in the convex hull. More...

bool	empty_sets_removed () const
	Returns true if `this` was constructed with remove_empty_sets=true. More...

const ConvexSet &	element (int index) const
	Returns a reference to the convex set at the given index (including empty sets). More...

int	num_elements () const
	Returns the number of convex sets defining the convex hull (including empty sets). More...

bool	IsEmpty () const

double	CalcVolume () const

bool	IsBounded (Parallelism parallelism=Parallelism::None()) const
	A ConvexHull is bounded if and only if each constituent set is bounded. More...

Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	ConvexHull (const ConvexHull &)=default

ConvexHull &	operator= (const ConvexHull &)=default

	ConvexHull (ConvexHull &&)=default

ConvexHull &	operator= (ConvexHull &&)=default

Public Member Functions inherited from ConvexSet
virtual	~ConvexSet ()

std::unique_ptr< ConvexSet >	Clone () const
	Creates a unique deep copy of this set. More...

int	ambient_dimension () const
	Returns the dimension of the vector space in which the elements of this set are evaluated. More...

bool	IntersectsWith (const ConvexSet &other) const
	Returns true iff the intersection between `this` and `other` is non-empty. More...

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. More...

bool	IsEmpty () const
	Returns true iff the set is empty. More...

std::optional< Eigen::VectorXd >	MaybeGetPoint () const
	If this set trivially contains exactly one point, returns the value of that point. More...

std::optional< Eigen::VectorXd >	MaybeGetFeasiblePoint () const
	Returns a feasible point within this convex set if it is nonempty, and nullopt otherwise. More...

bool	PointInSet (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=0) const
	Returns true iff the point x is contained in the set. More...

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. More...

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. More...

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. More...

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. More...

double	CalcVolume () const
	Computes the exact volume for the convex set. More...

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. More...

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`. More...

bool	has_exact_volume () const
	Returns true if the exact volume can be computed for this convex set instance. More...

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. More...

template<typename Archive >
void	Serialize (Archive *a)
	Implements non-virtual base class serialization. More...

virtual std::optional< bool >	DoIsBoundedShortcut () const
	Non-virtual interface implementation for DoIsBoundedShortcut(). More...

virtual std::vector< std::optional< double > >	DoProjectionShortcut (const Eigen::Ref< const Eigen::MatrixXd > &points, EigenPtr< Eigen::MatrixXd > projected_points) const
	Non-virtual interface implementation for DoProjectionShortcut(). More...

virtual std::optional< Eigen::VectorXd >	DoMaybeGetFeasiblePoint () const
	Non-virtual interface implementation for MaybeGetFeasiblePoint(). More...

virtual std::optional< bool >	DoPointInSetShortcut (const Eigen::Ref< const Eigen::VectorXd > &x, double tol) const
	A non-virtual interface implementation for PointInSet() that should be used when the PointInSet() can be computed more efficiently than solving a convex program. More...

virtual double	DoCalcVolume () const
	Non-virtual interface implementation for CalcVolume(). More...

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. More...

virtual std::unique_ptr< ConvexSet >	DoAffineHullShortcut (std::optional< double > tol) const
	NVI implementation of DoAffineHullShortcut, which trivially returns null. More...

	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. More...

Constructor & Destructor Documentation

◆ ConvexHull() [1/3]

ConvexHull ( const ConvexHull & )

default

◆ ConvexHull() [2/3]

ConvexHull ( ConvexHull && )

default

◆ ConvexHull() [3/3]

ConvexHull	(	const ConvexSets &	sets,
		const bool	remove_empty_sets = `true`
	)

explicit

Constructs the convex hull from a vector of convex sets.

Parameters

sets	A vector of convex sets that define the convex hull.
remove_empty_sets	If true, the constructor will check if any of the sets are empty and will not consider them. If false, the constructor will not check if any of the sets are empty.

Warning: If remove_empty_sets is set to false, but some of the sets are in fact empty, then unexpected and incorrect results may occur. Only set this flag to false if you are sure that your sets are non-empty and performance in the constructor is critical.

◆ ~ConvexHull()

~ConvexHull ( )

final

Member Function Documentation

◆ CalcVolume()

double CalcVolume

Exceptions

Not	implemented.

◆ element()

const ConvexSet& element ( int index ) const

Returns a reference to the convex set at the given index (including empty sets).

◆ empty_sets_removed()

bool empty_sets_removed ( ) const

Returns true if this was constructed with remove_empty_sets=true.

◆ IsBounded()

bool IsBounded

A ConvexHull is bounded if and only if each constituent set is bounded.

This class honors requests for parallelism only so far as its constituent sets do.

Parameters

parallelism The maximum number of threads to use.

Note: See parent class's documentation for more details.

◆ IsEmpty()

bool IsEmpty

Note: if called on an instance that was called with remove_empty_sets=false, this function will reconstruct the convex hull with remove_empty_sets=true. Therefore, it is recommended to call this function only once.

◆ num_elements()

int num_elements ( ) const

Returns the number of convex sets defining the convex hull (including empty sets).

◆ operator=() [1/2]

ConvexHull& operator= ( ConvexHull && )

default

◆ operator=() [2/2]

ConvexHull& operator= ( const ConvexHull & )

default

◆ participating_sets()

const ConvexSets& participating_sets ( ) const

Returns the participating sets in the convex hull.

If the constructor was called with remove_empty_sets=false, this function will return the original sets, including potentially empty sets.

◆ sets()

const ConvexSets& sets ( ) const

Returns the participating convex sets.

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

drake/geometry/optimization/convex_hull.h

Detailed Description

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ ConvexHull() [1/3]

◆ ConvexHull() [2/3]

◆ ConvexHull() [3/3]

◆ ~ConvexHull()

Member Function Documentation

◆ CalcVolume()

◆ element()

◆ empty_sets_removed()

◆ IsBounded()

◆ IsEmpty()

◆ num_elements()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ participating_sets()

◆ sets()