Detailed Description

The Cartesian product of convex sets is a convex set: S = X₁ × X₂ × ⋯ × Xₙ = {(x₁, x₂, ..., xₙ) | x₁ ∈ X₁, x₂ ∈ X₂, ..., xₙ ∈ Xₙ}.

This class also supports a generalization of this concept in which the coordinates are transformed by the linear map, {x | y = Ax + b, y ∈ Y₁ × Y₂ × ⋯ × Yₙ}, with the default values set to the identity map. This concept is required for reasoning about cylinders in arbitrary poses as cartesian products, and more generally for describing any affine transform of a CartesianProduct.

Special behavior for IsEmpty: If there are no sets in the product, returns nonempty by convention. See: https://en.wikipedia.org/wiki/Empty_product#Nullary_Cartesian_product Otherwise, if any set in the cartesian product is empty, the whole product is empty.

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

Public Member Functions
	CartesianProduct ()
	Constructs a default (zero-dimensional, nonempty) set. More...

	CartesianProduct (const ConvexSets &sets)
	Constructs the product from a vector of convex sets. More...

	CartesianProduct (const ConvexSet &setA, const ConvexSet &setB)
	Constructs the product from a pair of convex sets. More...

	CartesianProduct (const ConvexSets &sets, const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &b)
	Constructs the product of convex sets in the transformed coordinates: {x \| y = Ax + b, y ∈ Y₁ × Y₂ × ⋯ × Yₙ}. More...

	CartesianProduct (const QueryObject< double > &query_object, GeometryId geometry_id, std::optional< FrameId > reference_frame=std::nullopt)
	Constructs a CartesianProduct from a SceneGraph geometry and pose in the `reference_frame` frame, obtained via the QueryObject. More...

	~CartesianProduct () final

int	num_factors () const
	The number of factors (or sets) used in the product. More...

const ConvexSet &	factor (int i) const
	Returns a reference to the ConvexSet defining the `index` factor in the product. More...

std::optional< Eigen::MatrixXd >	A () const
	Returns a copy of the matrix A if it has been set, or nullopt otherwise. More...

std::optional< Eigen::VectorXd >	b () const
	Returns a copy of the vector b if it has been set, or nullopt otherwise. More...

bool	PointInSet (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=0) const
	Returns true if each subvector is in its corresponding set with tolerance `tol`. More...

double	CalcVolume () const

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

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

CartesianProduct &	operator= (const CartesianProduct &)=default

	CartesianProduct (CartesianProduct &&)=default

CartesianProduct &	operator= (CartesianProduct &&)=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< 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...

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...

	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

◆ CartesianProduct() [1/7]

CartesianProduct ( const CartesianProduct & )

default

◆ CartesianProduct() [2/7]

CartesianProduct ( CartesianProduct && )

default

◆ CartesianProduct() [3/7]

CartesianProduct ( )

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

◆ CartesianProduct() [4/7]

CartesianProduct ( const ConvexSets & sets )

explicit

Constructs the product from a vector of convex sets.

◆ CartesianProduct() [5/7]

CartesianProduct	(	const ConvexSet &	setA,
		const ConvexSet &	setB
	)

Constructs the product from a pair of convex sets.

◆ CartesianProduct() [6/7]

CartesianProduct	(	const ConvexSets &	sets,
		const Eigen::Ref< const Eigen::MatrixXd > &	A,
		const Eigen::Ref< const Eigen::VectorXd > &	b
	)

Constructs the product of convex sets in the transformed coordinates: {x | y = Ax + b, y ∈ Y₁ × Y₂ × ⋯ × Yₙ}.

Exceptions

std::exception when A is not full column rank.

◆ CartesianProduct() [7/7]

CartesianProduct	(	const QueryObject< double > &	query_object,
		GeometryId	geometry_id,
		std::optional< FrameId >	reference_frame = `std::nullopt`
	)

Constructs a CartesianProduct 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.

Although any geometry that can be used as a ConvexSet could also be a (trivial) CartesianProduct, we restrict this constructor to handling Cylinder geometry, which constructs the (non-trivial) Cartesian product of a HyperEllipsoid and an HPolyhedron. Most other SceneGraph geometry types are supported by at least one of the ConvexSet class constructors.

Exceptions

std::exception if geometry_id does not correspond to a Cylinder.

◆ ~CartesianProduct()

~CartesianProduct ( )

final

Member Function Documentation

◆ A()

std::optional<Eigen::MatrixXd> A ( ) const

Returns a copy of the matrix A if it has been set, or nullopt otherwise.

◆ b()

std::optional<Eigen::VectorXd> b ( ) const

Returns a copy of the vector b if it has been set, or nullopt otherwise.

◆ CalcVolume()

double CalcVolume

Exceptions

if	`set.has_exact_volume() == false` for any of the sets in the product.

◆ factor()

const ConvexSet& factor ( int i ) const

Returns a reference to the ConvexSet defining the index factor in the product.

◆ IsBounded()

bool IsBounded

A CartesianProduct 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.

◆ num_factors()

int num_factors ( ) const

The number of factors (or sets) used in the product.

◆ operator=() [1/2]

CartesianProduct& operator= ( CartesianProduct && )

default

◆ operator=() [2/2]

CartesianProduct& operator= ( const CartesianProduct & )

default

◆ PointInSet()

bool PointInSet

Returns true if each subvector is in its corresponding set with tolerance tol.

Note: Tolerance support for this query varies in the different convex set implementations.

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

drake/geometry/optimization/cartesian_product.h

Detailed Description

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ CartesianProduct() [1/7]

◆ CartesianProduct() [2/7]

◆ CartesianProduct() [3/7]

◆ CartesianProduct() [4/7]

◆ CartesianProduct() [5/7]

◆ CartesianProduct() [6/7]

◆ CartesianProduct() [7/7]

◆ ~CartesianProduct()

Member Function Documentation

◆ A()

◆ b()

◆ CalcVolume()

◆ factor()

◆ IsBounded()

◆ num_factors()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ PointInSet()