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Drake
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Drake
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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. | |
| Point | ( | ) |
Constructs a default (zero-dimensional, nonempty) set.
| 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.
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final |
| bool IsBounded | ( | Parallelism | parallelism = Parallelism::None() | ) | const |
Every Point is bounded by construction.
| parallelism | Ignored – no parallelization is used. |
| 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.
| void set_x | ( | const Eigen::Ref< const Eigen::VectorXd > & | x | ) |
Changes the element x describing the set.
| const Eigen::VectorXd & x | ( | ) | const |
Retrieves the point.