codac2::Parallelepiped Class Reference

Class representing a parallelepiped \(\mathbf{c} + \mathbf{A}\cdot[-1,1]^m\). More...

#include <codac2_Parallelepiped.h>

Inheritance diagram for codac2::Parallelepiped:

Public Member Functions
	Parallelepiped (const Vector &c, const Matrix &A)
	Constructs a n-parallelepiped object with a given center and shape matrix.
std::vector< Vector >	vertices () const
	Computes the vertices of the parallelepiped.
BoolInterval	contains (const Vector &v) const
	Checks if a given point is contained within the parallelepiped. The matrix A has to be square and invertible.
BoolInterval	is_superset (const IntervalVector &x) const
	Checks if a given box is contained within the parallelepiped. The matrix A has to be square and invertible.
Parallelepiped	operator& (const IntervalVector &x) const
	Computes the intersection of the parallelepiped with a given box. The matrix A has to be square and invertible.
Public Member Functions inherited from codac2::Zonotope
	Zonotope (const Vector &c, const Matrix &A)
	Constructs a n-zonotope object with a given center and shape matrix.
bool	is_empty () const
	Checks if the zonotope is empty.
void	set_empty ()
	Sets the zonotope to be empty.
Index	size () const
	Outputs the size of the zonotope.
IntervalVector	box () const
	Computes the axis-aligned bounding box of the zonotope.
Zonotope	proj (const std::vector< Index > &indices) const
	Projects the Zonotope onto the subspace defined by the given indices.
Zonotope	operator+ (const Zonotope &zonotope)
	Computes the Minkowski sum of this Zonotope with another Zonotope.

Static Public Member Functions
static Parallelepiped	empty (Index n)
	Constructs an empty n-parallelepiped.
Static Public Member Functions inherited from codac2::Zonotope
static Zonotope	empty (Index n)
	Constructs an empty n-zonotope.

Additional Inherited Members
Public Attributes inherited from codac2::Zonotope
Vector	c
	Center of the zonotope.
Matrix	A
	Shape matrix of the zonotope.
bool	empty_flag = false
	Flag indicating whether the zonotope is empty.

Detailed Description

Class representing a parallelepiped \(\mathbf{c} + \mathbf{A}\cdot[-1,1]^m\).

This class represents a parallelepiped in n-dimensional space, defined by a center point \(\mathbf{c}\) and a shape matrix \(\mathbf{A}\).

A parallelepiped is a special case of a zonotope where the shape matrix \(\mathbf{A}\) has \(m\) columns with \(m \leqslant n\).

Constructor & Destructor Documentation

Parallelepiped()

codac2::Parallelepiped::Parallelepiped	(	const Vector &	c,
		const Matrix &	A )

Constructs a n-parallelepiped object with a given center and shape matrix.

Parameters

c	Center of the parallelepiped (n-dimensional vector)
A	Shape matrix of the parallelepiped ( \(n\times m\) matrix with \(m \leqslant n\))

Member Function Documentation

empty()

Parallelepiped codac2::Parallelepiped::empty ( Index n )

static

Constructs an empty n-parallelepiped.

Parameters

n	Dimension of the parallelepiped

Returns

A new Parallelepiped object representing an empty parallelepiped in n-dimensional space

vertices()

std::vector< Vector > codac2::Parallelepiped::vertices

(

)

const

Computes the vertices of the parallelepiped.

Returns

A vector containing the unsorted vertices of the parallelepiped

contains()

BoolInterval codac2::Parallelepiped::contains

(

const Vector &

v

)

const

Checks if a given point is contained within the parallelepiped. The matrix A has to be square and invertible.

Parameters

v	The point to check

Returns

BoolInterval true if the point is inside the parallelepiped, false if is outside, and unknown otherwise

is_superset()

BoolInterval codac2::Parallelepiped::is_superset

(

const IntervalVector &

x

)

const

Checks if a given box is contained within the parallelepiped. The matrix A has to be square and invertible.

Parameters

x	The box to check

Returns

BoolInterval true if the box is inside the parallelepiped, false if is outside, and unknown otherwise

operator&()

Parallelepiped codac2::Parallelepiped::operator&

(

const IntervalVector &

x

)

const

Computes the intersection of the parallelepiped with a given box. The matrix A has to be square and invertible.

Parameters

x	The box to intersect with

Returns

A new Parallelepiped representing the intersection of the original parallelepiped with the box.

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

• /home/simon/codac/src/core/domains/zonotope/codac2_Parallelepiped.h