codac2::Ellipsoid Class Reference

Ellipsoid representation. More...

#include <codac2_Ellipsoid.h>

Public Member Functions
	Ellipsoid (Index n)
	Create a n-dimensional ellipsoid.
	Ellipsoid (const Vector &mu, const Matrix &G)
	Create an ellipsoid from a center and a shape matrix.
Index	size () const
	Return the dimension of the ellipsoid.
Vector	rand () const
	Return a random vector inside this ellipsoid.
IntervalVector	hull_box () const
	Compute the tightest axis-aligned box containing this ellipsoid.
BoolInterval	is_concentric_subset (const Ellipsoid &e) const
	Test if the provided ellipsoid is a subset of this ellipsoid, provided that the two ellipsoids share the same center.
Ellipsoid	proj_2d (const Vector &d, const Vector &v, const Vector &u) const
	Project the ellipsoid on the 2d plane (d,v,u)

Public Attributes
Vector	mu
	midpoint vector
Matrix	G
	shape matrix

Detailed Description

Ellipsoid representation.

References:

Concentric subset test and degenerate computations are inspired by the work of Morgan Louedec. Concepts and algorithms are provided in:

Stability analysis of the formation control of a group of underwater robots, with ellipsoidal enclosure. Morgan Louédec, 2024 PhD thesis, Université de Bretagne Occidentale, Brest, France. https://morgan-louedec.fr/thesis-of-morgan-louedec

Non-linear mapping of the nonsingular main case is inspired by:

A computationally inexpensive algorithm for determining outer and inner enclosures of nonlinear mappings of ellipsoidal domains. Andreas Rauh, Luc Jaulin 2021, International Journal of Applied Mathematics and Computer Science, doi: https://doi.org/10.34768/amcs-2021-0027

Constructor & Destructor Documentation

Ellipsoid() [1/2]

codac2::Ellipsoid::Ellipsoid

(

Index

n

)

Create a n-dimensional ellipsoid.

Parameters

n	number of dimensions

Ellipsoid() [2/2]

codac2::Ellipsoid::Ellipsoid	(	const Vector &	mu,
		const Matrix &	G )

Create an ellipsoid from a center and a shape matrix.

Parameters

mu	midpoint vector
G	shape matrix

Member Function Documentation

size()

Index codac2::Ellipsoid::size

(

)

const

Return the dimension of the ellipsoid.

Returns

number of dimensions

rand()

Vector codac2::Ellipsoid::rand

(

)

const

Return a random vector inside this ellipsoid.

Note

The seed of the pseudo-random number generator is voluntarily initialized outside this function, on demand.

Returns

random vector value

hull_box()

IntervalVector codac2::Ellipsoid::hull_box

(

)

const

Compute the tightest axis-aligned box containing this ellipsoid.

Returns

hull box

is_concentric_subset()

BoolInterval codac2::Ellipsoid::is_concentric_subset

(

const Ellipsoid &

e

)

const

Test if the provided ellipsoid is a subset of this ellipsoid, provided that the two ellipsoids share the same center.

Parameters

e	the second ellipsoid of same dimension

Returns

a BoolInterval

proj_2d()

Ellipsoid codac2::Ellipsoid::proj_2d	(	const Vector &	d,
		const Vector &	v,
		const Vector &	u ) const

Project the ellipsoid on the 2d plane (d,v,u)

Parameters

d	a point on the plane
v	a vector of the plane
u	a other vector of the plane, orthogonal to v

Returns

the projected 2d ellipsoid

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

• /home/simon/codac-simon/src/core/domains/ellipsoid/codac2_Ellipsoid.h